****************************************************************************** * Disproving Evolution with the Second Law? v2.00 * * Copyright 1996 by Roscoe A. Sincero * * * * Name of text: 2nd_law2.txt * * Approximate length: 3860+ lines (71 pages) * ****************************************************************************** No part of this text may be reproduced, stored, or transmitted for commerical use without prior written and signed permission by the author. The author hereby grant, to any suitably skilled organization or individual, permission to reproduce, store in a retrieval system, or transmit this text in its entirety by any means (eg. e-mail, Usenet postings, photocopying, recording, etc.) for non-commercial uses. The author encourages any individual or organization to distribute this text in its entirety WITHOUT modifications for non-commercial uses. The individual or organization is also granted permission to reproduce, store, or transmit any portions of this text for the sole purpose of discussion. The information contained herein is offered as a service to individuals or organizations involved in the creation vs evolution controversy and as a service to individuals or organizations who wish to learn more. Although the text is quite long, it is meant as a SUPPLEMENT for your arguments or education not as a substitute. Since the conditions of use of the information contained herein are outside of the control of the author, the author is not held liable for any damages that may incur (eg. emotional distress, loss of reputation). By reading the rest of this text or by distributing this text by any means, you agree to the conditions provided above. Contents i. Introduction ii. Changes iii. References 1. What is thermodynamics? 2. What is the First Law of thermodynamics? 3. Three Questions 4. What is the Second Law of thermodynamics? 4.1 The 2nd Law 4.2 The 2nd Law in The Real World 5. Does violating the law mean anything? 5.1 Law Limitations 5.2 Entropy is a State Variable 5.3 Steam Tables Tell All 6. Does evolution violate the 2nd law? 6.1 Entropy Balance 6.2 Violating the Law 7. What I Didn't Discuss 8. One Direction Processes 9. Conclusion 10. Gibbs Free Energy 11. About the Author A. Basic Concepts B. Additional Sample Problems for 2nd Law Analysis i. Introduction The title of the original text was _2nd law and Creationism v1.0_. That text was also written by me. I have decided to change the name to something that is more representative of what is really covered in the text. Many of you may be aware or may not be aware that one of the claims made by individuals who call themselves _scientific creationists_ is that "evolution violates the 2nd law of thermodyamics". The purpose of this text is to allow the reader with very little background in thermodynamics to determine for himself with very little effort and trouble if this claim is true or false. This text will give you all the information that you will need to make the proper determination. Previous attempts by creationists to explain their position and previous attempts by evolutionists to "disprove" them were not satisfactory in my view. To understand properly what the two sides are saying require that the reader have prior knowledge of thermodynamics. Without this knowledge, the reader is unable to properly determine which side is correct and which side is wrong. The reader, then, is tempted to side with the person with the best propaganda or the one with the most degrees rather than the one who is actually correct. I do realize that this text is very long. My previous versions were excessively long and wordy, too. However, to understand thermodynamics properly this "problem" can not be avoided. I can go ahead and assume you know some concepts such as a state variable and use thermodynamic terms such as equilibrium to shorten the text. But if you do not know these concepts or terms, then such a text would not be very helpful to you. The terms and concepts used in this text are found under the category of "classical thermodynamics" or to be more precise "engineering thermodynamics". The first thermodynamics course anyone takes and the thermodynamics that is discussed briefly in chemistry and physics course comes from classical thermodynamics. The thermodynamic principles used in the industry are usually from classical thermodynamics (eg. calculating the enthalpy change of steam). However, I will mention terms such as "disorder", "information" and others which do NOT fall under classical thermodynamics. The word "disorder", for instance, falls under statistical mechanics (sometimes called statistical thermodynamics). The bottom line, however, can be summed up in two statements: a) creationists claim that "evolution violates the 2nd law of thermodynamics", b) this text will provide you, the reader, with enough information to properly determine if this claim is true. Since this text is now greater than 50 pages, I like to officially designate this text as my first "book". ii. Changes Besides minor cosmetic changes, I have changed the order in which I present the material. The background material needed to understand some of the basic concepts have been moved to the Appendix. You, the reader, are encouraged to read that material first before proceeding if you are unfamiliar with some of the basic concepts such as equilibrium, intensive and extensive properties, types of systems, definition of system, and the like. I am now assuming that you know what these are. The discussion on the definition of thermodynamics itself and a discussion on the 1st law of thermodynamics are placed in its own chapter. The rest of the material is placed in the Appendix. You will find that you will reach the main body of this text much quicker in this version than any version since v1.00. I mentioned in all of my previous versions as well as in this version that the discussion on Gibbs free energy is NOT necessary to prove who is right or wrong. However, more and more people are now aware of Gibbs free energy (also known as the Gibbs potential) so I have decided to include a small discussion on Gibbs free energy AFTER I discuss the 2nd law of thermodynamics. iii. Reference The following books were used to make this text: _Chemical and Engineering Thermodynamics, 2ed_ by Stanley I. Sandler; John Wiley and Sons, New York: 1989. _An Introduction to Thermodynamics for Engineering Technologists_ by James P. Todd and Herbert B. Ellis; John Wiley and Sons, New York: 1981. _Theory and Problems of Thermodynamics with Chemical Applications, 2ed_, Schaum's Outline Series by M. M. Abbott and H. C. Van Ness; McGraw-Hill, New York: 1989. _Thermodynamics and an Introduction to Thermostatistics, 2ed_ by Herbert B. Callen; John Wiley and Sons, New York: 1985. _Physical Chemistry, 3rd ed_, by Gilbert W. Castellan; Addison-Wesley, Reading, Mass: 1983. _General Chemistry, 8th ed_, by H. F. Holtzclaw and W. R. Robinson; D.C. Heath and Co, Lexington, Mass: 1988. _Biological Science: A Molecular Approach, BSCS Blue Version, 5ed_ by Toby Klang; D.C. Heath and Co, Lexington, Mass: 1985. The first four books on this list are ALL thermodynamics books. These are not "creationist books" or "evolutionist books". These are examples of books EVERYONE uses to learn thermodynamics. The last book is a high school biology book that I used when I took high school biology. I should point out that Darwin's "theory" was introduced as a HYPOTHESIS, not fact and not theory. Later on in the text (many chapters later), it was finally refered to as a theory. The author of the 5th book on the list ("Physical Chemistry") was my professor for Physical Chemistry at University of Maryland at College Park. The year I took his course was his final year as a professor; he retired. The 6th book is a chemistry book obviously and not an "evolutionist book". 1. What is thermodynamics? Thermodynamics (Sandler, p. 1), contrary to popular belief, is the study of the CHANGES in the state or condition of a substance due to changes in its _internal energy_. Thermodynamics, then, is the study of ENERGY. Thermodynamics is NOT a study of matter, it is a study of energy. Thermodynamics, however, is what some would call a "macroscopic science". It deals with the average changes that occur among a very, very large number of molecules rather than the detailed changes that occur in a single molecule or a small group of molecules. Statistical mechanics (mentioned earlier) studies these detailed changes but not thermodynamics. Thermodynamics, therefore, is not the study of molecules, the movement of molecules, or the chaotic behavior of molecules. It is not the study of the amount of information that a substance have, either. It is simply a study of energy. If you want to study how information is lost or gained in a process, then study "information theory" and the like. This is not covered in thermodynamics. If you want to understand how molecules affect the properties of the substance, you would need to learn statistical mechanics. Callen described it best in "thermospeak" (Callen, p. 8): "Thermodynamics, in contrast, is concerned with the macroscopic consequences of the myriads of atomic coordinates that, by virtue of the coarseness of macroscopic observations, do not appear explicitly in a macroscopic description of a system." (The quote above should give you a pretty good idea how easy it is to read Callen's book. However, if you want a "children's book", the other books are MUCH better! In particular, I like Sandler's book.) The basic definition of thermodynamics (Todd and Ellis, p. 1) is: "That branch of science which deals with energy, its conversion from one form to another, and the movement of energy from one location to another." To reiterate a major point: Thermodynamics is a study of ENERGY. In thermodynamics, one studies how ENERGY affects the properties of the system; one studies how energy is transformed from one form into another. It is *NOT* a study of matter. It is NOT a study of information. 2. What is the First Law of thermodynamics? As we all learned from junior high (or middle school for you younger people), mass is conserved. That is, mass is neither created nor destroyed. We learned that this is the law of conservation of mass. We later learned that this law by itself assumes that the mass is NOT converted into energy from a fission or fusion reaction. However, thermodynamics is a study of ENERGY. Did we also learn something else in junior high? Yes, we did. We also learned that energy is conserved. That is, energy is neither created nor destroyed. We learned that this is called the law of conservation of energy. This law by itself, of course, assumes that energy is not created from matter in a fission or fusion reaction. Together, the two laws form the law of conservation of mass AND energy. This law, however, can take into account fission and fussion reactions. Now suppose you have a system. Let us call the INITIAL CONDITION of this system state 1 which I will represent with a box. In state 1, NOTHING is going in or out of the box. That is, there are no mass flows or energy flows. The system is in equilibrium. I will represent this state with a box as follows: --------- ! T1 ! ! P1 ! ! U1 ! --------- Figure 1 Figure 1 above says that the system has an initial temperature of T1, an initial pressure of P1, and an initial energy value of U1. There are no flows in or out; the system is in equilibrium. Now suppose the system undergoes a change. Some unknown process is causing this change. We do not know what this process is but we know that the system is changing. At some point, the system STOPS changing. The system has reached a FINAL CONDITION. The length of time this change took place we do not know nor do we care. Time is irrelevant. All we care about is that this change has stopped and no more flows of any kind is occuring. The system is again in equilibrium but at a different temperature, pressure, and energy level. I will represent this NEW EQUILIBRIUM state with a box as follows: --------- ! T2 ! ! P2 ! ! U2 ! --------- Figure 2 Figure 2 above says that the system has a final temperature of T2, a final pressure of P2, and a final energy value of U2. For the sake of argument, let us assume that the mass of the two boxes are the same. That is, NO MASS was added or removed and NO fission or fusion reaction is taking place. This means that the only reason that the temperatures and/or pressures can be different is by the difference in the energy levels. I will summarize what we have discussed so far: --------- --------- ! T1 ! ! T2 ! ! P1 ! ----> ! P2 ! ! U1 ! ! U2 ! --------- --------- Figure 3 Figure 3 DOES NOT say that something is flowing from box on the left to the box on the right. Figure 3 says that the box on the left is transforming to the box on the right. In thermodynamics, we would say that the system is changing from state 1 to state 2. Neither box have any flow rates of any kind. Moreover, the boxes are in equilibrium AND we know the properties of the system in these boxes. This is the "two box" method mentioned in the Appendix. The name "two box" is NOT a thermodynamic term -- it is a term that you will most likely find NO WHERE ELSE but in this text. It is a name used to allow you to remember the concepts better, nothing more. This "two box" method has two assumptions: a) both the initial and final states are in equilibrium or can be assumed to be in equilibrium and b) the properties of the system is known at these two states. If assumption (a) is not valid, then you MAY arrive to a wrong result. If assumption (b) is not valid, then obviously you can't use this method. By the law of conservation of energy, the value of U2 and U1 has to be the same. If the values are different, why? The only way these values can be different is if energy was either added or removed from the system. Energy from any mass flows is non-existent because there is NO mass flows -- the mass is constant and we stated that there are no mass flows, remember. So the only way energy levels can change is by transfering energy to or from the system. We know of two types of energy in transit. The first type of energy transfer is transfer of energy due to temperature differences. This type is called heat. All other types of energy transfer is collectively called work. Mathematically, we write this as, U2 - U1 = Q - W (1a) where Q stands for heat W stands for work We always write it as FINAL - INITIAL as in U2 - U1. This change is caused by the transfer of energy due to heat and/or work. Now you should be wondering, why is there a minus sign in front of the W instead of the Q? To answer this question, we have to dwell deeper into the meaning of Q and W. If U2 - U1 is positive (eg. an increase in energy) AND there is NO work involved, what does that mean? It means that heat was ADDED to the system which increased the energy of the system. Moreover, this term (whatever it is) must be positive to make the left-hand side of the equation positive. Now what does this all mean, then? It means that the Q term stands for heat ADDED TO THE SYSTEM. A positive Q means that heat was added, a negative Q means heat was removed. If equation (1a) was rewritten as, U2 - U1 = -Q - W (1b) then Q would stand for heat REMOVED FROM THE SYSTEM. A positive Q means that heat was removed, a negative Q means heat was added. Plug in a negative value for Q into equation (1b). The negative sign in front of the Q will negate the negative value of Q and make the entire term positive -- energy was increased due to heat being added to the system. Now what about W? When you work out, do you not get tired? What does it mean when you get tired? It means that when you get tired, your energy level is lower. Similiarly, if the system DOES WORK, the change in energy is negative (eg. a decrease in energy). Therefore, W stands for work DONE BY THE SYSTEM. If equation (1a) was rewritten as, U2 - U1 = Q + W (1c) then W would stand for work DONE ON THE SYSTEM. The typical unit for U is kiloJoules (kJ). The letter U is a symbol which stands for INTERNAL ENERGY. It is called internal energy because the energy is inside the system -- inside the box. In this text, when we discuss U, we are using the unit of kJ/kg (energy per mass). Internal energy per mass is called SPECIFIC INTERNAL ENERGY. Thus, when we discuss internal energy, we are really discussing specific internal energy. For the units to be consistent, the units for work and heat will also be kJ/kg. If you want to calculate the TOTAL amount of heat and/or work, you just simply multiply the value for the heat and/or work by the MASS OF THE SYSTEM. It is that easy. Now, equation (1) says that the difference in energy is caused by energy transfers in the form of heat and/or work. This equation (and the idea behind it) is called the 1st law of thermodynamics. What this law clearly state is that if we know what is going in and/or out of the system (ie. knowing Q and W), we can calculate the change in internal energy. However, knowing the change in internal energy DOES NOT in any way tell you how much heat or work was added into the system if both types of energy transfer was present. In other words, the left-hand side of the equation is known but the entire right-hand side is unknown (two unknowns). In thermodynamics, we would say that internal energy is a PROPERTY of the system while heat and work ARE NOT. There is NO SUCH THING AS A CHANGE in heat or work. These energies ONLY exist if energy is being transfered -- energies that is CROSSING the boundary of the system. When heat and/or work finally enters the system, for instance, it is NO LONGER heat or work; it is now internal energy. Thus, it is internal energy that changes, not heat or work. Remember this concept, anything that is CROSSING the boundary of the system (such as energy transfer in the form of heat) is NOT a property of the system. These transfers CAN affect the properties of the system such as internal energy discussed above but only after it finally enters or leaves the system. Any mass that is CROSSING the boundary is NOT the property of the system. It BECOMES a property of the system once it is inside. How? The mass that finally crossed the boundary and enters the systems, adds mass to the matter that was ALREADY in the system -- the mass OF the system gets larger in other words. Another example, the energy used to push the mass into the system (the flow work also known as boundary work) is not a property of the system UNTIL the mass becomes part of the system. In this case, the flow work becomes internal energy -- the internal energy of the system changes. The mass itself that is CROSSING the boundary has its own internal energy. Again, this internal energy is NOT a property of the system UNTIL this mass becomes part of the system (or surroundings if it is leaving). Once it is part of the system, the internal energy changes. Equation (1) is NOT the complete form because EXTERNAL ENERGY was not included. The following includes external energy, 2 2 (U + 1/2v + gz) - (U + 1/2v + gz) = Q - W (2) 2 1 where v stands for velocity g stands for gravitational constant z stands for height The term with the fraction is the kinetic energy of the system and the term with the gravitational constant is the potential energy of the system. These terms are called EXTERNAL ENERGY since it affects the entire system as a whole and it is not inside the system. In most problems, the sum of these two terms are numerically small when compared to the value of change in internal energy. Thus, these terms are often ignored. In the real world and if precision is not the top priority, numerically small usually means less than 2-3% error (sometimes greater). In textbook problems, numerically small means less than 10% error. Error refers to the error when ignoring the external energy. You will notice that in the kinetic energy term and potential energy term, the value for the mass is either a) missing or b) equal to 1. Remember, we are dealing with specific internal energy. Thus, the MASS OF THE SYSTEM was divided out in every term. That is, the U in the equation is really U/m, the Q is really Q/m and the W is really W/m. As you can see from equation (2), it is possible to have a change in internal energy WITHOUT adding heat or work. How? By changing the external energies of the system. The gain or loss in internal energy is equal to the loss or gain of the external energies. Equation (2) is the more complete form of the first law of thermodynamics. The first law of thermodynamics is the most general statement of the law of conservation of energy. There are NO KNOWN EXCEPTION to this law. As you can see from the equation, there are NO restriction on the conversion of one type of energy into another. All that is required is that the TOTAL ENERGY is the same before and after the conversion. We know that it is possible to convert any kind of energy into thermal energy (energy transfer in the form of heat). For instance, electrical energy (which is sometimes called electrical work) can be converted completely into heat. Your conventional ovens are examples of this. However, from experience we also know that thermal energy can NOT be totally converted into other types of energy (eg. mechanical energy for stirring). But the first law DOES NOT in any way provides us with any restrictions at all on the conversion. One conversion seems to be far less likely than the other. Thus, it appears that something else also governs energy -- some other law is also at work. This law is called the 2nd law of thermodynamics. To remind you, the changes in properties are determined between TWO EQUILIBRIUM STATES ("two-box" method). If you look at the boxes, it appears that the system is isolated. And yes, it is true that the system is isolated in these two states. However, this DOES NOT MEAN that the system must be ALWAYS isolated. All that matters is that the initial and final state are equilibrium states or it can be assumed to be in equilibrium. Some individuals like to falsely claim that the laws of thermodynamics (particularly the 2nd law) only apply to isolated systems which is, of course, one of the requirements for being in equilibrium. These individuals are simply being "clever". For instance, how can one calculate the amount of energy a car can consume if the car itself can not be approximated to be an isolated system? The engine gives off a LOT of heat and pollutants -- it can't be approximated to be isolated. From this point on, everytime we use the word "open", "closed", or "isolated" we are refering to the condition of the system as it goes from state 1 to state 2 or vice versa. These adjectives are not refering to the final state or the initial state but to the STATES IN-BETWEEN the initial and final states which are virtually always never in equilibrium or sometimes not even close to equilibrium. State 1 and state 2 are always considered in equilibrium or almost in equilibrium or assumed to be in equilibrium. If you apply the laws of thermodynamics and arrive to a result that is drastically different from the observation, do not assume that the law(s) are incorrect. And certainly do not assume that the change (whatever it was) is not possible; if it is observed then OBVIOUSLY it can happen. The deviation from reality is most likely caused by the assumption of equilibrium for a) the initial state, b) final state or c) both states being wrong. The assumption is wrong, not the law(s). If there are other assumptions made, then certainly you have to consider errors caused by these other assumptions too. 3. Three Questions Creationists claim that "evolution violates the 2nd law of thermodynamics". When you see this claim, at least three questions should come to mind: a) what is the 2nd law of thermodynamics? b) does violating the law mean anything? c) does evolution violate the 2nd law of thermodynamics? It should be obvious that you can not answer (b) or (c) without first answering (a). Therefore, I will tackle that question first. 