Talk:Carnot's theorem (thermodynamics)

Modifications

This article is about to be greatly modified by me because of significant errors.

1. The Carnot theorem is a product, rather than a stepstone towards establishment, of the second law.I plan to add a section proving it with second law in a few days.
2. Modern engines are not operating between two reservors whose temperatures are constant, let alone performing Carnot cycles.So the statement in section Description "Carnot's theorem sets essential limitations on the yield of a cyclic heat engine such as steam engines or internal combustion engines, which operate on the Carnot cycle. " are actually wrong.In addition, the section Example is misleading because it oversimplifies the problem.The model of inner combustion engines are mostly Diesel cycle in which the temperatures are varying.So I delete the entire Example section.Anyone is welcome to write another example,but don't refer to the REAL ENGINES because they almost never meet the condition of "two reservoirs".
3. Also planning to write a section clarifying the distinction between Carnot engine and Carnot cycle.

--Netheril96 (talk) 05:03, 3 October 2010 (UTC)

New section: applicability to fuel cells

As the fuel cell industry continues to grow, it's important to examine the question of whether Carnot's theorem applies to fuel cells; hence the creation of this new section. If anyone can add definitive information that resolves the controversy one way or the other (does it or doesn't it?), please do. 71.221.123.158 (talk) 03:59, 21 February 2011 (UTC)

Kbrose, you summarily deleted the new section on the grounds of "controversial topic, no context, and no valid reliable sources."

Since when are controversial topics off-limits for Wikipedia? It has an article on abortion, for example, and I hardly think Carnot's theorem is as controversial as abortion.

The first source I cited is Google's browser-friendly transliteration of a PowerPoint file published by Case Western Reserve University itself. Why do you feel this is unreliable? Would you prefer if I cited the PowerPoint file directly?

The second source was an abstract written by K. T. Jacob and Saurabh Jain, found on the web site of the Institut de l’Information Scientifique et Technique. Do you feel that the Institut did not reliably reproduce this abstract? 71.221.123.158 (talk) 05:23, 22 February 2011 (UTC)

Hello, I have come across an article that seems to prove that the Carnot efficiency DOES apply to fuel cells, after all, and thus, the maximum efficiency of a fuel cell is limited by this Carnot efficiency. It is:

"Thermodynamic comparison of fuel cells to the Carnot cycle", International Journal of Hydrogen Energy, Volume 27, Issue 10, October 2002, Pages 1103-1111, Andrew E. Lutz, Richard S. Larson, Jay O. Keller.

Would anyone like to read the relevant sections, and see if it's worth modifying this section of the article? Thanks. 217.127.0.107 (talk) 11:32, 3 June 2012 (UTC)

Removal of sections

I removed the sections entitled "'Proof' of D. ter Haar and H.N.S. Wergeland (Elements of Thermodynamics, Addison-Wesley, 1960)" and "What is wrong with the 'proof'".

The sections present an argument of ter Haar and Wergeland, and then highlight an alleged flaw in the argument. Although it can occasionally be helpful, in articles containing proofs, to present a facially appealing but incorrect "proof" of the result (see Cayley-Hamilton theorem), this is not one of those cases. The argument of ter Haar and Wergeland is much more technical and complicated than the presumably correct proof that the article already contains. Therefore, right or wrong, I do not think it has much facial appeal. It need not be included.

In addition, no reliable source is cited for the section "What is wrong with the 'proof'". Without a source, that section violates WP:OR.

It appears that similar edits were made to the Russian version of the page by the same editor. The edits were more apposite there (though still original research) because the principal proof offered in that article is that of ter Haar and Wergeland. That proof did not originally appear in the English version of this article, however, and for good reason -- it is overly technical. It is therefore not necessary to point out a purported disproof. --N Shar (talk · contribs) 05:22, 12 July 2013 (UTC)

Proposal of new figure

File:CarnotProofSimplified.jpg

CarnotProofSimplified

— Preceding unsigned comment added by Guy vandegrift (talk • contribs) 01:38, 12 December 2013 (UTC)

Forgot to sign--guyvan52 (talk) 02:04, 12 December 2013 (UTC)

By attempting to treat both theorems in one figure, we confuse the reader into caring which is which in the second theorem. The figure shown is for the second theorem. I will make another one dedicated to the first. Contrary to earlier claims (by me), there is no possibility that this is "original research" here -- I am just labeling the diagrams more clearly. And contrary to what I originally thought, we need two figures. My rewrite will follow the Ohanian reference shown below, and will be much more clear.

I will also clarify that when running a reversible cycle backwards as a refrigeration unit, low efficiency is a good thing. (That is why they use the COP instead of effeciency when evaluating air conditioners.) An air conditioner with a low COP dumps excess energy into the cold reservoir (i.e. your house in the summertime). But an air conditioner with a low Carnot efficiency dumps more heat into the hot reservoir (which makes it a much better air conditioner). That is why the second law 'bans' reversible engines if they have efficiency that is too low.

Here are the references I will use:

1. The current Wikipedia reference introduces the concept as two theorems, the "first" and the "second" Carnot theorems
2. Tipler's (very well known) text only proves that no engine can be more efficient than Carnots, although a problems at the end explore running the cycle in referse and could be used to introduce Carnot's second theorem.
3. Another good textbook by Ohanian also proves the two versions of the theory separately.
4. Course notes posted on the internet by Royal Holloway, University of London assert wthout proof that the Carnot cycle is the most efficient. "PH2610: Classical and Statistical Thermodynamics Section 3 page 18" (PDF). January 4, 2011. Retrieved December 11, 2013.</ref>
5. Powerpoint presentation posted by a professor at UNL (Nebraska) that treats it as two different theorems.
6. A 12 minute Kahn Academy video carefully presents one theorem and states the results at the other without proof."Kahn Academy: Proving that a Carnot Engine is the most efficient engine". Feb 7,2005. Retrieved December 11, 2013. {{cite web}}: Check date values in: |date= (help)</ref>

Many excellent sources of physics on the internet fail to mention Carnot's theorem, which I find surprising because is one of the few calculations that apply to something other than the ideal gas. Without Carnot's theorem, we have no proof that entropy even exists as a state variable.--guyvan52 (talk) 03:21, 12 December 2013 (UTC)