Talk:Carnot's theorem (thermodynamics)

message: This article is about to be greatly modified by me because of significant errors.
#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.
#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".
#Also planning to write a section clarifying the distinction between Carnot engine and Carnot cycle.
--Netheril96 (talk) 05:03, 3 October 2010 (UTC)
thread_title: Modifications

message: 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. -- 05:22, 12 July 2013 (UTC)
thread_title:  Removal of sections 

message: — Preceding unsigned comment added by Guy vandegrift (talk • contribs) 01:38, 12 December 2013 (UTC)
thread_title:  Proposal of new figure 

message: The problem with the old proof lies in the figure, which, while accurate, has a number of undesirable features.  
# The prime superscript \eta' forces every reader to re-examine the figure (often more than once). I have chosen the superscripts (M) and (L) for more and less efficiency.  (I would have preferred 'high' and 'low' efficiency, but that would have lead to confusion over whether 'h' meant hot or high.)
# The representations in a figure should be static.  The label 'Heat Engine' might mislead the reader into thinking that it is never a Carnot engine.  Its status as a reversible engine must be changed to essentially a Carnot engine (since it has the same efficiency.) In contrast, I call it the 'more' efficient engine throughout, although technically it is the 'not-less' efficient engine due to the possibility that \eta_M = \eta_L. To avoid confusion between 'Carnot' and 'reversible', I never call an engine 'Carnot' until after it is established that 'Carnot' and 'reversible' mean almost the same thing.  This reduces the vocabulary needed to understand the theorem by one word.
# By referring to the engines as 'more' or 'less' efficient, the one thing that remains static is its most important feature: The figure represents an 'impossible' situation throughout the discussion.   (In deference to Wikipedia's policy of neutrality, 'impossible' is qualified with a link.
# This is a minor point, but the new proof renders the so-called 'second' theorem more transparent than the 'first' part: Simply place the two reversible engines in the proper order and the violation of the 2nd law is apparent.  It is this part of Carnot's theorem that got me so interested in it.  Students learn that entropy is a state function only through the monatomic ideal gas, where entropy is shown to be a state function. This always left me wondering if there was another substance that would sustain reversible change with a different change in entropy.  The fact that all reversible engines are essentially Carnot cycles resolves this question.
Out of deference to the old way of doing things, I retained the link to the original proof (at http://faculty.wwu.edu/vawter/PhysicsNet/Topics/ThermLaw2/ThermalProcesses.html)
Is this original research?  The relabeling of the figure certainly is not.  But I could not find another presentation  of the theorem that focused on an energy flow diagram that is clearly paradoxical.  Nor could I find a discussion that focused more on the equivalence of all reversible heat engines than on the proof that no engine is more efficient than the Carnot cycle.  This might be an original way to present the subject, but it is not what I would call original research.guyvan52 (talk) 18:12, 13 December 2013 (UTC)
thread_title:  Why the proof was rewritten 

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thread_title:  External links modified 

message: That the maximum efficiency of a heat engine = 1 - Tc/Th can be demonstrated simply.
By conservation of energy, the maximum amount of work/energy that can be extracted from a heat engine = difference between heat/energy taken from the hotter reservoir (Qh) and heat/energy lost to the colder reservoir (Qc) = Qh - Qc. 
The efficiency of an engine is defined as:
 η = work out/ energy in = (Qh - Qc)/Qh = 1 - Qc/Qh
So what is Qc/Qh?  
By the second law, Entropy can never decrease so, as a minimum, the amount of entropy entering the colder reservoir (dS) must equal the entropy leaving the hotter reservoir (dS), i.e., dS = Qh/Th = Qc/Tc (where Th (resp. Tc) = temperature of the hotter (resp. colder) reservoir). If more heat than this Qc entered the colder reservoir (call it Qc+), less energy would be available for work, and dS = Qc+/Tc would be greater than in the minimum case so overall the entropy change would be positive. Therefore the maximum amount of work is extracted from the engine when the total entropy does not increase, i.e. when Qh/Th = Qc/Tc, which can be rearranged as Qc/Qh = Tc/Th.   
Therefore for the most efficient engine:
 η = 1 - Qc/Qh = 1 - Tc/Th.
The maximum amount of work/energy is extracted (the engine is most efficient) when the least energy is lost to the cold reservoir, which is precisely when the entropy does not increase. No more work can be extracted for a given input of heat energy Qh between any two temperatures Th and Tc because entropy would then decrease.  
The Carnot cycle is simply a way of carrying out changes in a working fluid (1. absorption of heat at an original temperature, 2. expansion and decrease in temperature, 3. rejection of heat, 4. compression and increase in back to original temperature) so that work can be extracted cyclically and there is no increase in entropy and no losses due to, e.g., friction or leakage of heat. (The compression and expansion are reversible and adiabatic, hence isentropic. The absorption and rejection of heat are arranged to involve equal and opposite changes in the entropy of the system.) Because some of the energy extracted when the fluid expands is required to raise the fluid back to the original temperature, each cycle extracts less net work than is extracted in the case of a simple 'one-off' process, however both are maximally efficient. Wodorabe (talk) 13:26, 20 December 2017 (UTC)
replies: text: Your comment is well written.  But I don't have the time to critically review it for technical accuracy.  My guess is that if you were not a physics major, then your insights might be correct, but not likely to "fit in" with how this subject is typically taught.  If you were a physics major, then you should contact me on my Wikiversity page, because we need people like you.  wikiversity:User talk:Guy vandegrift 01:34, 23 December 2017 (UTC)
thread_title:  More intuitive demonstration 

message: "First, we must point out an important caveat: the engine with less efficiency ( \eta _{L}) is being driven as a heat pump, and therefore must be a reversible engine. "
I understand that heat pumps (including irreversible) with efficiency less than Carnot's efficiency don't exist,
because heat engines with Carnot's efficiency exists, and if heat pumps with with efficiency less than Carnot's efficiency exist then second law of thermodynamics violates.
Why irreversible heat pumps with efficiency grater then Carnot's efficiency don't exist?
FeelUs (talk) 13:44, 14 February 2019 (UTC)
thread_title:  Irreversible heat pump 

message: The following is a paragraph from The Feynman Lectures on Physics, Vol. 1
'The results of thermodynamics are all contained implicitly in certain apparently simple statements called the laws of thermodynamics. At the time when Carnot lived, the first law of thermodynamics, the conservation of energy, was not known. Carnot’s arguments were so carefully drawn, however, that they are valid even though the first law was not known in his time! Some time afterwards, Clapeyron made a simpler derivation that could be understood more easily than Carnot’s very subtle reasoning. But it turned out that Clapeyron assumed, not the conservation of energy in general, but that heat was conserved according to the caloric theory, which was later shown to be false. So it has often been said that Carnot’s logic was wrong. But his logic was quite correct. Only Clapeyron’s simplified version, that everybody read, was incorrect.'
So, it seems Carnot's theorem is not based on Caloric theory if Feynman is correct.  — Preceding unsigned comment added by Bojjasaikiran (talk • contribs) 14:11, 25 April 2020 (UTC)
thread_title:  Is Carnot's theorem based on caloric theory?