4. What is the Second Law of thermodynamics? 4.1 The 2nd Law The most common complaint about their claim is that their version of the 2nd law of thermodynamics is _NOT_ the actual 2nd law of thermodynamics. Since it is not the real 2nd law, then it doesn't matter if evolution violates it. Their 2nd law is simply a deceptive ploy to fool the ignorant. At this point of your education, it is NOT relevant to discuss whether or not this criticism is legitimate. I will discuss this particular issue later but for now, it is NOT relevant. Saying that their law is not the real 2nd law does not in any way answer the question: What is the 2nd law of thermodynamics? It is true, however, that creationists and evolutionists have their own versions of the 2nd law. Which one has the real version I won't say for now. It is not relevant. But I tell you this: It doesn't matter which version you use. Concerning evolution, both versions yield the SAME RESULT! Again, I will discuss this in more detail later. For now, you will need to know what the 2nd law states, at least the way creationists state them. Creationists claim that for ANY REAL PROCESS to proceed in ANY system, the entropy change MUST BE greater than zero. Another way of saying this is that for any real process to proceed spontaneously, the change in entropy must be greater than zero. This, they claim, is the 2nd law of thermodynamics. They often describe this positive change in entropy as a system going "from order to disorder", "from disorder to more disorder", "from complex to simple", "from more information to less information", and so on and so forth. Sometimes, you might see a few creationists call this 2nd law as the "law of entropy". At times you might see them state the law as "while a system undergoes a change, the system always become more and more disordered, more and more simple". Other times, they state the law as "any system that undergoes any change will always go from order to disorder and will eventually break down". Still at other times, they would state the law as "any system that undergoes any change will always wind down". Obviously, there are a few ways on how they can state the 2nd law but the important thing to remember is that each of one of these variations mean the exact same thing -- the entropy change is positive. The change in entropy occurs in ONE DIRECTION and ONE DIRECTION ONLY. All REAL processes, then, have only one direction. A common example they like to use is that heat travels from hot to cold. Who will argue with that? They might state the law as "you can not create complexity out of nothing". They might also state the law as "a system can not change from simple to complex" or "a system can not change from disorder to order" and the like. This is their way of saying that the entropy change MUST NEVER be negative which is, of course, equivalent to the other variations mentioned above. Another common example you might see them use (an example you might also find in some college physics books) is that "you can't unscramble scrambled eggs". You can't go from "disorder" (scrambled eggs) to "order" (unscrambled eggs). I hope that these examples will help illustrate to you that according to their 2nd law, all processes proceed in ONE DIRECTION. According to creationists once you get TO point B FROM point A, you can NOT go back. Remember the eggs! If you are still having trouble remembering what the 2nd law says according to creationists because of the word "entropy", "order", "disorder", "complex", and so on and so forth then try to remember one of these: a) Things go downhill, not uphill. b) Things don't evolve, they devolve. c) Things deteriorate, not improve. d) Things degenerate, not regenerate. e) Things tend toward randomness. f) Things tend toward the chaotic state. All of these sayings mean the same thing -- the change occurs in one direction. You can NOT GO BACK to point A. Now at this point, relax, take a deep breath. Re-read this section before you continue. Many of you won't understand this section on the first pass. It will most likely take you 3 or 4 passes before you finally understand unless, of course, you are genius. I am not writing this text for "rocket scientists". It is for the "average Joe". Remember, things change in ONE DIRECTION ONLY. Because of this fact, the entropy change is only in one direction only. The direction of the entropy change has been determined to be positive -- this is the 2nd law of thermodynamics according to creationists. 4.2 The 2nd Law in The Real World Before I continue, I like to make sure you understand completely what the creationist 2nd law is about. I offer another way of explaining to you the 2nd law by showing you MORE real world examples of the 2nd law in action. Remember this is the 2nd law according to creationists. I will remind you what creationist say concerning the 2nd law. They claimed that all processes proceed in one direction, the entropy change is always positive, everything deteriorates, things go downhill and not uphill, things go from order to disorder, more information to less information, and so on and so forth. If you were explaining the 2nd law to an 8 year-old, a teenager or even grandma, how would you do it? The way I would do it is by explaining things they ALREADY UNDERSTAND. Suppose you were on top of a hill and you have a steel ball in your hand. Then you let the ball roll. Where does it go? The most likely scenario is that the ball will roll down the hill. Now suppose you were at the bottom of the hill and you let the ball roll. Will the ball roll up the hill? Obviously, it will not. The ball will naturally roll down hill but it will NOT naturally roll uphill. Thus, it appears that in nature some things ONLY go in one direction. This is what the 2nd law says: Things change in one direction only. Suppose grandma bought a brand new watch when she was only 15 years old. She is now 85 years old and she still has the watch. Do you think the watch still looks new? No, it doesn't. The watch deteriorated over the years and it did not look newer as it got older. Again, it appears that things change in one direction only. The watch didn't get newer, it got older. Things move in one direction. I just gave you two more examples showing the 2nd law in action and apparently the 2nd law mimics the real world well. Do you want more? I'll give you more. When grandma puts water in the pot and heat it, it boils away and the water becomes steam. She did this before and she can do it again. She knows this happens. However, the steam reaches the ceiling and water droplets form. Some of the steam is on the kitchen window and their is liquid water on the window, too. According to the creationist 2nd law, things move in one direction only. Thus, there should be NO water on her windows or ceilings. Again, to remind you: Things change in ONE DIRECTION ONLY. If you can change liquid water into vapor, you certainly can NOT change the vapor back into liquid according to their 2nd law. Now try telling Grandma that she was seeing things. The 2nd law says that those things should not happen. Those are not water droplets on the windows. If the droplets were water droplets then, the water droplets were already there to begin with, she just didn't notice them until after she boiled the water. Grandma simply has an overactive imagination. During hot summer days, the cool drink of lemonade can be refreshing. Grandma makes great lemonade drinks. Everyday Grandma makes the ice needed to make the drink cold and refreshing. The problem is that according to the 2nd law, Grandma SHOULD NOT be able to make ice because ice is more ordered ("less disordered") than liquid water. She didn't really make the ice, it was already there in the ice box or she bought it from 7-11. Is Grandma losing it? Obviously, something is wrong. You shouldn't go around telling Grandma that she is senile. Is the 2nd law wrong? Are there restrictions on the use of this 2nd law? You can convert mechanical energy COMPLETELY into heat but you can NOT convert heat ("disordered energy") completely into mechanical energy ("ordered energy"). The "completeness" is ONE WAY! You can transform one form of energy to another and vice versa. But according to creationists, this transformation CAN ONLY GO IN ONE DIRECTION. "Completeness" is irrelevant. Something is clearly wrong here. Are there any restrictions on the use of this law? Is the law wrong? Are there more examples? Yes, and I will list "a few". a) All the ice in the world was created long time ago when the universe was created. The reason for this is simple: Ice is more ordered than water, therefore, you can not go from disorder ("water") to order ("ice"). Since we have ice on this planet, this can only mean that the ice was created when the universe was created. b) Cans of coke were all created when the universe was created. The reason for this is the same as above. "Aluminum ores" are disordered while a can is a manufactured good. That is, the can is "ordered". According to the 2nd law, you can not go from "disorder" to "order". c) EVERYTHING including the computer you are using were ALL created when the universe was created. The reason for is OBVIOUSLY the same as above. Again to remind you, NOBODY can go from disorder to order. Thus, you can not build a computer ("order") from a bunch of parts ("disorder"). Only the Creator can violate the 2nd law and THIS IS ONLY AN ASSUMPTION. d) A basketball player can never improve his jumpshot. The reason for this is that, according to their 2nd law, NOTHING improves. Everything deteriorates. Now some would say that this is true: Maryland Terrapins were 7-29 from 3-point range against Santa Clara in the NCAA tournament. The flipside to this is that you can improve your jumpshot. But there is a catch -- you can always improve it. In fact, your jumpshot will improve so much that you will NEVER miss from any point on the court (or even off the court). It seems to me that there must be a BALANCE between always improving and always deteriorating. But according to the creationist 2nd law, you can only do one or the other but not both. Hint: Maybe Gibbs free energy which I will discuss much later can provide some insight on balance. e) All the water on the planet is evaporating away and is never coming back. The reason for this is that the entropy change for water becoming water vapor is positive. Thus, it can evaporate. However, the entropy change from water vapor to liquid is negative. Remember, things move in one direction only. Therefore, according to creationists, water won't condense. Thus, all the water you have now was created long time ago and it is disappearing. So you better save your bottled water. g) The Earth is suffering from a global drought that will last until the end of time. The reason for this is that since water vapor can't condense, then obviously there will be no rain. h) You are more simple (ie. less complex) now than when you were conceived. The reason for this is obvious: Things get simpler. Remember, as things change they go from complex to simple, not simple to complex. i) As you get older, you get less knowledgeable and stupider. Again, things do not improve, they deteriorate. Remember the 2nd law of thermodynamics according to creationists. You CAN NOT get smarter, you get dumber. You can't fill your head with information. You are actually LOSING information as you get older. You had more knowledge in your head when you were just one month old. j) When things cool, it loses entropy. Thus, things NEVER get cooler, it can only get hotter. So, hot coffee in a cup will ALWAYS stay hot. You'll never have to worry about your food getting cold. The flipside of this is that when things cool, it gains entropy. Thus, things NEVER get hotter, it can only get cooler. I mentioned this several times already but I am sure many of you still do not get it. According to the creationist version of the 2nd law of thermodynamics, THINGS CHANGE IN ONE DIRECTION ONLY. Creationists, however, do more than just claim that this change occur in one direction. They also claim to know which direction that is. Things go downhill, remember. AGAIN, I will point this out. If one direction is a gain in entropy then the OTHER direction MUST be a loss in entropy. It doesn't matter if you know which direction is positive (I will show you shortly) nor does it matter if you know what entropy is. Remember what creationists say about the 2nd law: When the system changes, the entropy change must be positive. This means that one direction is a positive change in entropy (whatever that is) while the other is negative change in entropy (again, whatever that is). What matters is the DIRECTION which they say is "downhill", "deterioration", "simple", "disorder", "chaotic", and so on and so forth. Therefore, you can either cool things or heat things but you CAN NOT do both. This is the consequence of the 2nd law of thermodynamics according to creationists. This is why you can't have ice. This is why you can't improve your jump shot. This is why you can't have rain. k) It is nice to know that my Dodge Omni is 10,000 years old -- the age of the universe according to most creationists. Or it is millions of years old according to some creationists. Now everything I listed above (a-k) is NOT true in the real world but this is what you should expect if their 2nd law was right. We do not see any of the things above, therefore, it should be painfully clear that there is something wrong with this creationist 2nd law. If it is not clear to you, then I suggest you go over it again. If you still do not understand the significance of the 2nd law, then I can not help you. I made the examples (and the explanations for those examples) as easy as possible so that a bright 8 year-old can understand. If you can't understand material that is meant for an 8 year-old to comprehend, then I suggest that you stop and forget about reading the rest of the text. You won't be able to understand the rest of this text. Reading the basic concepts found in the Appendix won't help you to understand. Why? Because I do not discuss the 2nd law in the Appendix and, more importantly, that material is probably the hardest part of the text to understand. You will only be confused more. I may sound harsh but that is because if you really thought about the subject, then this text should be easy to understand. In fact, this text would not have been necessary if you were able to figure out for yourself that if one direction is positive (eg. melting of ice, heating water) then the other direction has to be negative (eg. freezing of water, cooling water). This would mean, then, only one direction can occur at all at any temperature, at any presure, at any time. This 2nd law according to creationists would obviously be a bogus law. Can't freeze water?! It is my experience that people are taught what to think and how to memorize things efficiently. They are NOT taught how to think logically so people never bother to apply what they memorized to the real world (unless, of course, the application is trivial or the "new" information sounds strange.) Rather than memorize the examples I gave in that list, you should try to understand why each and every one of those examples is the result of the 2nd law in action and why each and every one of those examples violates what we REALLY SEE in the real world. Read those examples over again even if you THINK you understand. Enough with the talk, it is now time to prove them wrong by using real values of entropy. 5. Does violating the law mean anything? 5.1 Law Limitations Contrary to popular beliefs, a scientific law is not nature's "word of God". Scientific laws are _NOT_ proven to be true, either. Remember, all scientific laws are written by humans. Thus, these laws can be true or false, right or wrong. The real world does NOT follow the laws. The laws follow the real world. That is why some laws are shown to be wrong. Laws are, however, assumed to be true unless shown otherwise. There are many laws which we know are not accurate. Examples of these laws include the ideal gas law and Newton's law of viscosity. There are many examples in which the REAL WORLD violates scientific laws. Just because it is shown that a law is wrong, it doesn't mean it is no longer called a law. In some cases, laws are used because it is simple to use. Other times, laws are used because it is "close enough" in some applications. An example of this type is the ideal gas law. It is a bad law but people still use it because it is so easy to use. Ideal gas law is sometimes used to approximate air! If the process involves low temperatures, high pressures and moderate temperatures, very high pressure, or worse low temperatures and high pressures, then the ideal gas law can be very inaccurate. For precision work, the ideal gas law is not used regardless of pressure and temperature. For conditions of low to moderate pressures and/or high temperatures (which is true for many applications), deviation of real gases from ideality is usually less than 5 percent. The errors of the ideal gas should be obvious in another way. Just because H2O (water) in a closed container is at 100 degrees C and 1 atmosphere, it does not mean that it is all water vapor (eg. it boiled away). You can have saturated water at 100 degrees C and 1 atmosphere. You can even have a mixture of vapor and liquid. It should be obvious to you that the volume occupied by the liquid is different from that of the vapor. The ideal gas law does not predict at all the possibility of a phase change (ie. the change from liquid to vapor and vice versa, the change from liquid to solid and vice versa, and the change from solid to vapor and vice versa). So the ideal gas law may not be reliable if phase changes are present. All laws are assumed to be true UNTIL someone can provide one CLEAR example that violates it. So, until someone can provide an example that violates the actual 2nd law (which no one has), the law is assumed to be valid. If a law has many real world examples that violates it, then clearly it means nothing to violate it. For instance, many REAL GASES do NOT behave like an ideal gas so, therefore, these gases do not follow the ideal gas law. The BEHAVIOR is similiar to an ideal gas but the ideal gas law itself is inaccurate. It means nothing to say that carbon dioxide violates the the ideal gas law except to inform you not to use the ideal gas law to calculate its properties unless you wish to sacrifice precision. Laws that are disproven are still called laws. These laws are simply not used any more. Chien Shiung Wu of Columbia University stunned the world in 1957 when her research disproved what people thought was a basic law of physics -- the law of conservation of parity. In 1975, she became the first woman president of the American Physical Society. So, are there any real world examples that violate the 2nd law? Before I answer the question, I will state the 2nd law again. Keep in mind that this is the 2nd law ACCORDING TO CREATIONISTS and may NOT be the actual 2nd law. The 2nd law of thermodynamics according to creationists state that the change in entropy of any system undergoing any change must be greater than zero. 5.2 Entropy is a State Variable So, what is entropy? Judging from the many ways creationists state the 2nd law, it appears that entropy has something to do with "disorder" or "complexity". In another variation, entropy apparently has something to do with "information" or "information content". The definition of entropy, however, is actually not important. What is important is that entropy is a STATE VARIABLE. From this point on, when I say entropy I am really talking about SPECIFIC entropy. Specific entropy is the entropy (an extensive property) of the system divided by the mass (an extensive property) of the system. This means that specific entropy is an intensive property. Again, when I say entropy I really mean specific entropy. The tables (which I will discuss later) have values for SPECIFIC entropy. Please review section 2.3 if you do not understand intensive and extensive properties. Now, you must wondering what in the hell is a state variable!? It appears I am simply replacing one unknown with another. On the contrary, you probably already know what a state variable is but don't recognize it. Internal energy per mass is an example of a state variable. "So what?!", you say. To help you understand the importance of a state variable, I will provide an example -- using internal energy, of course. Internal energy per mass is called SPECIFIC internal energy. Internal energy and mass are both extensive properties but specific internal energy is an intensive property. From now on when I say internal energy I really mean specific internal energy. Suppose you have a system that is initially at a certain temperature and a certain pressure. Let P1 be the initial pressure and T1 be the initial temperature. In this example, these two properties defines your system. At this pressure P1 and temperature T1, your system also has a certain initial amount of internal energy. Let U1 be the initial amount of energy. This system also occupies a certain volume, V1. This system also has a certain amount of mass, M1. The system has a certain heat capacity, C1. The list of properties of your system can be quite long. However, you only need 2 properties for this simple system. (For systems