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Author
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Topic: Thermodynamics for Intelligent Design
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gedanken
Member
Member # 594
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posted 29. April 2003 14:37
Pim,
Did you mean that deltaS = log2(W2/W1)
or deltaS = S2 - S1 (where S2 = log2(W2), etc.)?
Note above had dS2-dS1 rather than S2-S1. You might want to correct above post if that is what you meant.
I emphasize difference in dS and deltaS because one of Chronos's (Jeptha's) favorite subjects is Prigogene’s formula dS = djS + deS --Here dS is the total change of entropy in the system, while djS is the entropy change produced by irreversible processes within it and deS is the entropy transported across the system boundaries. These are meant to be differential elements, not "delta". So reserve symbol dX for derivative or differential element, and deltaX for change as in the difference formula.
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Pim van Meurs
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posted 29. April 2003 15:00
Gedanken,
Thanks for your update. As far as Prigogine's formula is concerned, if that is Chronos's favorite formula then I fail to see where the problem lies?
quote:
There are several other entropies today in addition to that of Clausius. Prigogine's Entropy, for example, addresses what is called far-from equilibrium thermodynamics which looks at nonlinear dynamic processes and self-organizing systems such as the cells of our body. The equation for Prigogine's Entropy is:
dS_T = dS_I + dS_E
where dS_T is the total entropy change, dS_I is the change in internal, or Clausius' Entropy, the entropy produced by irreversible internal processes, and dS_E is the entropy exchanged with the surroundings (this term is zero for isolated systems for which Prigogine’s Entropy is identical to Clausius’ Entropy). While dS_I tends to increase, the term dS_E can increase or decrease or remain zero (it is positive if entropy enters the system and negative if entropy leaves the system). The important effect of Prigogine's Entropy is that the total system, entropy change of any open system, dS_T, can be positive, negative, or zero. Systems for which
dS_T lt 0 (i.e., where entropy is decreasing) are said to be self-organizing (Çambel, 1993).
Source
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Chronos
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posted 29. April 2003 15:01
“I have no doubt that you are using the same words as Feynman and Boltzmann. My questions are more related to whether you are using them correctly, not whether you are using similar word patterns.”
I would point out that I am using my own words, not the words of anyone else. It is true that I have quoted both of them and given references to back up those quotes but I’m certainly not ‘wording’ my argument using their terminology or logic. All that I’m borrowing from them is some math.
I did state that that if S is positive, entropy is increased. And this is not a tendency in this case. It’s a fact of this specific example. I would ask you to examine your logic. If entropy increases then disorder has occurred. If S is positive then entropy has increased because ‘S’ IS the entropy we are considering. If you are going to continue in this vein of logic, then I will have to ask you to show how that the tenets of thermodynamics is just wrong in that everyone has it backward. Rising entropy denotes order and decreasing entropy denotes disorder.
Also, you seem to want to take issue with my calculations. Yet you make no effort at all to point out how or why they are wrong. In a point/counter point forum in a free exchange of ideas such as is this one, if one is going to make a blanket assertion like this, then I hope that one would be expected to delve a little deeper into the subject and show how and why they are wrong. But, you asked me to back up my argument mathematically and I did. Now what? I take it that the discussion is over and you now agree with me that complex macroevolution could not have occurred and that CSI must be designed in order to exist? ![[Smile]](smile.gif)
And if you are going to assert that rising probability entropy is meaningless, then you are going to have to take on such greats as Eddington, Boltzmann, Schrodinger, Prigogine and Feynman because these guys rather strongly disagree with you.
As to Rex’s math: I appreciate his posts, but I don’t feel it is up to me to make his arguments for him. If he has a point, then it would be up to him to make it and then I will then address it. I would have no idea how he is tying in hydrogen and oxygen with informational entropy. But I feel it would be best for all to let him address his own posits as anything less is just idle speculation of his meaning.
Finally, I would have no idea what you could mean by asking for more detail. My posts were very detailed and that’s about as complicated as it gets. Any further details would just overcomplicate the assertions and serve to hide the conclusions in semantic smoke and mirrors.
