Maybe not really understood, what entropy means?

There is no concept of entropy. The second law of thermodynamics already contradicts itself.

- Why should the successful use of the concept of entropy be a matter of "foolishly worshipping entropy"? Here, with "successful" I mean the qualitative and quantitative understanding of measurements.

- You claim that "Later, it can be inferred that the Carnot efficiency is related to the thermophysical properties of the working fluid," and you specify "Thermophysical properties of working fluid: E=E (V, T), P=P (V, T)." But the latter equations just mean that, in equilibrium, the relevant thermodynamic quantities are state functions - i.e., that they are well defined; as one can see from real systems in equilibrium, this is obviously correct. This is a general property of systems in equilibrium. Therefore, as long as you don't specify a specific equation of state, you cannot claim that anything depends on specific properties of a specific substance.

- Also, I don't see the contradiction that you have in mind: You have only claimed that "the Carnot efficiency is related to the thermophysical properties of the working fluid," but you didn't show that this "being related" may lead to different expressions for the efficiency of a Carnot cycle when performed by different substances.

Unfortunately, the second law of thermodynamics does not match the experiment (see link for details) and contradicts itself.

Preprint The second law of thermodynamics is not the law of physics, ...

Here you say that "the second law of thermodynamics does not match the experiment," but in the link that you refer to you say that "The second law of thermodynamics is not the law of physics, but engineering experience." So what? The "validity" of a "physical law" is always just a matter of practical experience. This is the fundamental aspect about all natural sciences: Always the experiment, yielding a quantitative measurement, has the last word. All claims that cannot be substantiated by such measurements are unscientific. Also, if a conclusion from a theory predicts the outcome of an experiment wrongly, the theory is falsified. A single example for such a wrong prediction is suffcient to falsify a theory.

So, please (i) give a specific example where the 2nd law fails and (ii) state clearly the contradiction that you mean here in this discussion, instead of referring to another subject.

I really dislike those arguments spinning in the air.

The picture is a specific case.

Thanks for this specifc case; I will need some time to comprehend it. The picture you uploaded is rather compact; do you have an accompanying paper or draft where you discuss it in some detail?

Thank you very much for carefully reading the examples. I try to use simple and direct language, which is more conducive to quick understanding for everyone.

Well, I don't fully understand the mechanical coupling between the containers of gases A and B. I understand that each gas has a container of its own, and their volume is adjusted by an individual piston; probably they can also be individually cooled or heated. According to Eq. (1), work shall be transferred from one gas to the other, which requires some mechanical coupling between the two pistons. To fully understand your specific case, I need detailed information about this coupling.

It's a technical problem. I'll just make sure there's no problem with physics.

No, it's not just a technical problem: You have claimed that the second law of thermodynamics doesn't match the experiment. Such a claim requires that you consider an actual experiment, or that you at least refer to a technically feasible process. If your example isn't technically feasible, you haven't proven anything; therefore, you need to show that your example is able to work in real life.

From your Eq. (1) it follows that when P_A differs from P_B, also |dV_A| differs from |dV_B|. Hence a 1-to-1 coupling between the two pistons (e.g., by a connecting rod) doesn't work. A constant gear ratio doesn't work either because P_A and P_B depend nonlinearly on the respective volume. So, how can it work?

In addition, there is a problem with your argument related to Eq. (2): You claim that the expression for dQ is nonzero, and you justify this claim by stating that A and B are different gases. You explicitly show that dQ is nonzero for the case of A being an ideal gas and B being a real one, because then E_A doesn't depend on V_A since an isothermal process is considered, whereas E_B depends on V_B (even for an isothermal process).

However, even if both gases are real ones, it is not per se clear that dQ is nonzero because dV_A and dV_B aren't independent; instead, they are coupled by Eq. (1). This introduces a minus sign in Eq. (2), so there is the chance that dQ might be zero. Therefore you need to show explicitly that dQ is nonzero.

Thank you for your reply.