in which you have different types of chemical components, then you would need to specify 3 properties.) In this example, I chose temperature and pressure since those are the properties that I will change. The changes (if any) in the other properties (like internal energy, volume, mass, etc.) is simply the result from the changes in pressure and temperature that I made. Not all properties change, however. But some do. In this example, the mass doesn't change but the volume and energy will. For some systems (which I will discuss in more detail later) you can actually look up the value for U1 for a given pressure and temperature. Thus, you can determine the numerical value for U1 from a table. Now this system of yours undergoes a change. Suppose I changed the pressure and temperature of this system. The final pressure is P2 and the final temperature is T2. The change in energy OF THE SYSTEM is simply the final energy amount minus the initial amount. Expressed mathematically, dU = U2 - U1 where dU is the change in energy and U2 is the amount of energy in the system after you changed the pressure and temperature. The value of U2 like U1 can also be determined from a table since P2 and T2 is known. As I said, energy is a state variable. I told you that the change in energy is dU. I told you that the pressure and temperature was altered. I gave you a lot of information but I didn't tell you everything. What didn't I tell you? I did NOT tell you HOW I changed the temperature and pressure. Without knowing how the change took place, the amount of energy change can still be determined by knowing the initial points (eg. initial pressure and temperature) and the final points (eg. final pressure and temperature). You know that the system underwent a certain process but you have no idea what that process was. This is the importance of state variables. It does NOT matter how the change took place. The change in energy between the same two points is ALWAYS the same. It didn't matter if I used a hammer to change the pressure and temperature or I used a heater to change the pressure and temperature. The change in energy is the same. What matters is the initial and final points. It doesn't matter how the change took place. Doesn't this sound alot like my discussion on equilibrium? It should if you have read the Appendix. The intensive properties of systems in equilibrium are the state variables. Entropy is a state variable. Thus, if you know the initial and final points (eg. initial and final temperature and pressure, initial and final pressure and volume, etc.), you can determine the change in entropy of your system just like energy. Again, it does not matter how that change took place. What matters is that you know the initial and final points. To summarize what is meant by "entropy is a state variable": a) the condition in which the system is at DEFINES the system b) as a consequence of (a), if two systems have the same pressure, same temperature, same volume, same mass, same heat capacity, and so on and so forth, both will also HAVE the same entropy! c) also as a consquence of (a), it does NOT MATTER what process was used to get to the final pressure, temperature, volume, etc. Suppose you have two systems with two different initial starting points. Both of these two different systems undergo two different processes. The final states, however, are identical. This means that BOTH systems will have the same final pressure, same final energy, SAME FINAL ENTROPY, etc. If the two systems had the same initial starting condition but underwent two DIFFERENT processes that yielded the same final condition, the change in entropy and the change in the other properties for both systems WILL BE THE SAME! Okay, now you know that entropy is a state variable. "So what?", you say. It is important to know because there are tables containing values of entropy! If you know two points (eg. volume and temperature), you can look up the value of entropy. If you know the initial points and the final points, you can easily calculate the change in entropy by using these tables. 5.3 Steam Tables Tell All Where can you get these tables and what are they? Get a book containing SATURATED STEAM TABLES. I have Schaum's outline series: theory and problems of thermodynamics, 2ed with chemical applications by M.M. Abbott and H.C. Van Ness. Steam tables are tables containing values of various properties of steam. These tables can be used to look up values for entropy at a specified temperature and pressure. Saturated steam tables have values of properties for liquid water as well but at a PARTICULAR temperature and pressures. These particular temperatures and pressures are known as saturated temperatures and saturated pressures. Using the steam tables requires a 3rd-grade level math skill. Thus, it SHOULD be easy to use. To determine the entropy change from gaseous water (ie. steam) to liquid water, all you need to do is to look up the value of entropy for steam (your starting point) and the value of entropy for liquid water (your ending point). The entropy change is your final entropy value minus your initial entropy value. Suppose you have steam at 100 degrees C and at a pressure of 1 atmosphere. This steam is in a closed container. This container has a piston on top which moves when the pressure changes. The piston will move in such a way that it will keep the pressure constant. You want this steam to CONDENSE into a liquid that is also at 100 degrees C and at a pressure of 1 atmosphere. What is the entropy change of this steam? By using the saturated steam table, the approximate change in entropy is -6.0485 kJ/(kg K). Therefore, if one accepts their version of the 2nd law, I have just proved that you can not condense steam. Thus, according to creationists Grandma was seeing things. I just gave you an example that violates the 2nd law. Are there any more examples? Suppose you have steam at a pressure of 0.60MPa and a temperature of 1300 degrees C. This steam is, again, in a closed container. But this time, there is no piston so the pressure can change. An unknown process is used to force a change in the steam. In the end, you have steam at a pressure of 0.50MPa and a temperature of 300 degrees C. What is the entropy change of the steam? Using steam tables from _Chemical and Engineering Thermodynamics, 2ed_ by Stanley I. Sandler, p. 590, the entropy change is simply (7.4599 - 9.6906) = answer. I'll let you finish the calculation but it should go without saying that the entropy change is again negative which again violates the creationist version of the 2nd law. We know in the real world that it is possible to lower the temperature of steam from 1300 degrees to 300 degrees C. Thus, the creationist version of the 2nd law is wrong. If you accept the creationist version of the 2nd law, then you also have to accept the belief that you can NEVER cool things down. This means that the ice that Grandma didn't make for the lemonade CAN NOT be responsible in cooling the lemonade. The drink HAD to be cold in the first place. So, it should be apparent that there are more than one real world example that violates their version of the 2nd law. In fact, there are tables worth of examples. To recap what happened so far: a) creationists claim that the entropy change must always be greater than zero. b) using steam tables, I have shown that (a) is not true. 6. Does evolution violate the 2nd law? 6.1 Entropy Balance I had already shown in section 4.2 and chapter 5 that there are many real world examples that violate the creationist version of the 2nd law of thermodynamics. Therefore, it does not matter if evolution violates the law or not. But does it violate the REAL 2nd law? To answer that question, you will need to finally learn some real engineering thermodynamics. In particular, you will need to know how to use an ENTROPY BALANCE which I will teach you now. The following equation is the entropy balance equation for ANY TYPE OF SYSTEM: dS = Q/T + (MS) - (MS) + S (3) in out gen where Q stands for heat, T stands for temperature S stands for entropy M stands for mass Equation (3) says that the change in entropy is caused by heat flow, mass flow going in, mass flow going out, and some unknown generation term. Thus, (MS) = entropy added to the system due to mass flowing into the in system (MS) = entropy removed from the system due to mass flowing out of out the system Q/T = entropy added or removed due to heat flow S = entropy generation term. This is sometimes called entropy gen generated due to irreversibilities. If the process is reversible, this term is zero. Otherwise, this term is ALWAYS POSITIVE by convention. If the system is NOT changing at all, then this term is zero as well. dS = change in entropy of the system Q = term is positive if heat is added, negative if heat is removed T = temperature is always positive and greater than zero. The type of system, remember, refers to the type of system IN-BETWEEN the initial state and the final state. The initial and final states are both equilibrium states. The states in-between are not. Real processes proceed in one direction; real processes are irreversible. The CHANGE in a system does NOT have to be irreversible. In fact, it can be reversible. Systems involving reversible chemical reactions are examples. Processes move in one direction; CHANGES can be reversible. The entropy generated term is determined by the irreversibilities of the process. Real processes move in one direction. The mathematical equivalent of this is to always add a term or always subtract a term. By convention, then, the entropy generated term is alway positive which is the same as always adding a term -- the mathematical equivalent of a one way process. The effect of always adding a term is that the value of the entropy of the system at its final state is some maximum value AT THAT FINAL STATE. This does not mean that the CHANGE has to be positive. It says that the final value of entropy at the final state is the maximum value at that state. It is highly possible that this final maximum value can be lower than the initial value -- the change is negative. Similiarly, the value of entropy at the initial state is some maximum value for entropy AT THAT INITIAL STATE. At the maximum value, the system is in equilibrium -- the final state and final state are in equilibrium. The equilibrium state as we all know by now is a time-invariant state; the properties do not vary in time. That means that the change in entropy per second at the final state is zero. Mathematically, we write this as, dS/dt = 0 at equilibrium (4a) where t stands for time . dS/dt = S isolated system NOT at equilibrium (4b) gen . where S is the entropy generated per time gen This is always positive since entropy generated is, by convention, always positive. Thus dS/dt is always positive. This is for an isolated system. Remember, you have to consider the other factors for systems that are not isolated. The total entropy generation, S is simply gen . integrating S dt from initial to final time. gen If the system is isolated, then, clearly the total entropy change is equal to the total entropy generation. S = constant = maximum value at equilibrium (5) What do you notice about equation (5)? It is a VALUE of entropy. It is NOT the change in entropy. This value can be less than the initial value -- the change in entropy from state 1 to state 2 is negative. Sample application: You can apply the entropy balance of equation (3) to the universe but first, we have to write down any assumptions. Assumptions: a) Assume NO mass goes in or out This means that the mass of the universe is constant. b) Assume NO energy goes in or out This means that the energy of the universe is constant. By (a) and (b), the total energy is constant. These assumptions can only lead you to one thing: the universe is isolated. For the universe (our system), there is no heat flow in or out and there is no mass flow in or out. Thus the Q term and the two MS terms are all zero. The equation is then reduced to, dS = S (6a) gen If the process is reversible, then dS = 0 (6b) If the process is irreversible, then dS > 0 (6c) It is zero for reversible processes and greater than zero for irreversible processes. This is by convention. Thus we conclude that the entropy of the universe either stays constant or increase for any process to proceed. Remember how I arrived to this result. Three terms in the equation were zero. In general, these terms are NOT zero for other types of system. In isolated systems like the universe, these terms are always zero. Again, to reiterate a major point: although we derived this result by using the universe as the system, this result is true for ANY isolated system. Remember equation (4b). This result is sometimes called the 2nd law of thermodynamics -- the real 2nd law. In reality, it is a simple application of the entropy balance to the universe. Others call this the law of entropy. It does NOT say that the entropy change of any system must be greater than zero. It says that the entropy change of the universe (or more generally, of any ISOLATED system) is never negative -- "the law of entropy". I should point out that this result is also the source of the creationist version of the 2nd law. Again, recall how I arrived to that result. Three of the terms were zero. This is because in an isolated system, these three terms MUST be zero. The result above states that for any real process to proceed, the entropy change of the universe must be greater than zero. Creationists rewrite this result as: for any real process to proceed, the entropy change of the SYSTEM must be greater than zero. They simply replace the word 'universe' with 'system'. Or equivalently, if the actual law is stated as "for any real process to proceed, the entropy change of an isolated system must be greater than zero", they will rewrite the law as "for any real process to proceed, the entropy change of the system must be greater than zero". They simply leave out the word ISOLATED from the law. Those who are unfamiliar with thermodynamics would not know the significance of this deceptive change. For any system SMALLER than the universe, you will also have to consider its surroundings. This system (which is smaller than the universe) plus the surroundings make up the universe. Thus, when you calculate the total entropy change, you will also have to calculate the entropy change of the surroundings as well. That is, you will also have to apply the entropy balance to the surroundings, too. The total entropy change is simply the entropy change of the system PLUS the entropy change of the surroundings. This is equal to the entropy change of the universe. You then compare this to the result above which states that the change must be positive. There is NO restriction on the entropy change of the system (as long as it is smaller than the universe and it is not isolated like the universe) but there is a restriction on the total entropy change. For chemical reactions, you will still use the entropy balance equation. In this case, the system is the compounds (or the "box containing the compounds"). In this box, there are no flow-rates so the mass terms in the entropy balance equation is zero. However, in ALL chemical reactions, energy flows do exist. Therefore, there will be an entropy change due to energy differences. And, of course, there is the last term which represents irreversibilities. So when you look at tables containing values for "absolute standard entropies" and calculate the change of entropy by simply substracting the entropy values of the reactants from the entropy values of the products, you are really calculating the dS by some other mean. You are not using the entropy balance equation. This is because you are using the "two-box" method. You know the values of the final box ("the products") and the values of the initial box ("the reactants"). The difference is simply final minus initial. Therefore, you can view the tables as an indirect way of giving you the value for the left-hand side of the entropy balance equation. When you look at the entropy balance equation, you will realize that this change in entropy is due to heat flows and irreversibities. For chemical reactions, this entropy change is given a special name, _entropy of reaction_. When you use the steam tables, you are really using the "two-box" method. You looked up the final value for entropy and you looked up the initial value for entropy. The entropy change is then easily calculated. This change ALREADY takes into account the entropy change due to heat flow and any irreversibilities. When I showed you that the entropy change of cooling steam, I did not calculate the change in entropy of the universe. Why? Because according to the creationist version of the 2nd law, the entropy change of the SYSTEM had to be positive. I showed that this is not true. There was no need to calculate the entropy change of the surroundings at that point. If you want to calculate the entropy change of the universe for that case, you will need to calculate the entropy change of the surroundings as well. To this, you will need to calculate the amount of energy that was released by the steam to the surroundings. You use the tables for this since steam tables also contain values for internal energy. Remember, the steam was cooling! The entropy change of the system was ALREADY calculated. Once you know how much energy was absorbed by the system as heat, use the entropy balance to calculate the entropy increase of the surroundings. When you do the calculation on the surroundings, you will notice that there is a variable, T, you do not know about. T stands for temperature. Now the question is: "what is the temperature"? Since we do not know what the temperature is, you will need to estimate it. How? It is simple. You know that the temperature of the steam is reduced to 300 degrees C. Therefore, the temperature of the surroundings is at most 300 degrees C. Remember which direction heat travels! Keep in mind that when you do this calculation, your numbers will be off the actual answer. Part of the reason is, of course, rounding. But that is not where most of the error comes from. When you calculated the entropy change of the SYSTEM, you used values from the table. When you calculated the entropy change of the SURROUNDINGS, not only did you estimate the temperature but you also assumed that the heat transfer was reversible. Remember the last term in the entropy balance equation. This assumption will affect your calculation by UNDERESTIMATING the entropy increase of the surroundings. Even with these errors, you will find that the entropy change of the universe is positive. So for this case, the assumption did not drastically change your conclusion on whether or not it is possible to cool steam. The lower your temperature for the surroundings, the larger is your increase. You can do the same calculations for heating the steam to 1300 degrees from 300 degrees. Since I know that many of you are still not convinced, I will show you the calculations. You have steam initially at 1300 degrees C and 0.60 MPa pressure. By some unknown process, it is cooled to 300 degrees C and 0.50 MPa pressure. You have 1 kg of steam and it is in a closed container. A closed container means that you use the value for _internal energy_ from the steam tables, not enthalpy. Enthalpy is used for open systems. This is a CLOSED system. The change in entropy is simply (7.4599-9.6906) = -2.2307 kJ/K. The change in energy is simply (2802.9 - 4682.3) = -1879.4 kJ. Now, the system (ie. the steam) loses energy so, therefore, the surroundings gains this same amount of energy. The surroundings, of course, absorbs this energy as heat. As you can see, the entropy change of the system is negative which violates the creationist version of the 2nd law of thermodynamics. The entropy change of the surroundings is simply dS = (1879.4)/573.15 = 3.2791 kJ/K. You divide by 300 because the temperature of the surroundings is at most 300 degrees C which is 573 Kelvin (you use absolute temperatures). The entropy change of the universe is simply -2.2307 + 3.2791 = 1.0484 kJ/K. Thus, cooling the steam increases the entropy of the universe. Therefore, the ACTUAL 2nd law of thermodynamics is not violated. How about heating the steam from 300 degrees to 1300 degrees? If you want to heat the steam, it should be obvious then that the temperature of the surroundings would not be 300 degrees C. It has to be at least 1300 degrees C (or 1573.15 K). The change of entropy of the system will be +2.2307 kJ/K. Remember, the system is the steam. The change in energy will be +1879.4 kJ. The entropy change of the surroundings will be -1879.4 /1573.15 = -1.1947 kJ/K. It is negative because the surroundings is losing energy. The temperature of the surroundings is at least 1300 degrees C. Remember the direction that heat flows! The system is being heated. The entropy change of the universe is 2.2307 + -1.1947 = 1.0360 kJ/K. Thus, heating the steam increases the entropy of the universe. I just showed you that heating AND cooling steam from the same two states increases the entropy of the universe. I ignored irreversibilities so the actual increase in entropy of the universe is greater than what I calculated above for both cases. The process is irreversible; the change is reversibe. You can do the same type of calculations for the first steam example I gave -- the condensing steam at 100 degrees C. In this example, however, you can no longer ignore the irreversibility term in the entropy balance equation like I did for the example above. Ignoring irreversibilities, you will conclude that condensing steam is impossible unless the surroundings was at most 71.97 degrees C. If the temperature was any higher than that, you won't be able to condense steam. This is, of course, wrong. Therefore, you can not ignore irreversibilities. Just like chemical reactions, the entropy change of gas condensing to liquid (or liquid evaporating to vapor) has been given a special name. It is called entropy of vaporization. 