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Pim van Meurs
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posted 29. April 2003 15:25
Dear Chronos, thank you for your response which however fails to address many of the issues raised by the various posters.
First of all I would like to ask why you seem to be using S as a change in entropy AND as entropy? You said "I did state that that if S is positive, entropy is increased." and "If S is positive then entropy has increased because ‘S’ IS the entropy we are considering." But entropy might have decreased even if S is positive. S and DeltaS or dS are very distinct and different parameters.
There is a big difference between positive S and whether or not S increases or decreases. As I have shown S can increase or decrease depending on the values of W2 and W1.
I would also like to point out that "Rising entropy denotes order and decreasing entropy denotes disorder." seems to go against the common usage of the term entropy.
I fail to see how your simple examples take into account the various terms involved in macro evolution. As a counter example I would like to point to the works of Adami and Schneider who have shown that mutation and selection can in fact increase information in the genome and thus decrease entropy.
Rex's post showed how using your claims, one can 'prove' that hydrogen cannot burn. Rather than accept this conclusion one may thus want to ask if perhaps the claims are somehow erroneous.
Hence the question for a more detailed mathematical derivation of your claims. So far your usage of the terms entropy, dS etc seem to be suffering from inaccuracies, contradictions etc.
Thus your claim that "I take it that the discussion is over and you now agree with me that complex macroevolution could not have occurred and that CSI must be designed in order to exist?"
ignores the lack of any scientific foundation for such claim, ignores the contradictions that arise from such claims (Rex's example) and fail to account for a clear and accurate mathematical foundation.
I suggest that given even your own confusion on the terms entropy S and dS (change of entropy) that you take us step by step through your argument by relating the various terms in a mathematically sound manner.
Lets take your 'example' about the 4 mutations realized versus the 100 million possible, the entropy change would be DeltaS=log2(4/100,000,000) a clearly negative number.
[ 29. April 2003, 15:33: Message edited by: Pim van Meurs ]
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Chronos
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posted 29. April 2003 16:12
Hello Pim:
Our lack of agreement on whether S=0 or dS=0 is really not that important to the gist of the argument. Can we just say that S is minimum and leave it at that?
I’m not entirely sure where you are coming from in that there must be a “need” for theories of science before these theories can exist in reality or govern nature. The reason this would rightly be called a ‘law’ if it is not falsified, is because the word law is distinctly different from the word ‘theory’ in the scientific method. A scientific law describes natural events in a mathematical connotation, but fails to determine why they occur. A scientific theory shows a correlation between an effect and its cause. So if the fifth law is anything at all, it must be a law by the very definition of the word law.
Now let’s see if the scientific method was followed in achieving my conclusions:
1. Form an observation – I observed that in nature, some unknown law seemed to be governing the diffusion of loose information.
2. Form a hypothesis – I hypothesized that there is a law of nature that dictates a tendency toward increased informational entropy as loose information is diffused.
3. Test the hypothesis – I put this hypothesis through rigorous experimentation. Two of which I detailed here on the forum. In fact, I can’t even form a mind experiment that would show loose information ordering as it is diffused. Can you?
4. Draw conclusions - With any diffusion of loose information, entropy will tend to increase unless sufficient energy is inputted into the system to stabilize it.
Addionally, Let me show where there are some problems with your math: “DeltaS=log2(W2/W1) where dS=S2-S1 and 2 and 1 are after an before states.” The problem lies in logic. You are trying to mathematically state that there are two entropies and two possible microstates, a ‘before’ state and an ‘after’ state. I see your point and let’s see if I can clarify it a bit. The concept of entropy is to determine if any specific event or reaction increases entropy or decreases the entropy of a system and we are only concerned with the after state of that particular reaction. We really couldn’t care less what the entropy of the system was before the reaction. In fact, there may not have been any reactions before the one we are studying in that system; and thus there may not be any entropy at all in the before state.
With this said. There may be certain conditions in thermodynamics where this formula is useful. But I would advise that you change it to: deltaS = (log2W2) +/- (log2W1). This way one can simply add/subtract the entropies together to get the total entropic change. Now, I have a job for you. Let’s do some brainstorming.