Dear Bo Miao,

it is good to analyze the second law of dynamics logically. You've been doing this for at least five years.

During this time, you published 3 very similar articles on ResearchGate (RG) and opened a discussion on RG 3 times, always in the form of the same question as in this discussion.

I looked through the replies to the questions, but I didn't see anyone focusing on the essence of the issue being raised. You raised an objection against the second law of thermodynamics (Law II), but no one supported or refuted it. Law II's statement may have its problems, but that doesn't mean your objection has to be correct.

***

REFUTATION OF THE OBJECTION OF CONTRADICTION.

I will give it in points:

I) Your objection is not to Law II, but to the alleged derivation of Law II. This is about the alleged assumption that the efficiency of the Carnot engine does not depend on thermal parameters.

II) You implicitly equate Law II with Carnon's statement. Explicitly, the current state of science does not state Carnot's statement as a statement of Law II itself. Yes, I have personally formally proven such equivalence, but it is not yet completely universally and consciously recognized. Scientists think so, but until 2022 no one has proven it completely formally.

III) Your objection only concerns the derivation of Carnot's statement, not the statement itself, and not Law II. You are simply referring to a derivation that is incorrect. A false derivation refutes itself, but does not necessarily refute the thesis being derived (Carnot's statement, Law II).

IV) Neither Carnot's statement nor Law II can be derived only from the first law of therodynamics (Law I). The idea that such a derivation exists is wrong. In principle, the laws of physics cannot be derived, but the implication or equivalence of certain laws can be proven. That is, one can argue for the equivalence (or lack of equivalence) of Law II's statements. However, it is impossible to prove Law II from Law I. However, it would be possible, in a sense, to derive Law I from Law II, because the second law assumes the first law (but not the other way around).

***

I will limit myself to these clearly critical points I-IV. However, this entire discussion results from certain problems of Law II. However, your allegations did not pinpoint the real source of the problems, but only give an intuition that something may be wrong somewhere.

Best regards,

Grzegorz M. Koczan

If Carnot's law goes wrong, thermodynamic entropy cannot be defined. Negating the second law of thermodynamics is the only way out

"If Carnot's principle fails" - but it doesn't, so the assumptions and conclusions are false.

Ad. IV. The efficiency of the Carnot engine can be derived, so in a sense the second law of dynamics can be derived. This conclusion is a bit of a surprise to me.

How do you explain the self contradiction in the picture? I won't just talk about concepts.

Dear Bo Miao,

The explanation of the contradiction is literally simple. You printed out the false sentence "Carnot does not depend on temperature" and attributed it to Carnot. Well, you received a contradiction upon request.

However, the reasoning could be improved and statements that actually do not depend on temperatures or specific temperature values could be identified. These are Kelvin's statement and Clausius' first statement.

Dear Bo Miao,

how will you defend yourself against my rejection of your contradiction? Failure to respond to an argument means no counterargument and tacit acceptance that your contradiction does not exist.

On the other hand, I wonder what exactly Carnot's statement is based on. If it can be derived, it means that the second law of phenomenological thermodynamics can be derived. The question is whether Carnot must be based on Clausius's entropic statement - probably not. A more difficult question is whether the derivation of the Carnot statement must be based on the Carnot cycle of an ideal gas? In this approach, we have temperature dependencies from the very beginning.

Or maybe it is possible to derive Carnot's formula from general considerations? What I mean here are T(S) diagrams, where the variable S is introduced provisionally without assuming its properties. In this approach, the assumptions about T and S are unclear (or the lack of such assumptions), but the formula for maximum efficiency seems trivial. This is closest to your reasoning, but difficulties do not necessarily mean contradictions.

Dear Bo Miao,

I would like to inform you that you have been mentioned in the thread below. Please note that in addition to criticism, it also points out some deeper reasons for your doubts:

https://www.researchgate.net/post/Do_you_really_know_the_second_law_of_thermodynamics_Can_you_formulate_it_precisely_Do_you_think_this_is_a_fundamental_principle/3