6.2 Violating the Law Does evolution violate the 2nd law of thermodynamics? Now to answer the big question, you will need to do a few things: a) Identify the system b) Identify all heat flows in and out c) Identify all mass flows in an out d) Identify what is meant by evolution Criteria (a) should be self-explanatory but obviously it is not. Entropy is a property of the system. True, it is a "mathematical abstraction" just like energy. But LIKE energy, it is a property of the system. It is NOT the property of the process. If you need to calculate any changes in energy, entropy, temperature, pressure, volume, mass, and so on and so forth, you need to identify the system. Why? Because it is the SYSTEM that is changing. Criteria (b) and (c) should also be self-explanatory but again, obviously it is not. To determine the entropy change in a system, you NEED TO KNOW what causes these changes. You do NOT need to know HOW it changes. That is, you do NOT need to know the details of the process. All you need to know is WHAT CAUSES these changes. The change in entropy is due to three things: changes in energy due to heat flows, changes in mass and/or composition due to mass flows, and any irreversibilities in the process itself. If you looked at the entropy balance equation, you should have known this already. Now what is evolution? Is it a process? Is it a system? What is it? The idea of evolution (Klang, p. 71) is actually a very old idea. It dates back to at least 25 centuries ago to a Greek philosopher named Empedocles. He proposed that the development of life was a gradual process. In other words, the CHANGES in life was a gradual process. However, the term _evolution_ was not used until the 19th century. So again, what is evolution? In the 18th century, many biologists (who were all creationists at the time) became interested in this idea called evolution. In 1794, Erasmus Darwin (Charles Darwin's grandfather) published a long poem entitled "Zoonomia". The poem contained the belief that evolution probably occurred in plants and animals. However, he did not propose any hypothesis to explain HOW it happens. That is, he did not propose a PROCESS of evolution. So the question remains: What is evolution? And another question now comes up: How does evolution occur? In 1809, the very same year Charles Darwin was born, Jean Baptiste Lamarck published a book called _Zoological Philosophy_. This book presented Lamarck's ideas on how evolution occurred. Lamarck, a French biologist, reasoned that great change in the environment of a population of animals (belonging to the same species, of course) would result in the need for a corresponding CHANGE IN THAT SPECIES itself. This "need" for CHANGE would cause the animal to form new habits in its attempt to adjust to its new environment. At this point, it now should be obvious that I just answered BOTH of the questions. The word "change" seem to come up a lot. That is intentional. Why? Because the CHANGE itself is evolution. Evolution is not a process although for non-biologists such as myself find it to be sometimes convenient to think that it is. That is, it is easier to view the "evolution process" as all the chemical reactions necessary to cause this change called evolution. However, evolution is not a process, it is the term given to the CHANGE in the population. When I say that I have the value for "entropy of vaporization", what does that mean to you? Is it a special type of entropy? Is it a special type of entropy change? You should know this since I already went over this briefly. It is NOT a special type of entropy. When a gas condenses to a liquid, the entropy of the substance changes. This change has been given a special name and it is "entropy of vaporization". But other things BESIDES entropy can change when a gas condenses to a liquid. The amount of energy in the substance changes, too and it is called "latent heat of vaporization" sometimes called "heat of vaporization" , "latent heat" or "enthalpy of vaporization". So clearly, other changes can take place and these OTHER changes can not be all called "entropy of vaporization". Similiarly, not all changes in a species can be called evolution. But the important thing to remember AT THIS POINT is that evolution means CHANGE. Thus, the next question that should come up is: What changes have to be made so it can be called evolution? In thermodynamics we would phrase the question this way: What property of this system changes so it can be called evolution? So far, I have successfully transformed one question into another. The second question which concerns how evolution occurs was answered by Lamarck. He believed that the changes (eg. the evolution) of species is caused by the changes in the environment. The new "habits" that a species develop is then passed down to future generations. His theory of evolution is based on two major assumptions. The first assumption is known as the principle of use and disuse. Lamarck assumed correctly that as any part of the body is used more and more, it develops and enlarges. Those parts that is not used gradually weakens and becomes smaller or even disappear. His second assumption is called the inheritance of acquired characteristics. Lamarck assumed incorrectly that traits that an animal acquired or gained during its lifetime can be passed on to its offsprings. Thus, its offsprings would inherit those same characteristics. From these two assumptions, new species can evolve from old ones after many generations of acquiring new traits or losing old ones. The often-quoted example of Lamarck's reasoning is his explanation on how the giraffe's neck grew so long. However, as mentioned, his second assumption was wrong. Thus, his theory of evolution was wrong too. That is, his EXPLANATION on HOW evolution occurred was wrong. To put it in another way, the PROCESS that Lamarck proposed was wrong. The MECHANISM that Lamarck proposed was wrong. So Lamarck's theory of evolution was wrong. The world had to wait another fifty years for another explantion on HOW evolution occurred. In other words, the world had to wait 50 years for someone to describe a PROCESS which this change called evolution can occur. This person's name was Charles Darwin. Darwin's book on evolution was entitled _On the Origin of Species by Means of Natural Selection_. In his view, Darwin believed that evolution occurs by the PROCESS of _NATURAL SELECTION_. A summary of the steps involved in this process is as follows (Klang, p. 77): 1) all organisms TEND to increase in number at a geometric rate 2) this increase, however, does not go on forever. Many offsprings die, killed, or eaten. Thus, the number of individuals in a population remains nearly the same. 3) So there is a struggle to survive. 4) There are variations (which can be inherited) found among the individuals in this population. 5) Some variations are more favorable than others. Those with the most favorable traits are able to reproduce abundantly. The "reward" to having the more favorable trait(s) is to have more babies. 6) Given enough time, these changes will accumulate to the point that a new species will evolve from the original members of the population. That is, the individuals in the 20th generation is so different from the 1st generation that this generation is considered a different species. (I am not saying, however, that natural selection is the only process that can cause evolution and evolution means change remember. In this text, however, it is the only one that is going to be considered.) This process was introduced as Darwin's HYPOTHESIS on evolution in the high school biology book that I was using. It later became Darwin's theory of natural selection. This is Darwin's "theory of evolution" that creationists have been refering to. You will notice that NOT A SINGLE step or idea of Darwin's theory uses the concept of "spontaneous generation", disproves or proves God's existence, creates matter or energy out of a vacuum, or any other claims that creationists have been making. And again, I will point out that this "theory" was NOT introduced as a theory but as a HYPOTHESIS. It was NOT introduced as a fact, either. Many creationists have been saying to the public, time and time again, that "evolution is taught as a fact" or "evolution is taught as a religion". In reality, this is not so. Because creationists have been making these claims so often, teaching evolution has become very controversial so MANY if not MOST teachers in the United States either avoid teaching it or only cover it very briefly. (Some students don't even take biology). The CHANGE itself is fact; thus evolution is fact. It is unfortunate, but I have failed to find anywhere in my biology book which tells the student that it is FACT that species do change. It appears that the student is left to figure it out for him or herself which often DOES NOT happen. The student simply memorize a bunch of facts so he or she can simply "spit" it back out on tests. How many students realize that Lamark's theory is also a "theory of evolution"? Not many. The PROCESS in which this change called evolution takes place is the theory which was INTRODUCED as a hypothesis, not as a fact contrary to the false claims of creationists. Darwin's theory has been refered to as THEORY after its introduction which is, again, contrary to the false claims of creationists that Darwin's theory of evolution is taught as a fact or a religion. If it is not obvious to you by now, I will make it obvious: Creationists have been lying. Their claims mentioned above is NOT for your benefit or my benefit, it is for THEIR benefit. Creationists know for a fact that evolution is rarely taught properly in public schools so, therefore, they are taking advantage of these students. Ask these students what is evolution and most will respond with steps #5 and #6 outlined above of Darwin's theory of natural selection (assuming they will respond at all). Many common dictionaries include "science" dictionaries define evolution on the basis of Darwin's theory of natural selection. Sometimes the dictionaries include both; the correct definition and Darwin's theory. Dictionaries tend to include common usage of words in the meanings. The students were "taught" Lamarck's theory but do NOT even realize that his theory is also a theory of evolution. This inability to think for themselves plus incorrect or poorly worded definitions of evolution in the dictionaries, combined to make an excellent recipe for a successful campaign on misinformation. What is worse is that many individuals like to pick and choose definitions so it doesn't even matter if the dictionaries actually include the correct definition -- it is simply ignored. This is the sad state of American education and also proves that the typical American mind is no longer capable of figuring simple things out. (I will define evolution for you very shortly.) Many of today's scientists worry about the progress (if any) this country will have 50 years from now. Americans are NOT taught how to think logically. They are taught how to memorize things well and what to think. This teaching style as we all know is not good for the student, not to mention very boring too. In fact, it is too boring and the student don't even pay attention in many cases. Thus, many students do not even know what they were supposed to have memorized. Moreover, many people did NOT even take biology while they were in high school or college. Thus, creationists are able to publicly make bold claims which THEY KNOW IS A LIE. For the gullible people, new books WILL BE ORDERED. Who publishes these books? Creationists, of course. Who write these books? Creationists, of course. Besides money, there is the old fashion "stroking of the ego" that one gets if he or she is able to convince a gullible person that "Darwin's theory of evolution is taught as a fact" or "evolution violates the 2nd law" or any other claim. I remember one creationist who had his ego really stroked when he was successful in convincing a young person that Mt. Ararat was the tallest mountain in the world. One has to only imagine what would happen if this person had some real talent and used his abilities for other things such as changing the school curriculum of America or passing some law to fire any teacher who is caught teaching the students that evolution is a fact. Now back to the subject at hand, I have identified a process which explains the details on HOW evolution occurs. So far, I have informed you that evolution concerns the CHANGES in a population. However, I have not inform you what those changes are so it can be considered evolution. So now you need to know what those changes are. In other words, what is the definition of evolution? Evolution is defined as "the changes in allele frequency of a population over a period of time". Not just any change in the population can be called evolution. In other words, if the population shrank from 10,000 members to 1,000, it is still not called evolution. True, the population did change but it did not change in a certain way so it can be called evolution. Or if the average height of the members in this population grew by 4 inches due to better eating habits, this change is still not called evolution. Now if this same population changed such that in the beginning most members have 5 fingers but in the end most members have 7 fingers then this change can be called evolution. Why? The changes in the number of fingers can only be caused in changes in allele frequency. Thermodynamically, we will say the "allele frequency" is the property of the system. Changes in this property called "allele frequency" is called evolution. That is, when the system changes in such way that this property called "allele frequency" has changed, then this change is called evolution. So now we are back to the first critera -- identify the system. If you use the Earth as the system, then you will have identified the following: 1) The net entropy change from mass flow is positive since the Earth receives matter from space in FAR greater quantities than matter escaping the Earth's gravitational pull. 2) The net Q term is positive since the Earth receives heat from the sun. 3) The last term is, by definition, never negative. When you identified all the terms (which I listed for you above), you will realize that everything on the right-hand side of the entropy balance is positive. Thus, evolution caused by natural selection increases the entropy of the Earth. To be more accurate, the entropy of the Earth is increasing! At this point, I should note that evolution does not violate the creationist version of the 2nd law. The entropy change of the system is, indeed, positive which they claim must be so. The system is, of course, the Earth. Don't celebrate yet! The calculation is not complete. You still need to calculate the entropy change of the surroundings. Remember what I said about the universe. As long as your system is smaller than the universe, your system PLUS the surroundings is the universe. If you add up the entropy change of your system AND the surroundings, you will have the total entropy change of the universe. From the previous section, we already know which direction the entropy change of the universe is. This is where the creationist version differ from the actual. They do not take into account the entropy change of the surroundings. With a little thinking, you will realize that the entropy increase of Earth due to mass flow is equal to the entropy decrease of the surroundings due to mass flow. Thus, these cancel. What you have left then is the entropy generated term (the last term) and entropy change due to heat flow. The last term is never negative so you don't have to worry about that. What we need to do is compare the entropy increase of the Earth due to heat flow and the entropy decrease of the surroundings due to heat flow. The entropy increase of the Earth due to heat flow is simply Q/T where Q as stated before is positive. Why is it positive? Because the Earth receives this heat and, by convention, Q is positive when the system receives heat. The system is the Earth, not the universe. At this point I want to stress ONE important fact to you. The system that I am using to make this general calculation is the EARTH. The system is the Earth. When discussing this topic, some individuals wish to apply this same analysis to ANOTHER system such as the universe and then claim that you are wrong in considering the Sun to be not part of this system (ie. universe). When you use the Earth as the system, it should be clear to you that the Sun is not part of the Earth. It is part of the universe but it is not part of the Earth. The entropy increase of the surroundings is also Q/T. Now this Q has the same magnitude as the previous Q mentioned in the previous paragraph. Why? Because this is the SAME heat that is leaving the surroundings and entering the system. The sign of this Q, however, is negative since heat is LEAVING the surroundings and entering the system. Since the entropy increase is negative, then this means that the surroundings has an entropy DECREASE. There is only one more variable you will need to look at and that is T. T stands for temperature. The T for Earth is obviously the temperature of the Earth and T for surroundings is the temperature of the sun (since the sun is the one giving off the heat). What do you know about the two temperatures? Answer: the sun has a much higher temperature than the Earth. Therefore, Q/T of the Earth is FAR GREATER than Q/T of the sun. This means that the net Q/T term of the entropy balance for the universe (Earth plus surroundings) is positive. This means that the entropy of the universe is INCREASING! At this point, I had just shown that natural selection (which causes evolution) on Earth does not violate the actual 2nd law of thermodynamics. Or more accurately, I had just shown that the entropy of the universe is increasing again. But as I pointed out, it does not matter which version of the 2nd law you accept. The claim that evolution violates the 2nd law is wrong. Both versions yield the SAME RESULT! However, some would say that you need to put an "asterisk" by this conclusion. Why? Because natural selection is just one of the MANY, MANY processes that is going on simultaneously on Earth. All that we really know is that the entropy of the Earth is increasing and the entropy of the universe is increasing. However, on occasion there will be some who do not care about this "asterisk". They will simply say that evolution violates the second law and that all I did was show that the sun shining on Earth does not violate the 2nd law. These comment(s) are made not to convince the educated individual but to convince individuals who are not taught thermodynamics. These individuals are often high school graduates, high school dropouts, and college graduates with little or no courses concerning thermodynamics. These individuals often include lawyers, politicians, and "the average Joe" on the street. What did I say about the entropy balance and the system? You need to identify the system. After that, you need to identify EVERY TERM in the entropy balance and this, of course, includes the sun since the system in this case is the Earth. Remember the Sun is the bright object in the sky that provides HEAT to the Earth. Since the Earth is receiving HEAT from the Sun, this heat have to be taken into account in the entropy balance. It is that simple. If you want to know if a PARTICULAR process increases the entropy of the universe, what do you need to do? You need to: a) identify the system b) identify all (relevant) mass flows c) identify all (relevant) heat flows This assumes that you can actually isolate that process. You will run into trouble when multiple processes are occuring and these processes have an effect on each other. In that case, these multiple processes behave like ONE big process. To reiterate a major point: IDENTIFY THE SYSTEM. I mentioned this several times already but I know that MANY (not just some) will apply the laws of thermodynamics to "something" without telling anyone what that something is. Evolution MEANS CHANGE. It is NOT a system so you need to identify the system BEFORE you even consider applying the laws of thermodynamics. Take a look at the steps involved in the natural selection process. As mentioned before, natural selection is the process that causes evolution. However, many of the steps themselves are a collection of processes. Thus, these multiple processes behave like one big process. In this case, we call this big process natural selection. The "struggle to survive" (or "the process to survive") is a process (or a collection of processes) which can be performed in MANY different ways depending on the animal, the predator(s), the environment, etc. The reproductive portion of the process is different for different species. Different species, of course, have an effect on each other. Remember, some are predators while others are prey. Moreover, this portion involves a large number of chemical processes (chemical reactions) which need to be identified. These chemical reactions, of course, either gives off energy or requires energy. This obviously means that you would need to identify any and all heat flows going out or into the system due to these chemical reactions. If you know the initial properties of the system and the final properties of the system, then the details of the chemical reactions is not necessary. However, the initial and final properties of the system is usually not known. Moreover, the entropy change due to mass flows in and entropy change due to mass flows out are usually not known, either. (That is, you know the amount of material in MASS that is going in and out but you do not know the amount of change in entropy caused by these flows.) Therefore, you will need to identify every chemical reaction involved. Non-biological processes such as storms can affect the reproduction portion of natural selection as well as affect the population's ability to "struggle to survive". Thus storms affect the evolution of a system. We know that plants obtain its energy from the sun in a series of chemical reactions known as photosynthesis. We know that the energy that animals used when they eat plants come from the sun. We know that the energy needed to power thunderstorms, hurricanes, etc. come from the sun. Thus the sun is the source of energy for the evolution of systems. These mulitiple process behave like one big process so you can remove the "asterisk" from the proof. The idea that the I only proved that the sun shining on Earth does not violate the 2nd law is idiotic! The sun is an important factor for any biological and non-biological process on Earth. One can safely say that the sun is THE most important factor. As I mentioned in section 3 it does NOT matter HOW the change took place. The process does not matter. I had just shown that the entropy of the Earth is increasing. In the absence of knowing the initial and final points, you will need to know what is coming in and out of the system. These "comings and goings" is increasing the entropy of the Earth and in turn is increasing the entropy of the universe as well. I do realize, however, the creationists will not accept this result. The only choice they have, then, is to change