I’m looking to put together a formula for logical and informational entropy where deltaS will come out negative if it is negative and positive when it is positive without having to change the probability formula to –S = -log2W. Any ideas?
If you are going to assert that I have a lack of a solid mathematical foundation then I would ask you to state for the forum why and how you come to this conclusion. The math on this is not complicated and there is no need to complicate it. There is no necessitation, and I in fact, would see no way that we COULD go any deeper, mathematically. The entropy has been calculated using a well accepted formula taught in most basic probability classes. What would you see a need to calculate next to show that entropy has increased?
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Rex Kerr
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posted 29. April 2003 16:15
Chronos, you conclude that evolution would have had to go against an entropy of S=26.6 (per generation? mutation?) and thus is impossible.
In my example, I show that burning hydrogen has to go against an entropy of S=10 (per tiny box I've put it in), and thus burning hydrogen is impossible.
What am I missing in my analysis? And when you find it, and add it back, can you also add it to your analysis of evolution? Given my result, it is obviously important.
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gedanken
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posted 29. April 2003 17:32
Pim, still a couple of instances of dS not changed to deltaS, while one case was changed.
Chronos:
Here is what I said before, which you never answered:
quote:
quote:
S = log2W, S = log2(100,000,000), S = 26.5754247590989, therefore S is positive showing a tendency of disorder.
Chronos, if W, the number of states by some measure, is greater than 1 then S will be positive by your formula. Thus any number of states will be "showing a tendency of disorder." Is this what you meant, that any system whatsoever that has any degrees of freedom whatsoever is showing a tendency of disorder? And if that is not what you meant, could you explain your concept in greater detail? Thanks
And you responded in a later post:
quote:
Also, you seem to want to take issue with my calculations. Yet you make no effort at all to point out how or why they are wrong. In a point/counter point forum in a free exchange of ideas such as is this one, if one is going to make a blanket assertion like this, then I hope that one would be expected to delve a little deeper into the subject and show how and why they are wrong. But, you asked me to back up my argument mathematically and I did.
So first I pointed out what was wrong with your calculation. The calculation was:
A) Calculation was always showing a positive S. It did so because the calculation was based on the number of possible states, then taking the log. (Yes of course it is a correct formula taken in some sense, the problem is that the interpretation was not consistent with what the formula was aobut). That number, S=log2(W) where W is some number of states, is always a positive number, unless there is only one possible state W=1 wherein S=0. This has absolutely nothing to do with whether entropy S is increasing.
B) The calculation was irrelevant because even if it was negative (if it were possible for there to be less than 1 state W) that would not bear on whether S was increasing. S would be increasing if at a later time W was increasing, and S would be decreasing if at a later time W was decreasing. Nothing was given to demonstrate the trend of W. So the entire calculation was irrelevant. The problem in the arguments above is giving some mathematical formula and having the reader seem to think that they mean something, while the formulas don’t relate to what is being said.
Then you did nothing to address the various cases, you simply claimed that you did. As I will not be posting any more responses until there is some mathematical basis, the conversation is over as you suggested. I only request the reader to read back and see if questions were really answsered, or if the only response was to claim that some mathematical response was given. I think that most readers will see this. My request is for mathematical accuracy and mathematical relevance -- that formulas given should actually bear on statements they are claimed to relate to. That is why examples of the use of the formulas was requested. The readers should continue to ask for examples to be given. If none are given that make any sense, they will be rightfully suspicious of the statements given that are claimed to be related.
Pim’s post above with the quote from Cambel says what is important. (Corrected link to Pim’s source here.) One only needs for the entropy leaving the system to exceed the entropy entering plus the locally generated entropy for the system to be “self organizaing” or having a decreasing entropy. Calculations that do not address that issue are irrelevant.
An example of mixed up reasoning is “deltaS = (log2W2) +/- (log2W1).” Why ask for “+/-“? There is only one sensible case. The change from time 1 (W1) to time 2 (W2) has a change of deltaS when and only when there is a subtraction, when deltaS = log2(W2) - log2(W1). You can’t choose to add to find the increase or decrease! The increase or decrease is only found by subtracitn the former from the latter. This is abasic measurement methodology. Presenting this clearly is basic to making sense of the subject.