the system. This means that they have to identify the new system. Remember, natural selection is a process, it is not a system. It is the SYSTEM that changes. And this change is given a name called evolution. Therefore, you need to identify the system. The next time someone tells you that "evolution violates the 2nd law", ask them what was the system? If they say Earth, then you have detail analysis to prove them wrong. If they identified something else, then ask them to identify all heat sources, all mass flows, and how did they determine the value for the entropy generated term. In the absence of knowing the initial and final points, and mass flows, the creationist will then have to identify EVERY chemical reaction that is directly or indirectly involved in evolution. All heat flows, however, must be still identified. At this point, you should realize that I provided NO creationist-proof answer to the big question. You learned that the entropy of the Earth is increasing. What does that tell you? If evolution violates the 2nd law as creationists claim, then the system would not change at all due to evolution. Why? Because it would violate the 2nd law and so, it won't happen. The system, of course, does change but it is NOT by natural selection. If natural selection does NOT violate the law, then it would be one of the many processes on Earth that increases the entropy. Creationists will, then, claim that the other processes increases the entropy, not natural selection (often refered to as the "evolution process" or the "process of evolution"). So far, it appears there is no way to tell what is the right answer. The only way to determine the answer is to do an experiment. Create a system in which the evolutionary process called natural selection is being used. Identify all mass flows and heat flows. Then calculate the entropy change. To this date, not a single creationist ever performed such an experiment and publish their results. Why? There are experiments showing evolution in action (eg. Discover, May 1994). Unfortunately, I did not see any calculations on entropy. Why? Because the researchers were not looking to calculate entropy but to observe other changes in the system. In May 1994 issue of Discover magazine, a population of RNA-cutting ribozymes became a population of DNA-cutting ribozymes. The experimenters were using Darwin's Natural Selection process! Methinks, they did NOT know how to calculate the entropy change anyway. Such calculations would require knowledge of EVERY chemical process (chemical reactions) involved. Such knowledge is lacking. This population of ribozymes is not like steam where you can look up values for entropy from a table. Therefore, they would need to know all the chemical reactions involved. If they do not know all the reactions, then they still need to know the increase in entropy due to mass flows going in and out of their population. This, too, is not known. All they know is how much in mass is going in and out. But they do not know the value of the entropy change caused by these flows. For scientists to know these values, they would need to know what we call "entropy of formation" for all those ribozymes. Which means that they would again need to know all the chemical reactions needed to form those ribozymes. This is the reason that creationists never publish their results of their experiments. This assumes, of course, that they know what the "evolution process" is and they actually tried to do an experiment. The creationist does not know every chemical reaction involved nor do they know the entropy values for the mass flows so, therefore, the creationist can not calculate the entropy change of their system (and, of course, the surroundings, too). This ignorance of what really happens does not stop them from claiming that "evolution violates the 2nd law". Since experiments that show evolution in action actually exist, then it should be obvious that evolution does not violate the 2nd law. If something can be observed, then obviously it does not violate any laws of nature. For some reason, my last statement seems to be beyond the grasp of understanding for many people. Just because you observed it to happen, it doesn't mean it can happen?! This kind of twisted logic puzzles me. From personal experience I have seen two types of responses when REAL experiments are provided to show that evolution does occur in real systems. Creationists either a) claim that the experiment does not show evolution in action or b) ignore it and talk about something else. In one of my previous discussions concerning the ribozymes experiment, one creationist claimed that the results was due mainly to manipulation of statistics while the other asked: "When and how did fish decide to walk on land?" The entropy balance equation can be found in _Chemical and engineering thermodynamics_ by Stanley I. Sandler. 7. What I Didn't Discuss When I proved to you that the creationists version of the law is wrong, I did not discuss several issues. Well, now is the time to discuss it. 1) I didn't discuss the definition of entropy! It is not needed. All you needed to know is that you can look up these values. The reason for this is that entropy is a state variable. It is unimportant to know that "entropy is a measure of disorder" which is the actual definition of entropy from statistical thermodyamics. You can NOT LOOK UP values for disorder. Moreover, you will need to define what disorder means. Most people do not bother to define it. It is assumed that disorder in thermodynamics means EXACTLY the same thing as disorder used in the general public. This is not the case. Disorder has to be defined. The reason that disorder needs to be defined is that one person's view of disorder may not be another person's view as disorder. Disorder does not mean chaotic as people assumed. A bunch of bricks randomly placed on a table might look chaotic ("disordered") to one person but it is art ("ordered") to another. Disorder in statistical thermodynamics has a specific definition in which everyone goes by. When one defines entropy as "a measure of disorder", one is simply replacing one unknown with another. To avoid this problem altogether, you will need to recognize that you do not need to know what entropy means. To calculate the change in internal energy, I did not have to know what energy means! This is the same for entropy. Sometimes, entropy is related to "complexity" or "information content". Or creationist related the 2nd law to "information content" and the like. Again, these are unimportant. You can not look up values for "information content" and the like. You can, however, look up values for entropy. In practice, people use words such as "information content", "complexity", or "disorder" to confuse the issue. Rather than argue the validity of the 2nd law, people begin arguing the validity of the "definitions" and how it is used. For instance, they might argue whether or not a system has an increase in "information content" or "complexity", etc. Since you can not calculate or look up values for "information content", one person can claim that the information content has increased while the other can say it decreased. Who do you end up believing? A SMOKESCREEN develops. You will most likely end up trying to figure out who appears to be right. Right about what? You will end up trying to figure out who really knows about the change in "information content". In other words, you are worried about the "information content" of a particular example rather than the validity of the creationist version of the 2nd law. Look up values for entropies and use the values to see if the law is correct. It is that simple. 2) I didn't discuss types of systems. One of the more common complaints of the creationist version of the 2nd law is that they apply the real 2nd law to "isolated" systems. The results they get is then applied to ALL other types of systems as well. Although this complaint is legitimate, it is unimportant. In practice, when someone begins to discuss types of system, another SMOKESCREEN develops. Participants will begin to argue the difference between open, closed and isolated systems rather than argue the validity of the creationist version of the 2nd law. In using the tables, it does not matter if the system is open, closed or isolated. You can use the values in ALL types of systems. For your convenience, I will describe the three types of systems used. Open: energy and mass flows can exist between the system and its surroundings. Close: energy flows exist. NO MASS FLOWS. Isolated: NO ENERGY FLOWS. NO MASS FLOWS. 3) I didn't discuss how the change took place. All you need is the initial and final points. Then use the tables to calculate the change in entropy. In the absence of one or both of these points, you will then need to know what is entering and leaving the system. From this, you can calculate the CHANGE in internal energy (first law of thermodynamics or the "energy balance") and the CHANGE in entropy (using an entropy balance) although you may not know the initial values for either of them. 4) I didn't discuss Gibb's free energy. Saying that there is another indicator used to determine if a process will proceed spontaneously does not "prove" creationists wrong. Or to put it more accurately, to say that there is another indicator to show that a CHANGE will occur spontaneously does not prove creationists wrong. (In discussing chemical reactions, the word "process" and "change" are used interchangeably. To be accurate it is the CHANGE that occurs spontaneously, not the process.) In practice, discussion on Gibb's free energy only confuses the issue which is the reason that creationists are not "proven" wrong. You don't "prove" anything if the reader is confused! Understanding Gibbs energy sufficiently will require knowledge in thermodynamics which MOST PEOPLE do not have. In my discussion, you will find NO "complicated" equations. In the discussion of Gibbs, an equation is usually provided as well as an introduction to enthalpy. To discuss Gibbs, you will need to talk about entropy, enthalpy, and temperature. You will also need to talk about constant pressure and constant temperature processes. The reader might as well take a course in thermodynamics then. You are trying to prove creationist wrong, not prove that there is another way of doing things! Nevertheless, I will discuss Gibbs free energy shortly. 5) I didn't discuss the relationship between probabilities and entropy. Such discussion will only make things very confusing for the reader. The best one can do is to provide simple examples. But for more complicated systems, the reader would be lost! There is a mathematical relationship that relates probabilities to entropy. The derivation of which is more complicated than the discussion of Gibb's free energy. Moreover, this discussion is not needed to prove or disprove their version of the 2nd law. Discussing something that can be confusing will only make it more difficult to show how wrong creationists are! Furthermore, disorder is actually a function of probabilities. Therefore, the limitation you have in discussing disorder is also true for probabilities. But you must be wondering how is disorder related to probabilities? To answer this question, I would have to define what is meant by disorder. To do this, I will list several requirements for the MEASURE of disorder. Disorder then is some mathematical property that follows all these requirements. a) the measure of disorder should be defined entirely in terms of the set of numbers {f } j b) if any one of the f is unity (and all the rest are zero), the j system is completely ordered. The quantitative measure of disorder should then be zero. c) the maximum disorder corresponds to each f being equal to 1/L. j d) the maximum disorder should be an increasing function of L e) The disorder should compound additively over "partial disorders". At this point, these requirements SHOULD LOOK VERY CONFUSING! Now do you see why I didn't discuss it? Moreover, it appears I did not show how disorder is related to probability. On the contrary I did. Criteria (c) above can be stated in another way. But first I have to defined what L means. Suppose you have a house. Your system is your house, then. In this house, you have a certain number of rooms. Since you are in this house, you are in one of these rooms. L, here, is the number of rooms. The probability, f, that you would be in ANY of the rooms is simply 1/L. This also means you don't have any preference to any of the rooms. Thermodynamically, then, L stands for the number of different states (or conditions) your system can be in for a GIVEN pressure, temperature, volume, mass, and so on and so forth. This number can be quite large. But the bottom line is that each state has an EQUAL PROBABILITY. If one state is more prefered or less prefered over the other states, then the system has not reached maximum disorder. This is what criteria (c) is stating. If L gets bigger, the probability for each state gets smaller. However, from criteria (d), the disorder must be larger as L gets larger. This, however, is only two of the requirements. There are others, too, that must be followed. If you wish to read more on this subject, read _Thermodynamics and an introduction to thermostatistics, 2ed_ by Herbert B. Callen. As you can easily see, discussing probabilities and disorder can be quite confusing. Why make it hard on yourself? You can not look up values for disorder nor can you look up values for probabilities. You can, however, look up values for entropy. 6) I didn't discuss "informational entropy" (sometimes called entropy of information). The entropy I have been discussing so far is the thermodynamic entropy. The units of this entropy is ENERGY divided by TEMPERATURE. Thermodynamics is the study of ENERGY or as someone puts it: the study on the organization of energy. Therefore, the 2nd law of thermodynamics applies to thermodynamic entropy. However, there is NO such "2nd law" for informational entropy. Since this entropy does not follow the 2nd law, mainly because there is no 2nd law for informational entropy, there was no need to discuss it. Moreover, discussing informational entropy can be confusing. Take the hot-water vs. cold-water example. When you cool the hot-water to make cold-water, the thermodynamic entropy of the system (ie. water) decreases. But what about the informational entropy? How does cold-water hold "less" or "more" information than hot-water? Both are water but at different temperatures! Suppose you heat the cold-water to make hot-water, you still end up with the same question. Before you even begin to answer the question, you would also need to know what is meant by "information". Before long, you will be arguing about what is meant by "information" rather than trying to figure out if their law is correct. Yes, another smokescreen is created! 8. One Direction Processes As mentioned previously, creationists claim that all REAL processes have one direction. Guess what? It is true but they are using this fact to deceive you. In going from point A to point B, you use a certain process that allows you to do so. Since all REAL processes have one direction, creationists want you to believe that you can not go from point B to point A. Remember the eggs! Their reasoning is 100% wrong. You can go from point B to point A. How? You will have to use a DIFFERENT process! In scrambling the egg, you used a certain process. To "unscramble", you will need to find ANOTHER process to get the whole egg back. You do not operate the scrambling process in reverse. If you could operate this process in reverse, then this process would have TWO directions and not just one. And it would be called a reversible process but all REAL processes in the universe is irrevesible. All REAL processes have only one direction, not two. (When I say that a reversible process has two directions, I assumed that you do realize that only one direction is in effect at one time.) You need to find a whole new process to get the whole egg back! In this process, however, the entropy increase in the surroundings has to be GREATER than the entropy decrease of the egg. Remember, the entropy of the UNIVERSE (system plus surroundings) must be greater than zero. I should point out that I am NOT saying that we, humans, do know of a process to "unscramble" an egg. The law does not claim that the process does not exist, either. It says that IF such a REAL process exist, the entropy change of the universe must be greater than zero. The result of which means that the entropy INCREASE of the SURROUNDINGS must be greater than the entropy decrease of the egg. In other words, an irreversible process means that you can NOT restore BOTH the system AND the surroundings back to its original state. It may be possible to get the egg back but you will not be able to restore the surroundings to its original condition. This is the result of using TWO different processes. One process is used to transform the whole egg into scrambled egg, the other to transform it back. If you were operating the SAME process but in reverse, then you would be able to not only restore the system to its original state but also the surroundings. These REVERSIBLE processes do not exist. All REAL processes that do occur are irreversible. To explain this again more rigorously, if a reversible process is imposed on a system, the system never leaves equilibrium. Since the system is always in equilibrium, the DIRECTION of this process can be reversed. Hence, this type of process is called reversible. However, any process acting on any system always forces that system to be in a non-equilibrium state. Thus, all real processes are irreversible. In short, the CHANGE in the SYSTEM is reversible but the processes involved may not be. If the process is also reversible, then the CHANGE in the SURROUNDINGS will also be reversible. Remember what a process is. A process is what CAUSES THE CHANGE! The change in the system is reversible for both an irreversible and reversible PROCESS. The change in the surroundings is reversible ONLY for the reversible process. Ice-water is a better example I can use. You will use heat to melt ice to form water (ie. point A to point B). However, you will use a refrigerator which REQUIRES ENERGY to freeze water to form ice (ie. point B to point A). The melting process is obviously different from the freezing process. You don't use the refrigerator to melt ice nor do you use heat to freeze water so these processes obviously proceed in one direction. For the SPECIAL CASE of an isolated system, there exists only ONE set of processes. Either you can find a process that gets you from point A to point B or you can find a process that gets you from point B to point A. This is obviously different from what I have been saying. Remember what an isolated system is. It does not interact with the surroundings at all. Therefore, the entropy change of the surroundings is ZERO! The only change in entropy is that of the system. Thus, the entropy change of the system plus the surroundings must be greater than zero. Since the entropy change of the surroundings is zero, this means that the entropy change of this ISOLATED system must be greater than zero. The entropy change for an isolated system must be greater than zero. So, if going from point A to point B increases the entropy, then going from point B to point A is not possible. Or, if going from point B to point A increases the entropy, then going from point A to point B is not possible. This restriction exist because the system is ISOLATED! As you can see, this is another source of the creationist deception. They claimed that only ONE process exist. You can not return to point A from point B or vice versa. This is ONLY true for ISOLATED systems. They simply removed the word "isolated" and applied this result to ALL types of systems. This is, of course, dishonest. To reiterate a major point: suppose you have a system initially at state A. It undergoes a process and reaches final state B. To get back to state A, we often SAY that "to get back, we just reverse the process" (or something to that effect). In reality, you do not really "reverse" the process. You use a DIFFERENT process. What you do reverse is the direction of the CHANGE in the system. The direction of the energy flows may also be reversed, too. Remember the ice-water example. The direction of the heat flow is clearly reversed. The process used in adding the heat is obviously different from the process used in removing the heat. You can unplug the refrigerator and the ice will melt. Plug it back in and the liquid will freeze to form ice. In the melting case, there was no machine needed. In the freezing case, you did use a machine. To melt the ice, you didn't run the machine backwards! Do not get confused between the DIRECTION you can go with respect to initial and final states (eg. the change), and the DIRECTION you can go with respect to the processes that connects the initial and final states. With respect to initial and final states, the direction is clearly reversible. With respect to ANY real process, the direction is not. Chemical reactions are perfect examples to help you remember this. Suppose you have the following reaction: 2H + O <-> 2H O. 2 2 2 The symbol "<->" means that the reaction is reversible. But what does "reversible" really mean in terms of chemical reactions? The symbol "<->" does NOT mean that the process is reversible, it means that the reaction is reversible. Or equivalently, the direction with respect to initial state (hydrogen and oxygen) and final state (water) is reversible. How do you get from a bunch of diatomic atoms to water? The answer is simple. Light a candle and the reaction will proceed by itself as the following: 2H + O -> 2H O. 2 2 2 In this reaction, energy will be released. The surroundings would absorb this energy as heat. We say that this reaction is exothermic since it releases heat. The candle is there to provide the initial spark since all reactions need energy to start. To reverse the reaction, do you just simply blow out the candle?! No, of course not. Keep the candle lit and all you get is hot water. You need another process. Maybe electrolysis would work. In that case the reaction will proceed as the following: 2H O - > 2H + O . 2 2 2 Heating the water (eg. keeping the candle lit) would obviously not do the job. In the "forward" direction, energy was released as heat. In the "reverse" direction, energy is required. But adding heat would not do the trick. All you get is hot water. Electrolysis is used instead. In this reaction, energy is required. The surroundings would have to provide the energy. We say that this reaction is endothermic since it requires energy. Two very different processes connect the same two states. Although I use the terms "chemical process" and "chemical reaction" interchangeably in the text, I really mean chemical reactions. The example above should help remind you that the process maybe irreversible but the CHANGE does not have to be. This example should also help you to remember that the word "reversible" in "reversible reactions" does not mean that the process that made the reaction go is reversible but the change itself is reversible. 9. Conclusion I have shown by the use of steam tables that the creationist version of the 2nd law is wrong. I have shown how creationists try to deceive others by misapplying the actual 2nd law of thermodynamics. I have shown how creationists try to deceive people by the use of smokescreens. I have shown that no matter which version of the 2nd law you use, evolution does not violate the 2nd law. I have shown that to apply the laws of thermodynamics, the system MUST be identified first. 10. Gibbs Free Energy The full equation for Gibbs free energy is as follows, dG = -SdT + VdP + v dN + v dN + v dN + v dN + .... (7) 1 1 2 2 3 3 4 4 where v's stand for the chemical potential of a particular substance dN stands for change in the number of moles of a particular substance Numbered subscript stands for substance number 1, substance number 2, etc. When you look up values for _standard molar Gibbs Free Energy_ from a table, you are looking up values for the v's. Standard molar Gibbs Free Energy is also called CHEMICAL POTENTIAL. At constant temperature (dT = 0) and pressure (dP = 0), equation (7) reduces to, dG = v dN + v dN + v dN + v dN + .... (8a) 1 1 2 2 3 3 4 4 Suppose you have the following reaction, aA + bB ---> cC + dD (8b) The chemical potential for every compound is known (ie. the v's are known). How would you calculate dG? First, you start by looking at (8b) and saying to yourself, "a moles of A and b moles of B is transformed to c moles of c and d moles of D". Thus, dN = -a, dN = -b, dN = c, dN = d (8c) 1 2 3 4 The minus sign in front of a and b comes from the fact that compounds A and B are being consumed. Now plug these values into (8a), dG = cv + dv - av - bv (8d) 3 4 1 2 This is the same as, dG = (cv + dv ) - (av + bv ) (8e) 3 4 1 2 That is, the value of dG for the reaction is simply the sum of the chemical potentials of the products minus the sum of the chemical potentials of the reactants. This value of dG has a special name and it is called Gibbs free energy of reaction. As you can see from (8c), this calculation assumes that all the reactants is consumed -- a complete reaction. The full equation of enthalpy is, dH = TdS + VdP + v dN + v dN + v dN + v dN + .... (9) 1 1 2 2 3 3 4 4 Substituting equation (9) into equation (7), you get, dG = -SdT - TdS + dH (10) At constant temperature and pressure, equation (10) reduces to, dG = dH - TdS (11) Equation (11) is the equation most people are familiar with. There are two ways in which you can calculate dG. You can use equation (8) or equation (11). If you know the entropy of reaction and the enthalpy of reaction, you can easily calculate the Gibbs free energy of reaction by using equation (11). Equation (11) can be found on page 574 in my general chemistry book (see references at beginning of text) as well as in my physical chemistry book and thermodynamics books. The "defining equation" for dS for reversible heat transfer is, dS = Q/T (12) Real changes are spontaneous changes. For any real change, dS > Q/T (13) This is the same as, dS = Q/T + S (14) gen which is simply the entropy balance without the mass terms Now from the first law, we have dU = Q - W (15a) or, Q = dU + W (15b) Rewriting (13), TdS > Q (16) Plug in (15b) into (16), we have, TdS > dU + W (17a) or, -dU - W + TdS > 0 (17b) Now, W includes all kinds of work so let us separate boundary work, W = PdV + W(others) (18) Plug in (18) into (17b), we have -dU - PdV - W(others) + TdS > 0 (19) If there is no other work being done, then (19) reduces to, -dU - PdV + TdS > 0 (20) Now d(PV) = PdV + VdP which means that the change in the product of PV is caused by the change in volume at constant P plus the change in pressure at constant V. Similarly, d(TS) = SdT + TdS. Now at constant temperature, d(TS) = TdS (21a) At constant pressure, d(PV) = PdV (21b) Substitute (21) into (20), you get, -dU - d(PV) + d(TS) > 0 (22) This can be rewritten as, -d(U + PV - TS) > 0 (23a) The relation U + PV - TS has been given a special symbol and name. It is called the Gibbs Free Energy, so (23a) becomes, -dG > 0 (23b) where G = U + PV - TS or dG < 0 (23c) Equation (23c) says for any process to proceed spontaneously (naturally), the change in Gibbs energy is negative. This is the result that both creationists and evolutionists can agree on. Now what creationists want you to believe is that if a reaction (at constant temperature and pressure) has a positive dG, then the reaction will NOT proceed naturally. For instance, aA + bB ---> cC (24) If dG for this reaction is positive, creationists claim that this reaction will NEVER occur. In fact, they claim that only the OPPOSITE reaction will actually happen (assuming you had any C compounds). So, if you put in a bunch of C compounds in a closed container, eventually you will have all A's and B's. On the other hand, if you put in a bunch of A's and B's in a closed container, you will NOT have any C's. If you put in a bunch of A's, B's, and C's in a closed container, eventually you will have no C's and end up with more A's and B's than you started out with. This is what creationists claim. Now what assumption are they using? They are assuming a COMPLETE REACTION. That is, one of the reactants in (24) is completely consumed in producing C. In my experience, NOT ONCE DID I EVER SEE a creationist make you aware that they are using an assumption. Even my chemistry book (p. 578) mentions this assumption but no creationists that I know ever makes you aware of this assumption. In other words, they leave you in the dark. This is the reason that creationists do not talk about composition. Why talk about composition if the reaction is 100% complete or 0% complete? When dG is calculated, it is calculated on the basis of a COMPLETE REACTION. I hope you can understand the significance of not telling an unsuspecting individual of this assumption. In the real world, a complete reaction does not have to occur. In a closed container in which the products and reactants mix, an equilibrium COMPOSITION would be reached. Rather than just talk about it, I will provide you with an example. In Sandler (p. 503), you have the following reaction, N O (g) <---> 2NO (g) (25) 2 4 2 The temperature of the reaction is 25 degrees C and the pressure is 1 atm. Since pressure is only at 1 atm, we assuming ideal gas. The molar Gibbs energy for N O (g) is 23.41 kcal/mol. 2 4 The molar Gibbs energy for NO (g) is 12.26 kcal/mol. 2 The Gibbs Free Energy of reaction is, dG = 2(12.26) - 1(23.41) = 1.11 kcal/mol = 4.644 kJ/mol Obviously, dG is positive. According to creationists, the reaction does not proceed to the right. It only proceeds to the left. How do we calculate the equilibrium constant? From high school chemistry, we have, 2 [NO ] 2 K = _______ (26) [N O ] 2 4 You did take high school chemistry, right? Or are you another Pat Buchanan? How is the equilibrium constant related the Gibbs energy of reaction? Pick up the chemistry book or a thermodynamics book and you will discover, ln K = -dG/RT (27a) The full equation is actually, dG = dG + RTln K (27b) T The second term (the log term) on the right-hand side of the equation takes into account that we have a MIXTURE of compounds and not pure components. As an analogy, suppose you have a room full of heterosexual males. There are 10 males in the room. Thermodynamically, we say that the composition of males in the room is 100% or 1. Thus, the second term in the equation is zero. Now suppose one of the males leave and another male takes his place who is also heterosexual. Do you think there would be some kind of reaction? Probably not. However, suppose another male leaves and is replaced with a beautiful female. Do you think there would be some kind of reaction? Yes, there would be. The second term takes into effect the interactions that different compounds ("different gender") have on each other. At equilibrium, the symbol K stands for the equilibrium constant and dG = 0. T At equilibrium, dG is zero so (27b) reduces to (27a). T Now suppose we started out with only 1 mole of N O . 2 4 Now according to creationists, we will always have this one mole. NO REACTION WILL TAKE PLACE. Guess what? They are wrong. We know the temperature, R, and dG so everything on the right-hand side of equation (27) is known. Now let x stand for the number of moles that reacted. Again, according to creationists, x must be zero -- no reaction. So at equilibrium, we would have 1 - x of reactants and 2x of products. Look at the equation (25). The two comes from the fact for every 1 mole of reactant consumed, 2 moles of product is produced. The total number of moles at equilibrium is (1 - x) + 2x = 1 + x. So the concentration of reactant is, [N O ] = (1 - x)/(1 + x) (28a) 2 4 The concentration of product is, [NO ] = 2x/(1+x) (28b) 2 Substitute (28) and all known values into (27). You will calculate x to be approximately 0.192 moles. Therefore, the final amount of reactant is 0.808 moles and final amount of product is 0.384 moles. The value of the Gibbs free energy change of reaction (the value of dG) if you have 0.808 moles of N O and 0.384 moles of NO is zero. 2 4 2 The value of dG is zero at this composition. If you have more of the reactant than 0.808 moles, the reaction will proceed to the right only. If you have less, the reaction will proceed to the left only. At this composition, both the reverse reaction and forward reaction occur at the same rate -- the composition does not change. The result is drastically different from what creationists claim. Again, according to them, we should have NO product at all. I hope you do realize that to have any products at all if you start out with NO products and ALL reactants, a reaction MUST OCCUR! Now what happens if you remove the product as soon as it is produced? Well, the system will never reach equilibrium if the product is removed. Thus, the system will continue to produce the product as it TRIES to reach equilibrium. So, it is possible to have a nearly complete reaction EVEN though dG is positive for the above complete reaction. In looking at the reaction (25) as going from left to right, we have determined that for a COMPLETE reaction, the Gibbs free energy change of reaction is positive. That is, dG > 0. However, for an INCOMPLETE reaction in which the number of moles of reactant is GREATER than the equilibrium composition for the reactant, the actual value of the Gibbs free energy change of reaction is NEGATIVE [see equation (27b)]. This is the reason that the reaction proceeds to the right even though the Gibbs free energy change of reaction for the COMPLETE reaction is positive. The closer you get to the equilibrum composition, the closer the value of dG gets to zero. If you started out with all products, the reverse reaction will occur until you reach the equilibrium composition. The real value for dG is, again, negative. The closer the reaction gets to equilibrium, the closer the value of dG gets to zero. At equilibrum, the value of dG is zero. The more common sense example that should be obvious to everyone is the evaporation of water at 25 degrees C. H O (l) ---> H O (g) (29) 2 2 I will let you do the calculations on your own but it should go without saying that the value for dG for (29) is POSITIVE. According to creationists, no liquid should evaporate. Now with my discussions with creationists, they do admit that water can evaporate even though dG is positive. Obviously, there is a contradiction here. How can you claim that a reaction with a positive dG can not happen if you can provide an example proving that it does? The answer to that is simply the l-word -- lying. Now equation (24) is a very general equation. I did not specify any compounds. However, suppose those compounds involve "life-producing" compounds. They claim that life can not be created because the dG for that reaction (whatever that is) would be positive. This is THE REASON for the lies. If a reaction can occur even if dG is positive, then logically speaking life could also be produced from these "life-producing" compounds even if these reactions have a positive dG. So these creationists proudly proclaim that these reaction can not occur if dG is positive even though they proudly proclaim that water can evaporate at 25 degrees C. An individual who claims to have the name of Joseph Kaduc in talk.origins newsgroup is a perfect example of one who tries to abuse Gibbs free energy. In his case, he uses the production of sucrose and oxygen from carbon dioxide and water as the "life-producing" compounds. Their inability to be honest when it comes to equilibrium conditions is not their only problem. For example (Castellan, p. 246), suppose you have, TiO (s) + 2Cl (g) ---> TiCl (l) + O (g) (30) 2 2 4 2 This is the reaction for producing titanium tetrachloride from the common ore TiO . Clearly, it is extremely desirable to produce the products but, 2 the Gibbs free energy of reaction is 152.3 kJ. Again, dG is positive. According to creationists, this reaction is NOT possible but I have already proved that they are wrong. We already know that some of the product will be produced. However, since dG is large in the positive direction, we won't have much of the product. Increasing the temperature will help BUT it won't help enough and it can be very costly. (It costs money to heat things!) Suppose another reaction is present such as, C (s) + O (g) ---> CO (g) (31) 2 2 The Gibbs free energy of reaction for this reaction is -394.36 kJ.. If we combined the two reactions together, we get, C (s) + TiO (s) + 2Cl (g) ---> TiCl (l) + CO (g) (32) 2 2 4 2 The Gibbs free energy of reaction for this reaction is -242.1 kJ. This is a large negative number; reaction proceeds very far to the right. The example I just gave you is an example of a COUPLED REACTION. Reaction (31) consumes one of the products of reaction (30). What happens if one of the products of reaction (30) is consumed? That is, what happens to the direction? Look at reaction (32). What do you notice? Well, I noticed that it looks like oxygen is not produced. However, we know that oxygen IS produced but it is also consumed. You wouldn't know that if you simply looked at (32). What does that tell you about how chemical reactions are written? What I just showed you is an example of a reaction that can be made to proceed spontaneously if and only if it is coupled with another reaction with a Gibbs energy of reaction that is more negative than the original reaction is positive -- overall Gibbs energy of reaction is negative. Coupled reactions are very important in biological systems. A trivial example that Castellan gives (p. 246): The lifting of a heavy barbell over your head is a nonspontaneous process that involves a positive dG. Since dG is positive, are we led to believe that no bodybuilder can lift any weight above his/her head? No, obviously this is not true. The chemical reactions involved in the movement of the muscles is coupled with the lifting of the weights. These chemical reactions have a value of dG that is more negative than the "weight-lifing dG" is positive. In some biological chemical reactions, the reactant side of the chemical reaction might have 4, 5, 6, or even 7 or more reactants. Do you really think that all 7 reactants combined to form one compound and THEN split off to form the products? Such a scene is highly unlikely. Many biological reactions are really COUPLED REACTIONS. Rather than list ALL of the reactions involved, only one overall reaction is provided. Sometimes, they only list the RAW MATERIALS as the reactants rather than list all of the reactants. An example of this is the reaction that involved photosynthesis. In my chemistry book and biology book, the following reaction is provided: 6CO + 6H O ---> C H O + 6O (33) 2 2 6 12 6 2 This is an example of a reaction in which ONLY THE RAW MATERIALS are listed. The other reactants involved is not listed. Reaction (33) looks like water reacts with carbon dioxide. Although this is possible, in a photosynthesis process this is NOT what happens. Light from the sun reacts with water in plants to produce hydrogen ions and oxygen. The oxygen then is released. The hydrogen ions then reacts with the carbon dioxide along with other materials found in plants (eg. adenosine triphosphate, etc.) to produce the products (ie. sugar) in a 12 step carbon cycle. The oxygen comes from the water, not from carbon dioxide. You can not tell that a carbon cycle (in which 12 different reactions are involved) is used or that water is broken up into hydrogen and oxygen by light simply by looking at the chemical equation. The appearance of the chemical equation, then, does not have to tell you everything. So when you look at a chemical reaction, read it like this: I have a bunch of chemicals on my left being transformed into a bunch of chemicals on my right. If you can think of a process (any process, it doesn't matter which) that can make this transformation process happen, then obviously the transformation is possible. So if I can think of a process that can make the transformation in reaction (33) possible, than that reaction can occur. It doesn't matter if you have only a 50% yield, 99% yield or 0.0000000000000000000001% yield. What is important is that the transformation (ie. the reaction) is possible. The analysis based on Gibbs free energy tells that you can have sugar but this argument is not as strong as KNOWING A PROCESS THAT CAN ACTUALLY MAKE SUGAR FROM CARBON DIOXIDE AND WATER! Now this process involves other reactants not listed but the point is that it is very possible to transform carbon dioxide and water to oxygen and sugar. That is what reaction (33) is saying. Can we transform carbon dioxide and water into a sugar and oxygen? Yes! You might find a creationist use this reaction, 12CO (g) + 11H O (g)---> C (H O) + 12O (34) 2 2 12 2 11 2 From (34), it looks like water reacts with carbon dioxide to produce the sugar. The oxygen from carbon dioxide is then released. This does not happen, however, in the biological process called photosynthesis. The appearance of the chemical equation was meant to deceive. If the person wanted us to believe that water itself reacts with carbon dioxide, then the most likely product would have been carbonic acid, H CO , not sugar. 2 3 However, since the water in the chemical equation is water vapor, the person probably was not talking about carbonic acid. Carbonic acid is formed in when small amounts of carbon dioxide is dissolved in LIQUID water. So again, I conclude that the appearance of the equation was meant to deceive. I just provided you with two different ways in which a positive dG does not mean that a chemical reaction won't occur. From my experience and from my observation of the responses (what responses?!) to Paul J. Gan's discussion on coupled reactions, creationists will ignore any comments on composition and coupled reactions. They are simply lying as they try to convince those with little background in thermodynamics or those with little patience to learn thermodynamics that they (the creationists) are right. However, the creationist stupidity does not stop here (a third way). We know that at some temperature, dG is positive. For instance, at 25 degrees C, dG is positive for the production of water vapor from liquid water. At 110 degrees C (above the boiling point of water at 1 atmosphere), do you still think that dG is positive? It is NOT. Look at equation (11), for instance. Temperature is part of the equation. This means that the value of dG is also a function of temperature. What does this all mean then? It means that dG can be NEGATIVE at some other temperature. In other words, dG for the production of water vapor at 110 degrees C is negative. Just because some liar wants you to believe that a reaction won't occur at 25 degrees C, it does NOT mean this same reaction won't occur at some other temperature. To be more accurate, just because some liar wants you to believe that the Gibbs energy change of reaction is positive at 25 degrees C, it does NOT mean that the Gibbs energy change of reaction is positive at every other temperature. Now in the examples I gave above, I could easily have created my own problems -- anyone can do it. The reasons that I didn't are: a) problems are already worked out b) if I created my own, the creationists will claim that the results were bias. 11. About the Author My background is not in evolutionary biology but in chemical engineering. I received my BS degree in May of 1993 from the University of Maryland at College Park. As an engineering major, we were required to take courses in thermodynamics. Besides chemical process thermodynamics, we were also required to take Physical Chemistry I which is virtually a course in thermodynamics for chemistry majors. We were also required to take engineering physics which, of course, covered thermodynamics as well. I have also taken a graduate level course in Advanced Classical Thermodynamics from the mechanical engineering department, a graduate level course in chemical thermodynamics from the chemistry department as well as the graduate level chemical engineering thermodynamics from the chemical engineering department. I like to believe that I am no longer a "novice" when it comes to discussing some of the basic concepts of thermodynamics. I hope nobody would accuse me of discussing thermodynamics without taking a course in it first which is a common accusation against creationists. But like everyone else, I am still learning the subject. So I do not pretend to be an expert. I am not an expert. I do, however, know the subject well enough to explain the basics. Hopefully, I did not make any mistakes in this text or that I explained it properly to you. Everything (except for the portions discussing natural selection, most of the discussion on Gibbs free energy, values used for calculations and direct quotes) were recalled from memory. My rule of thumb is: If I can remember it, then it must be basic. Hopefully, this text was easy enough for you to understand. The purpose of this text is obvious; to prove that the creationist argument against evolution using thermodynamics is completely wrong. The claim that evolution