I ask that the reader take the time to examine and analyze these issues for himself/herself. I cnnot answer each post over and over when no details are given to the mathematics showing how they are intended to work, and when formulas are mixed up in seemingly random fashion. “…lack of agreement on whether S=0 or dS=0 is really not that important to the gist of the argument” is way off the mark. Rather such mixing up of formulas is the core of the problem, as the arguments depend on correct use of formulas, but the presentation is so unclear as to mix up such basics as the total entropy and the change of entropy. Without clarity on such basics, there is no basis for further discussion, and repeated responses will be a waste of time. That is why working through some mathematical examples would be useful in understanding what you are presenting.
Answering Rex’s question with a detailed example of the use of the calculations would be useful. Why don’t you do that?
Thanks
[ 29. April 2003, 17:49: Message edited by: gedanken ]
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Chronos
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posted 29. April 2003 17:41
The delta that goes before S is a given in that deltaS is used in the mathematical description of the law. I simply don’t bother to type the delta in to conserve the entropy being increased within my body via the typing on my keyboard. This is quite common in thermodynamics. Observe Rutger’s University physics dept. using the formula: “thermodynamic definition of entropy: S = Q/T ,T given in absolute Kelvin!”
If one does not understand this, then I would suggest that they haven’t studied the second law enough to be reading the page. But if this confuses you I will be happy to include the deltas before S and Q in the future. I’m easy to get along with.
You have misunderstood me. I am not positing: "Rising entropy denotes order and decreasing entropy denotes disorder." This was in a post to Ged, and I pointed out that this seemed to be HIS argument. This is exactly backward, of course.
You would have to back up the work of Adami and Schneider if this is true and to be taken to be a credible argument from you. And you would have to show me mathematically that this is true as I did you. Until you do this, I will have to assert that I just don’t believe it to be true.
I found it interesting that you would use “DeltaS=log2(4/100,000,000)” to calculate entropy. You are not calculating the entropy of the microstates with this formula because remember: “We measure "disorder" by the number of ways that the insides can be arranged, so that from the outside it looks the same. The logarithm of that number of ways is the entropy”. In your vein of logic, matter actually orders as it diffuses through microstates because you seem to be able to show it mathematically. You will find no thermodynamicist from any aspect of the discipline that will agree with you.
And I fail to understand your logic here. Throw the math aside for a moment and just think this through. We know that in the case where the bad mutations became fixed within the human genome that the genome disordered. Why then would one even attempt to show mathematically that it has ordered??? This simply makes no sense to me.
[ 29. April 2003, 19:16: Message edited by: Chronos ]
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Chronos
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posted 29. April 2003 17:57
No, I didn’t conclude that evolution would have had to go against an entropy of S = 26,6. I concluded that the genomic entropy in humans increases 26.6 per generation. There’s a difference.
But you ask me what is wrong with your mathematical analogy? Now let me tell you why it makes no sense, thermodynamically. You are attempting to tie in logical entropy with the burning of hydrogen which is heat and is thermodynamical entropy. You cannot mix these two using the formula S = log2W. If you are even going to bring this argument you are going to have to calculate it properly. And when you do, you will see that your conclusion is simply incorrect. The proper formula to calculate this would either be S = K log W, or S = K (lnW). IOW, the analogy is nonsensical without Boltzmann’s constant somewhere in the formula.
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gedanken
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posted 29. April 2003 18:05
quote:
Throw the math aside for a moment and just think this through.
When you can't make sense of the math, then "Throw the math aside".
But of course you can’t throw the math aside. The math is the basis of the concepts of entropy.
Why don’t you answer Rex’s question with an example of working through the mathematical complexity? If the mathematics can’t be made to work out, then I suppose the argument won’t work out either.
Rex’s original question was:
quote:
Suppose we have a box with 2 molecules of H2, 1 molecule of O2 and enough space for, say, 2^10 molecules if packed solid. This has an entropy of S = log2(W) = log2(1024*1023*1022/2) ~= 10+10+10-1 = 29.