violates the 2nd law of thermodynamics is one of the top three common lies that creationists make. Some would argue it is the number one lie. One of the other top lies I already addressed in the text -- the theory of evolution is taught as a fact or religion. The other lie I did not discuss is that the theory requires a continuous number of transitional fossils (if the gullible person realizes that transitional fossils exists) or the claim that there are no transitional fossils (if the gullible person does not know what transitional fossils are). FAQs on this topic alone already exists. It is hoped that this text combined with a good text on thermodynamics will give you all the ammunition you need to PROVE (not simply argue that) the creationist argument is wrong. You, the reader, may be able to contact the author at the following sites: a) legion@eng.umd.edu b) Tsunami's Wave BBS (410)551-1374, 30-min per day full-access FREE account. Additional time can be added with donations. My user account is legion of doom. Address all questions, corrections or comments to the above sites. APPENDIX A. Basic Concepts The following discussion was lifted from previous versions of this text. I made some modifications on the discussion on equilibrium. Unlike the main body, I rushed through this portion. a) What is energy? I mentioned that thermodyamics is the study of ENERGY. But what is energy? If you do not know what energy is, then how can you understand what thermodynamics is? Here, we have a problem. Energy is what some people call a "primitive" concept. It has NO PRECISE definition and no synonyms. Energy is a mathematical abstraction that has no real existence EXCEPT for its relationship to variables that DO have a physical interpretation and can be measured (Abbott and Van Ness, p. 1). For instance, kinetic energy of a substance is a function of its mass and its velocity. Mass can be measured as well as velocity. From these two variables that have "physical interpretation and can be measured", the kinetic energy can be calculated. We can feel the effects of energy (eg. increase in temperature which is also a property that can be measured) but energy, itself, can not be directly observed. This is very similiar to gravity. Nobody can directly observe gravity. But the EFFECTS of gravity can be measured and analyzed. These effects have been analyzed so often and the effects are so predictable that it is considered a scientific fact that gravity exists. This is also true for energy as well as another mathematical abstraction called _entropy_ discussed later. _Internal energy_ of a substance mentioned previously is the energy associated with the motions of the molecules, interactions among the molecules, and the chemical bonding of the molecules. This energy is inside the substance and thus, it is given the name _internal energy_. Other types of energy such as potential and kinetic energy act on the ENTIRE substance as a whole. It is not inside the system. These types of energy is what some would call _external energy_. The total energy of a substance, then, is the sum of the internal energy, kinetic energy, and potential energy of the system. However, there are other types of energy as well. When you touch a hot cup of coffee, you hand gets very warm. Why? This is because you are absorbing energy from the cup. This type of energy ONLY EXISTS when energy is being transmitted. There are two types of "energy in transit". The first type (Sandler, pp. 13-14) is the transfer of energy as a result in a temperature difference (such as touching a hot cup of coffee). All other types of energy transfer is collectively called work. Once heat and work is transfered, it becomes part of the system (or the surroundings). In the case of the hot coffee, the energy is transfered to your hand in the form of heat. This energy, then, becomes part of your hand. The internal energy of your hand increases. At this point, there is no more heat. It is now converted totally into internal energy. This increase in internal energy of your hand is related to the temperature increase of your hand. That is, your hand gets hotter. From middle-school science classes (or Junior High for some of the older crowd), you should remember that ENERGY IS CONSERVED. This means that for energy to be conserved, it has to be converted from one form to another. In the hot coffee cup discussed above, all the heat is converted to internal energy. The law of conservation of energy, therefore, dictates that energy can never be created nor destroyed. From this law, the first law of thermodynamics is born. You might have seen the following before: dU = Q - W (1) where Q stands for heat and W for work, dU stands for change in internal energy and U stands for internal energy. The equation above is called the first law of thermodynamics. It is NOT the complete form since it does not include changes in EXTERNAL energy, for instance. Some call this 1st law, the law of conservation of energy. It says that the change in the internal energy of the system is caused by the addition and/or removal of energy in the form of heat and/or work. Or equivalently, heat and work is converted into internal energy or internal energy is converted into heat and work. I should note that U, internal energy, is a property OF THE SYSTEM. Q, heat, and W, work, are not properties of the system. These type of energies only exist if energy is being transferred. Once the energy is finished being transferred, the energy becomes part of the system (or surroundings if the energy is being removed) and we call this energy _internal energy_. So when I use the word CHANGE (and I used it many times throughout the text), the change refers to the change in a PROPERTY OF THE SYSTEM. The first example of this is the CHANGE in internal energy. Obviously, when a property of the system changes, the system is different. That is, the system changes too. In some thermodynamics text, they use the word "evolve" rather than "change". So in these texts, you will see the words "evolution of the system". To evolve, as used here, means "to change" and evolution means "a change" or "the change". b) What is a system? A few times I used the word "system" rather than "substance" in the previous sections. This question should come up: "What is a system?" A system is a region of space that is being studied. It can be a specified volume of space or a quantity of matter. EVERYTHING OUTSIDE the boundaries of a system (except for the universe) is the surroundings (environment). There are, however, three types of systems. An open system is a system that allows material (eg. mass) and energy to cross the system boundaries. Mass and energy can flow into the system and out of the system. If mass and energy is flowing, where is it going? The exact location is not important. What is important is that it is crossing the boundaries. Mass and energy passes between the system and the surroundings. Thus, we often say that open systems INTERACT with its surroundings. A closed system is a system that ONLY allows energy to cross the boundaries. No mass flows are present in a closed system. An isolated system is a system that does NOT allow any energy or mass to cross the boundaries. Such a system does NOT interact with the surroundings at all. This should go without saying but I will say it anyway. The system PLUS its surroundings make up the universe. The only exception is the universe itself. It is assumed that the universe has no surroundings. Nothing goes in or out of the universe. Thus, the universe is an isolated system with no surroundings to interact with. c) What is an equilibrium state? An equilibrium state is the condition of the system which has the following properties (Sandler, p. 5): 1) the condition of the system does not vary with time, 2) the system has uniform properties throughout, or if it is composed of several smaller subsystems each of which is uniform, 3) all flows (mass, heat, or work) both within the system and the system and surroundings are zero, 4) the net rate of all chemical reactions are zero. In addition, these equilibrium states do not in anyway depend on HOW it got there in the first place. For instance, suppose you have a system with a certain pressure, temperature, mass, volume, heat capacity, index of refraction, composition, etc. It does not matter if you heated the system or if you beat the system with a hammer to have that pressure, to have that temperature, etc. Another way of saying this is that the PROCESS does not matter. Others would say that the path does not matter. Moreover, each equilibrium state for a system has a particular volume, particular composition, particular mass, particular pressure, particular temperature and so on and so forth. Each and every equilibrium state for that system, then, is unique. Criteria 4 does not mean that there are no chemical reactions. It simply means that if there are any reactions taking place, the composition of the system does not change. That would mean that the reactions are reversible. If A is becoming B in one part of the system due to some reaction, then in some other part of the system, B is becoming A at the same time. The net result is that the composition of the entire system does not change. Criteria 2 simply means that every part of the system (or every part of the subystem) has the same temperature, pressure, composition, etc. Criteria 3, if you look very closely, appears to say that thermodynamics can only be applied to systems that are isolated. In other words, for a system to be in equilibrium it has to be isolated. No REAL system that we humans currently deal with is actually isolated. However, some systems can be easily approximated to be isolated (eg. thermos bottles, space suits) but other systems can be "redrawn" so it is isolated. For a system to go from one isolated system and become another isolated system (ie. going from state A to state B), at least two of the properties of the two isolated systems will be different. This difference between one isolated system and another isolated system, therefore, requires that the properties of both these systems be known. If you take a look at the criterias, it seems that equilibrium states would rarely occur. In reality, it happens quite often. If you place a can of coke in the refrigerator, eventually the can will have the same temperature as everything else inside the refrigerator. Some systems have what we call steady flow and steady state properties. That is, you have an equal amount of mass entering the system and an equal amount leaving. Such (steady flow) systems can also be treated as systems in equilibrium even though these systems APPEAR not to satisfy critera 3. For instance, suppose you have the following: ---------------------------- ! ! in ------> ! ! -------> out mass ! ! mass T1, P1 ---------------------------- T2, P2 | | ---> unknown energy out The figure above states a few things: There are two mass flows and one energy flow. The energy flow is unknown and you wish to calculate the amount. This energy flow represents the TOTAL amount of work that exits the system. Rather than drawing a bunch of lines, I drew only one line to make the figure easy to read. (When I say MASS FLOWS, I mean the amount of MASS flowing into or out of the system. This means that the units I am use is mass per time such as kg per second. I am not talking about meters per second or feet cubed per hour. I am talking MASS.) This OPEN system is in steady FLOW so we know that the rates in which the mass is entering the system and leaving the system are equal. The temperatures and pressures (eg. the T's and P's) are different for the two flows. This difference allows energy to be removed by some unidentified process. The system is in steady state so no properties of the system changes with time. There are mass flows (as well as energy flow coming out) so it definately does not follow the criterias for a system in equilibrium. How do you go around this problem? First, identify what you have. You have a machine which has mass going in, mass going out, and energy going out. Thus, your system is this machine. Obviously, this system does not satisfy the conditions for equilibrium. So, change the system. To help you understand, I will draw another figure. ---------- ---------- ! ! changing ! ! ! T1, P1 ! ---------> ! T2, P2 ! ! mass ! to ! mass ! ---------- ---------- In this figure, I am NOT saying that there is a flow from "box 1" to "box 2". I am saying that a box with a certain mass at a certain initial pressure and initial temperature changes to a condition in which it has the same mass but at a different pressure and temperature. The box on the left represents what is going into the original system (first figure). The box on the right represents what is going out of the original system. Both of the systems in the "boxes" are in equilibrium. Remember, I changed the system. The system is no longer "the machine", it is the material itself. In engineering, we usually say the "working fluid" is the system. So we have one system that was in equilibrium being forced to change by some unknown process. In the end, the system ceases to change and it reaches another state of equilibrium. The difference in the properties of these two equilibrium states (eg. difference in temperature, pressure, internal energy, etc.) will allow you to calculate the amount of energy that is leaving the original system. In between the initial and final state of the system, the system itself is NOT in equilibrium. In thermodynamics, we usually say that the system goes from state A (left box) to state B (right box). Others might simply say that the system undergoes a CHANGE from equilibrium state A to equilibrium state B. Or they might shorten it to just "a system undergoes a change". Thus, the word "box" represents the STATE or the CONDITION of the material. Both boxes have ZERO flows (mass and energy) going in or out. So when you "redraw" the problem in this manner, the problem now satisfies criteria 3. That is, the problem now has two isolated systems. The properties of both of these systems are assumed to be known. The difference in the properties of the two systems will allow you to determine a few things about the process that caused the change. You will not be able to determine the details of the process itself but you will be able to determine what was going in and out of the system to get from state A to state B. That is, you will be able to determine the changes caused by the process. Sometimes you do not know enough of the properties of the system in state A or state B, but you know what was going in and out. Thus, hopefully, you may be able to determine the DIFFERENCES (eg. changes) in the system by analyzing what is going in and out of the system. But without any points of references, you would not know the exact values for the properties. For instance, from the 1st law you can determine the changes in internal energy by noting how much heat or work was added or subtracted from the system. But you will not know the value of internal energy at its final state or the value of internal energy at its initial state (unless, of course, one of these values were provided.) Now if I sound like I am repeating myself, it is because I am. I am simply reinforcing ideas into your head. The material I am going over now and the rest of the material in this section happens to be material that seem to be easy to understand but when it comes to applying it, many people end up having problems. And it is also happens to be material that is hardest to explain. And one thing you should always remember when you use the method just described in the above paragraph: the initial state and final state are EQUILIBRIUM states. Although you use the 1st law to determine the changes in internal energy, it is always assumed that this change is between two equilibrium states -- the boxes are in equilibrium. When you redraw the problem in this matter, you have to notice one important thing. When you push something into a container, do you not use energy? Yes, you do. In the first figure, the material (whatever it is) is flowing into the system. It takes energy to push that material in. Once the material is inside the system, this energy becomes part of the system. When material leaves the system from some other point, it also takes energy to push that material out. This energy is called flow work (or boundary work). So when you convert the "open-flow" problem into a "no-flow, isolated" problem, the properties inside BOTH boxes in this example MUST take this flow work into account. There are examples, of course, in which only one of the boxes includes flow work. For instance, you have material going in but NO material coming out. In the first box, you have to consider flow work. In the second box, there is no flow work. To help you understand, I will try to express what I just described above in the previous paragraphs mathematically. Let us first analyze the box on the left of the second figure. The things you will learn in this "two box" example will be applied later to the original problem. Let U equal the internal energy of the MASS in the box. B1 This mass in the box REPRESENTS the mass flowing INTO the machine. Let the product PV equal the amount of energy needed to push this MASS in the large box in the first figure ("the machine"). Remember what the left box is supposed to represent. This REPRESENTS the mass at state 1 which is being pushed into "the machine". That is, this box includes the internal energy of the mass AND the flow work. Moreover, this box is in equilibrium; there is no flows in or out of the box. Thus, the total energy of the 1st box itself with the flow work is, U + (PV) = H (2) B1 1 1 where the subscript 1 stands for state 1 which is represented by the left box. H is the symbol used to represent this sum. We can do the same analysis for the box on the right and arrive to the following equation. U + (PV) = H (3) B2 2 2 Remember, the mass in the right box represents the mass FLOWING out of the machine. Now for the sake of argument, let us pretend FOR NOW that in the first figure, the mass flows into "the machine" but NO MASS FLOWS OUT. Now what changes do you need to make? Hint: Look at the right box. Since there is NO FLOW going out, the box on the right will have NO FLOW WORK. Remember what the boxes is supposed to represent. The right box represents the state of the material in state 2. In state 2, there is NO FLOW, therefore, the flow work term is zero. This means that equation (3) reduces to, U = H (4) B2 2 Now from the law of conservation of energy that we all learned in middle school, the energy of the first box has to equal the energy of the second box, right? So, let us set them equal to each other. U + (PV) = U + (PV) (5) B1 1 B2 2 This equation reduces to, U + (PV) = U (6) B1 1 B2 which is the same as, (PV) = U - U = dU (7a) 1 B2 B1 Equivalently, H = U (7b) 1 B2 Equation (7) says that the flow work in state 1 (left box) becomes part of the system as internal energy in state 2 (right box). The "working fluid" absorbed the flow work. Now if you do an experiment or analyze a real existing system and noticed that the equation is NOT equal, this means that energy was either added or subtracted in the form of heat and/or work. Mathematically, we express this as, U - H = Q - W (8) B2 1 Remember the law of conservation of energy. Equation (8) is simply an application of that law. To remind you AGAIN, the boxes are in equilibrium and you know the properties of the system. If you do not know the properties, then you can determine the change ("the differences") in energy if and only if you know the energies going in and out of the system. That is, you either know the properties or you know what is going in and out. Now if there was NO FLOW work in either boxes, equation (5) reduces to, U = U (9) B1 B2 That is, the energy in box 1 is the same in box 2 as it should be if it is the same material at the same temperature and pressure. Equivalently, the energy in state 1 is the same as state 2. If there is a difference, simply apply the law of conservation of energy again like I did above. U - U = Q - W (10) B2 B1 You often see this equation as, dU = Q - W (11) Equation (11), if you recall, is the first law of thermodynamics. This equation (11) says that the change in internal energy of the MASS is caused by the flow of heat and/or work. Now if BOTH boxes have flow work, then equation (5) becomes, H = H (12) 1 2 This equation (12) says that the sum of the energies (which is given the symbol H) has to be equal for both boxes. As before, if there is a difference, then apply the law of conservation of energy. The equation has to be equal, therefore, the difference had to be caused by addition or removal of energy in the form of work or heat. So, equation (12) becomes, H - H = Q - W (13) 2 1 This equation is usually expressed as, dH = Q - W (14) Equations (8), (11), and (14) are all different forms of the 1st law of thermodynamics. Now what if I try to combine the concepts you had just learned mathematically with equations (2) - (14) and apply it to "the machine" of the first figure. Is it possible? Yes, it is and you will see why I was able to convert the open flow problem into a "two box" problem. Let U be the state 1 of the machine. Let U be state 2, the final state. 1 2 We don't care how long it takes for the machine to get from state 1 to state 2. And we do not even know if either of these states are true equilibrium states. Now look again at the first figure. Let me remind you that there is a mass flowing in and a mass flowing out. There is also an energy flow. Thus, the system is not in equilibrium as shown in the figure. Thus, we can't even imagine a "state 1" or a "state 2" for this machine. There is always something going in and going out of the system. Now let us analyze the inlet flow first. The mass entering the system adds energy to the system due to the fact that the mass itself has internal energy. This flow ALSO adds energy to the system due to flow work. Now let us analyze the outlet flow next. The mass leaving the systems removes energy because the mass itself has internal energy too that is subtracted from the system. Moreover, it takes energy to push this mass out. This energy is called flow work. Now what else do we know? We also know that there is energy in the form of work leaving the system. And we know the law of the conservation of energy. Now apply the law of conservation of energy to the first figure. What does the law say? It says that the energy in the first state (whatever that is) is equal to the energy of the second state (whatever that is): U = U . 