Suppose we look at the box later, and we find 2 molecules of H2O. This has an entropy of S = log2(W) = log2(1024*1023/2) ~= 10+10-1 = 19. Entropy has gone down.
Therefore, hydrogen cannot burn.
Chronos, what is wrong with this analysis?
Severe appologies for liberal quoting, but the subject seems to have been dropped or avoided.
Chronos suggested using the formula “S = K log W, or S = K (lnW)” rather than S=log2(W). This is fine, it simply computes a scaled version of S by a different scale factor, Boltzmann’s constant rather than based on log 2. Where is there any difference? The entropy increase, or it decreases, no matter which formula is used. Chronos, use your formula with Boltzmann’s constant, and then work through Rex’s example! Do you know how strange this argument is, that you claim Rex is using the wrong formula to determine if change in S is positive or negative, when the formulas differ only in a positive scale factor? This is an indicator of how sound the arguments presented were in terms of mathematical relevance.
=====
Also could Chronos or someone fix the link above that stretches out the screen. Thanks.
[ 29. April 2003, 18:23: Message edited by: gedanken ]
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Chronos
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posted 29. April 2003 18:58
No, I don’t postulate “any system whatsoever that has any degrees of freedom whatsoever is showing a tendency of disorder.” Look at my marble analogy. The floor of my office space is always microstates when gridded off. But if there are no marbles laying on my desk to seek those microstates the entire analogy is moot. In fact, even considering that marbles WERE on my desk there still is no increase in entropy unless they spill from the bag, react and diffuse. We can draw from this then, that only in a system that contains microstates and matter to react, considering that said reaction would be spontaneous if the matter reacted; and if that matter DOES react is any of this applicable to that system.
Thank you for taking the time to make some criticisms of my calculation. And if you DO find a problem with them, then I would most certainly admit it, thank you for it, and be glad to understand where I’m wrong and attempt to correct that oversight.
But, I’m afraid that what you are pointing out is simply not true. First, you say that there is a mistake because S is always positive. But this is not true because S is sometimes negative. You ignore my analogy about the marbles ordering from microstates through a hole in the floor and concentrating themselves into a tin cup sitting beneath the cup. Here, S is most definitely negative. On this point, your criticism is moot.
Then you attempt to show that the calculation is irrelevant but DO admit it is a reliable and readily used formula. You write “The calculation was irrelevant because even if it was negative (if it were possible for there to be less than 1 state W) that would not bear on whether S was increasing. S would be increasing if at a later time W was increasing, and S would be decreasing if at a later time W was decreasing.”
Here and later when you write: “Nothing was given to demonstrate the trend of W” you are, in all due respect, just showing that you don’t have a good grasp of the subject. W doesn’t change in a stable system. Therefore, there is no such thing as a ‘trend’ to show for W because there are either 100 microstates in the system or there is some other amount of microstates. This point is moot.
Then you accuse me of refusing to address other various cases. What, pray tell, would be these other various cases? I seemed to have missed that post.
But Pim’s post stating something: ‘only needs for the entropy leaving the system to exceed the entropy entering plus the locally generated entropy for the system to be “self organizaing” or having a decreasing entropy’ is what is most irrelevant. Why? Because once again someone on this thread is confusing informational entropy with thermodynamical entropy. The two are not the same and I labored for three long posts to explain the differences. Pim is taking Prigogine’s methodology for considering heat exchange in a system and trying to apply it to information. This will not work because the two entropies are apples and oranges. Thus, this criticism is, unfortunately, moot.
And you obviously misunderstand my suggestion to use this formula deltaS = (log2W2) +/- (log2W1).” in lieu of the division which makes no sense at all. Surely you can see that if one wants to figure the difference in beginning entropy and ending entropy that all one would need to do is to subtract one from the other and see what remains. But, again, this is moot. Because this is not used, in the field of thermodynamics, to calculate the entropy in the example I gave for information.
”YOU WROTE: I ask that the reader take the time to examine and analyze these issues for himself/herself. I cnnot answer each post over and over when no details are given to the mathematics showing how they are intended to work, and when formulas are mixed up in seemingly random fashion.”
Translation for the reader: “I ask you not to believe this. I have no argument to bring against this logic, I just ask you not to believe it.” Sorry, Ged, you set yourself up for that one.
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Chronos
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posted 29. April 2003 19:07
"Chronos suggested using the formula “S = K log W, or S = K (lnW)” rather than S=log2(W). This is fine"
No. I would disagree that 'This is fine.' This formula is impossible to calculate without heat in the equation because the burning of hydrogen is, quite obviously, heat.
I respect Rex's arguments, but this time he was basing the entire mathematical analogy on a mathmatical logical fallacy and the the thread couldn't understand why I wouldn't address it. ![[Wink]](wink.gif)
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gedanken
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posted 29. April 2003 20:37
Chronos, could you please re-read your post dated posted 29. April 2003 17:57, just a few posts above?
In it you discuss how to calculate the problem "properly". You use a formula. Can you please re-read the formula that you say is the "proper" way to calculate the problem of Rex's case of burning hydrogen and oxygen in a box? Remember that the problem was given in detail by Rex, and that I reposted the problem in case you lost track of the original. Rex asked a very specific question. You appeared to make an attempted answer. If that was not meant to be your attempted answer, could you answer it again, or revise your post above time stamped posted 29. April 2003 17:57 that appears to be the intended answer? (I ask this because I don't understand the combination of Chronos's most recent answer and that answer dated above.)
[Deleted statement.] Since Rex gave specific numbers that he says are the states in question, you can calculate the entropy from those states. You can use whatever type of entropy is the correct type to use to answer the question. Rex asked what was wrong, but the answer is most certainly not that one has to know some value of "heat", because that was not the variables at hand.
The variables at hand are the ones that Rex gave. Now if the principle you have given is correct, it should be something that you can calculate in terms of what Rex presented. You should either agree that the principle you presented is wrong, or you should calculate the mathematics of your principle in Rex's example and explain how they give the results that they give -- and you do that calculation in terms of the type of entropy you intend for your concept, because this is your concept that you are trying to present and it shoudl be done in the terms you are trying to present. I think that it is important to actually address potential difficulties in any new concept.
Any other answer is simply an evasion of the issue. If you choose to evade the issue, the readers will never be able to understand the concept, or become confident in the concept's correctness. Thanks
[Deleted statement. Please note this is how I intend this post, and have removed statements that I thought were slightly more inflamitory. So I should be quoted with what I intend to leave as the final version.]
[ 29. April 2003, 22:03: Message edited by: gedanken ]
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Moderator
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posted 29. April 2003 21:07
I'm ready to shut this thread down. Be careful.
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Chronos
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posted 29. April 2003 21:20
First, Is there any way I could get you to let Rex handle his posts if he cares to? But yes, I did give him the correct formulas to intertwine both heat and the disorder of matter in a given reaction.
And yes, he asked a specific question but one posed in faulty math, with miscalculated entropies that are simply impossible to address because they are incorrect. What can I do to refute something that is not a logical question to begin with?
And please be specific. Please list the claims that change all over the map. This is going to be a little hard for you, because they do not exist. I can’t help it if you still don’t understand the three entropies. I did my best to explain them in detail. Perhaps it would behoove you to go back and re-read those three posts. I will then be happy to walk you through whatever it is you are missing.
And you are just wrong that I could calculate his entropy for him. It would be impossible to calculate entropy because thermodynamical entropy considers Joules and degrees Kelvin or calories and degrees Celsius. This is not given information. And if it were, I would not calculate someone’s formulae for them who are arguing against me. That would be silly, wouldn’t it? But why don’t we just let Rex handle his argument if he chooses to do so. I can tell you this much, if he wishes to properly calculate that entropy, the problem will go away and I will have nothing to explain.
Ged wrote: ”Any other answer is simply an evasion of the issue. If you choose to evade the issue, the readers can observe that.”
What issue is it you believe I’m evading? You keep saying this, but I’ve answered every issue you’ve raised, and very directly. I fear that if these vague posts that don’t really address the issues keep coming, the moderators might just step in end this deal and I wouldn’t blame them a bit. So please, just in case others might want to participate later, if you wish to address the issue or one of my points, then please do so directly and logically.
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