1 2 Now, if it is NOT equal, what does that mean? Well, it means that energy was added to the system and/or removed from the system. We just analyzed this energy differences so let us put all we know into an equation. The difference in energy is equal to work done by the system plus energy added to the system by mass flowing into the system plus energy removed from the system by mass flowing out of the system. This difference, in turn, equals to the change in energy of the final state and initial state. U - U = -W + U + (PV) - (U + (PV) ) (15) 2 1 B1 1 B2 2 This equation is sometimes called the energy balance equation. Now this equation (15) can be rewritten as, U - U = -W + H - H (16) 2 1 1 2 Now let me make the problem a little more complicated by ADDING heat to the system, too. So equation (16) becomes, U - U = Q - W + H - H (17) 2 1 1 2 This equation (17) can be rewritten as, dU = Q - W - dH (18) Remember how we got dH. The dH refers to the MASS, not the machine. Moreover, the boxes (the left box and right box), as you recall, are in equilibrium. Can we say the same thing for the machine? No. But if we know dH, Q, and W we can determine the change in energy of this machine anyway. We do not know the initial amount of internal energy nor do we know the final amount. But we can calculate the CHANGE. However, we have a problem. We have too many unknowns. We either know Q and W but not dH or we know dH but not Q and W. And we do not know what dU is, either. So what do you do then? Assume steady flow (equal flow rates for the inlet and outlet flows) and steady state (properties of the system at any point in the system does not change). If the flow rates are equal, this means that NO mass is accumulating in the machine. If the properties of the system (ie. the machine) does not change, this means that dU is zero -- it does not change. So equation (18) reduces to, dH = Q - W (19) Does this equation (19) look familiar? It should. We just derived equation (14) again. Assuming steady flow and steady state allowed us to easily convert this open system problem into an isolated system problem of the two boxes. FOR THIS PROBLEM, these assumptions were made but take a look at equation (18). The only assumption you really need is to assume that dU is zero or in the real world, the value of dU is very small when compared to the sum of the terms in the right-hand side of the equation so dU can be ignored (ie. set dU to equal zero). However, if the problem is not steady flow (eg. mass can accumulate in the system) then there is a strong possibility that dU is not zero or small. What happens? Well for simplicity, let us pretend for now that there is no heat or work entering the system and that no mass is flowing out of the machine. So equation (18) becomes, dU = -dH (20a) This is the same as, U - U = -(H - H ) (20b) 2 1 2 1 This equation (20) says that the energy loss of the mass is equal to the energy gain for the machine. Now what is dH? dH = H - H = U + (PV) - (U + (PV) ) (21) 2 1 B2 2 B1 1 Since there is no mass flowing out of the system, what changes do we need to make? No mass is flowing out, so therefore, the mass stays in the machine. This also means there is no flow work. If NO MASS is flowing out of the machine and NO FLOW WORK is involved, what does that mean about H ? 2 Remember equation (7). In that case, we were looking at the working fluid itself or "the boxes". In this case, we are looking at the machine. But the ideas are similiar. NO mass is flowing and no flow work, this means that H is zero. 2 Do you remember what U stands for? B2 That variable stands for mass flowing out of the system. Since there is no mass flow, the value is zero. The mass is not flowing out of the machine so, therefore, it becomes part of it. That is, its internal energy becomes part of the machine. You can no longer separate the internal energy as separate entities. That is, you can't say that this internal energy is from the machine and this internal energy is from the mass. This means that U is B2 absorbed into U . 2 No flow work means the flow work term is zero. Thus, equation (21) becomes, dH = - (U + (PV) ) = -H (22) B1 1 1 Equation (20) becomes, dU = H (23a) 1 Now remember equation (7b). Equation (23a) becomes, dU = U (23b) B2 This means that the change in energy of the machine is equal to the amount of energy it received from the flow of mass entering the machine. This is very similiar to equation (7) where it says that the working fluid absorbed the flow work energy. Equation (23b) says the absorbed flow work energy and the internal energy of the mass becomes part of the machine. Now if in a real system, equation (23) is not equal, what do you do next? Apply the law of conservation of energy again. Equation (23) becomes, dU - H = Q - W (24) 1 This is, yet, another form of the 1st law of thermodynamics. Now what does this mean? Well, it means that if there is no steady flow then there is a strong change that dU is not zero [see equation (23)]. Thus, you can not just assume steady state without assuming steady flow too. If heat (Q) and work (W) are involved and are unknown, then you will have too many unknowns. Todd and Ellis have two specific example problems on pages 90-93 involving open systems. Although not mentioned in the text, the solutions were based on the concept just discussed. That is, the system is NOT the machine but the mass (the "working fluid") that is undergoing the change itself. The figures in the book, however, have the machine as the system. The calculations have the mass itself as the system. If you read the problem statement (and don't look at the figures) you will see that they indeed used the mass (ie. superheated steam and gas) as the system and not the machine. You may have heard the term _ENTHALPY_ before. In open flow systems (including systems with chemical reactions), enthalpy is used. The examples in Todd and Ellis uses enthalpy. Enthalpy is simply defined as the internal energy of the material added or subtracted from the system PLUS the flow-work required to do this addition or subtraction. Thus, the symbol H used earlier stands for enthalpy and the flow work term is simply the product of the pressure and volume. Remember, when you add mass into a system, that mass has its own internal energy which adds to the system. Moreover, it takes energy to push that mass in. The sum of this internal energy and the flow work is called enthalpy. Once the material is inside, the flow work and the interal energy of the material becomes part of the system. That is, the flow work is converted into internal energy and internal energy from the material is added. When material leaves, flow work is needed. Thus, some of the internal energy is converted into flow work which is used to push the material out. The word "flow" in "flow work" refers to the flow of the material, not to the flow of energy in the form of heat or work. Remember, this energy refers to the energy used to push the material. If there is no movement of material, then there is no flow work. In these cases, the enthalpy and internal energy are numerically equal (ie. H = U ). 2 B2 There are tables that contain values for both enthalpy and internal energy of a substance at a specified temperature and pressure. Enthalpy is used for open systems that involves the movement of material (eg. mass flows). Thus, the value of enthalpy ASSUMES that the material is moving. To be more precise, the enthalpy value in the tables already includes the energy needed to push the material into or out of a system. Remember, the flow work is depended on the pressure and volume of the material and NOT the process itself. If there is no mass flow, then, obviously you use internal energy. The change in internal energy can, of course, be caused by chemical reactions, work added into or subtracted from the system, etc. The change in enthalpy can be caused by a change in internal energy, a change in flow work (ie. flow work needed to push the material out is different from the flow work needed to push the material in), or a combination of both. To help you remember this concept of flow work (and, of course enthalpy) I offer an analogy. Suppose there is a cart full of people. There are 10 people in this cart. There is a house that has people in it. In the beginning, there were 35 people in the house. Now you wish to push the cart into the house. It takes 4 people to push this cart. So 4 people are pushing a cart containing 10 people into the house. How many people are in the house now? There are 4 + 10 + 35 = 49 people in the house. The pushers ("flow work") become part of the household. Memorize the "two-box" figure. It is the basis on how I will teach you thermodynamics from now on. Everytime I say that something changes or that state A goes to state B, remember that figure. I will refer to that figure as the "two-box method" later on. Unfortunately, you will not be always successful in making a system that appears to be not in equilibrium to look like it is in equilibrium like I did above. In fact, this should be case majority of the time. What do you do then? In such a system, you assumed that all "fast" processes have occured and all "slow" processes can be ignored. This means that system changes from state A to state B due to the "fast" processes. Since state B is not truely in equilibrium, it is changing due to the "slow" processes. We ignore the "slow" processes because it may take "cosmic times" for it to complete. In such systems, we assume a _metastable equilibrium_. In these systems, apply thermodynamics as if it was in true equilibrium (Callen, p. 15). That is, pretend that the system is in equilibrium. If you apply the laws of thermodynamics and arrive to a conclusion that is DIFFERENT from observations, it means that the assumption of _metastable equilibrium_ was not valid for your system. It does not mean that the laws of thermodynamics were wrong or that the change is impossible. If you observed the change, then OBVIOUSLY it is not impossible. The error comes from the assumption of equilibrium. When an individual claims that the laws of thermodynamics only apply to a closed system (they really mean isolated systems), they are actually referring to one-half of critera 3 of the conditions for equilibrium. The individual is simply trying to be clever. Obviously, if thermodynamics only apply to systems that are ALWAYS isolated, then the laws of thermodynamics are useless. The tables for enthalpy and internal energy are useless. No REAL system is truly isolated. You can't even determine the amount of energy your automobile uses since the laws of thermodynamics for these clever people only apply to isolated systems. Since when can you approximate an automobile to be isolated? Are these clever people trying to say that your car does not give off any pollutants or any heat to the environment? If you put in 20 pounds worth of gas, by the law of conservation of mass, the car will give off 20 pounds worth of pollutants as well UNLESS you want to believe that everytime you fill the gas tank, your car is getting heavier and heavier. I also invite them to touch the engine while the car has been running for 10 minutes. If the car is isolated, then their hand should not burn. People don't die from carbon monoxide poisoning. It is all a scam. Clever people are just too clever. d) What does reversible mean? In thermodynamics, one reads about "reversible" and "irreversible" a lot. I even used it once briefly when I discussed chemical reactions earlier. However, what does it mean? The classic definition of reversibility (Todd and Ellis, p. 111) is "When a fluid undergoes a reversible process, both the fluid and its surroundings can always be restored to their ORIGINAL state." A system that undergoes a thermodynamic reversible process goes through a continuous line of equilibrium states starting from the initial equilibrium state to a final equilibrium state. In other words, the system is ALWAYS in equilibrium. No real process is truly reversible. Thus, all REAL processes are irreversible. Some real processes are close to reversible processes so they are often analyzed as reversal processes. But the important thing to remember is that all real processes are irreversible. I discussed this in more detail later in chapter 8. e) What is an intensive and extensive property? An extensive property is a property that depends on the SIZE of the system. For instance, suppose you have a system that is composed of two parts. Let us call one part, subsystem A and the other subsystem B. The volume of subsystem A is 10 cubic feet. The volume of subsystem B is 20 cubic feet. What is the volume of the system? The answer is 30 cubic feet -- the sum of the two volumes of the subsystems. The volume of the system depends on the size of the system. Thus, volume is an example of an extensive property. An intensive property is a property that is size independent. If system A has a temperature of 30 degrees F and system B has a temperature of 30 degrees F, what is the temperature of the system? The answer is 30 degrees F. You don't add the temperatures together like you would with volume. Thus, temperature is an example of an intensive property. If the system is in equilibrium, it will have the SAME temperature throughout the system. This is what it means when we say that temperature is an intensive property. It does not depend on the size of the system, therefore, the value of this property must be the same everywhere in the system. Another example of an intensive property is pressure. Extensive properties CAN BE made to be LIKE intensive properties. Examples of this is density. Suppose you have a block of an unknown metal that weighs 10 pounds. It occupies a volume of 10 cubic feet. If you divide the mass by its volume, you will get 1 pound per cubic feet which is its density. This density is the same throughout the block. Thus, it behaves like an intensive property. Although these are not TRUE intensive properties, in this text extensive properties of this type are considered intensive properties. Of all the semi-intensive properties (eg. extensive properties made to behave like intensive properties), only one is truly an intensive property. Specific Gibbs free-energy is this one and only property. I will not discuss Gibbs free-energy but I just thought I should mentioned it. If for some reason you are debating evolutionists, you can impress them with your knowledge by telling them this little fact. B. Additional Sample Problems for 2nd Law Analysis I have already proven to you that the creationist version of the 2nd law is wrong using steam tables. Now, I know many of you are still not convinced -- thinking that these steam tables (whatever these are) are examples of some type of an evolutionist conspiracy. So, I will give you additional problems that does not require the use of steam tables. In fact, I will give you problems that came directly from my chemistry book. Many years ago, people discovered that a certain gas is the lightest element on Earth. Not only is it the lightest but this gas can be used to lift objects into the sky. Do you know what that gas is? This gas is called hydrogen. They used hydrogen gas in blimps many years ago. However, people soon discovered that hydrogen can burn very easily in the presence of another gas like oxygen which is found in the atmosphere. Therefore, they have discovered that hydrogen is a very dangerous gas to use in blimps. They have switched to helium. The reaction that takes place that made hydrogen use dangerous is as follows: 2H (g) + O (g) ---> 2H O (l) (1) 2 2 2 Suppose this reaction takes place at 25 degrees C. That is, the temperature of the atmosphere was initially at 25 degrees C. From (1), I hope you can see that this is a combustion reaction -- hydrogen is burned. In my chemistry book (see references), the following data is provided. compound entropy (J/mol K) enthalpy (kJ/mol) H 130.57 0 2 O 205.03 0 2 H O 69.91 -285.83 2 This problem is worked out on page 571 of my chemistry book. Let us calculate the change in entropy of this reaction (1). dS = 2(S ) - 2(S ) - 1(S ) (2a) H O H O 2 2 2 Plug in the values for (2a), dS = 2(69.91) - 2(130.57) - 1(205.03) (2b) = -326.25 J/K According to creationists, the entropy change must always be positive. From (2b), we can see that the entropy change for reaction (1) is negative. Thus, according to creationist we are led to believe that hydrogen does not burn in the presence of oxygen. We know this is not true. Therefore, their law is wrong but does it violate the real law? To evaluate the TOTAL ENTROPY CHANGE, we must also calculate the entropy change of the surroundings, too. How do you calculate total entropy change? The total entropy change is simply the entropy change of the system plus the entropy change of the surroundings. So, this means we have to know what the entropy change of the surroundings is in order to calculate the total entropy change. The entropy change of the surroundings is due to any thermal energy that the surroundings absorbs or releases. This means we have to calculate the change in energy caused by the reaction (1). To calculate the "heat of reaction", we simply do this, dH = 2(H ) - 2(H ) - 1(H ) (3a) H O H O 2 2 2 Plug in the values, dH = -571.66 kJ (3b) Equation (3b) says that the reaction (1) releases 571.66 kJ of energy to the surroundings. This means that the surroundings absorbs 571.66 kJ of energy. Mathematically, we write the change of entropy of the surroundings as, dS = -dH/T (4a) Why? Because we know that, dH = TdS + VdP (4b) And we also know that there are no chemical reactions in the SURROUNDINGS, only in the system. At constant temperature and pressure, (4b) reduces to, dH = TdS (4c) This is the same as, dH = Q (4d) Plug in (4d) into (4a), we have dS = -Q/T (4e) This is the "defining equation" for entropy. This is the entropy change for the SURROUNDINGS, however and NOT the system. That is why we have a minus sign in front of the heat term. As you can see, (4e) is simply the entropy balance equation for the SURROUNDINGS without the mass terms and irreversibility term. And Q stands for the heat absorbed by the system. Since the system is giving off heat, Q is negative which we have already determined in equation (3b). The minus sign in equation (4e) negatives this sign and makes the entire term positive -- the entropy change of the surroundings is positive. The temperature, T, as you should remember is 25 degrees C or 298.15K. Thus, dS = 1917 J/K (5) This POSITIVE result is what we expect. The TOTAL ENTROPY CHANGE is then, dS = -326.35 + 1917.35 = 1591 J/K (6) From equation (6), we conclude that the total entropy change is positive. That is, if this reaction was placed in an isolated system like the universe, the entropy change of the universe is positive. This agrees with the REAL 2nd law of thermodynamics. So we conclude that reaction (1) CAN happen in the real world contrary to what the creationist version of the law claims. If you calculate the Gibbs Free Energy of reaction for (1), you will discover that dG is negative; the reaction does proceed to the right. This does NOT mean, however, that the reaction does not proceed to the left at all. The large negative value means that the equilibrium condition is very far to the right. Thus, you will have very, very, very little amount of reactants left. I will give you one more example. The pollutant sulfur trioxide is produced from the burning of high-sulfur coal. The production of this pollutant is obviously not desirable. The production of any pollutant is not desirable. So is there a way to get rid of this pollutant? Yes, there is by using the following reaction. CaO (s) + SO (g) ---> CaSO (s) (7) 3 4 The temperature is 25 degrees C. This problem is worked out on page 573 to 574 of my chemistry book. We will use the following data which came from my chemistry book. compound entropy (J/mol K) enthalpy (kJ/mol) CaSO 107 -1432.7 4 CaO 40 -635.5 SO 256.6 -395.7 3 Following the SAME APPROACH as the previous example, dS = -189.6 J/K (8) Again, according to the creationist version of the 2nd law, this reaction will not occur. dH = -401.5 kJ (9) This reaction is highly exothermic just like the previous example. Now, the entropy change of the surroundings is simply, dS = 401.5kJ/(25 + 273.15) = 1346.66 J/K (10) The total entropy change is simply, dS = -189.6 + 1346.64 = 1157.04 J/K (11) The total entropy change is positive. Thus just like the previous example, the REAL 2nd law says that this reaction can happen contrary to what creationists want us to believe. You can also calculate the Gibbs Free energy change of reaction for (7) using, dG = dH - TdS (12) Plug in the values, dG = -345 kJ (13) According to dG analysis, the reaction does proceed to the right. All calculations concerning the total entropy change and entropy change of SURROUNDINGS were performed by me. All other calculations (including the calculations on the entropy change of the system) can be found in the chemistry book. Since many of you believe that steam tables is simply an evolutionist conspiracy, it is hoped that you do not feel the same way with chemistry books. I like to end my discussion with a quote from my high school physics book concerning entropy change. "It can be shown that for any transformation occurring in an ISOLATED SYSTEM [emphasis added], the entropy of the final state can never be less than that of the initial state." (p. 210) This quote is from: _Modern Physics_ by J. E. Williams, F. E. Trinklein and H. Clark Metcalfe; Holt, Rinehart and Winston, Publishers; New York: 1984. The quote is simply more proof that creationists are LYING when they say that the entropy of the system must increase. They simply remove the word "isolated" even though high school physics books include it. Creationists realize that like biology, many people either a) did not take the course in physics or b) simply memorized a bunch of facts for a test and then forget about it. Thus, creationists can publicly claim that the entropy of the system must increase and do not have to worry about anyone correcting them. Even if someone did, that someone wouldn't be believed anyway. A good liar is almost always believed by at least one person. Hence, my inability to "prove" a creationist wrong when he claimed that Mt. Ararat is the tallest mountain in the world. The lack of honesty that these people possess is mind-boggling. I also like to point out that the words "It can be shown that ..." should be removed from the vocabulary of every would-be textbook writers. What better way to NOT teach the students then by using these words. Textbook writers are simply giving creationists more ways to lie to people. Copyright 1996 by Roscoe A. Sincero