I want to analogize that the efficiency of a heat engine is not related to the working fluid, which goes against common sense. Please do not bring up irrelevant issues.

The Carnot Cycle is a model for a thermal engine that operates through particular reversible, quasi-static, ideal processes between a heat source and a heat sink, with an ideal gas as a working fluid.

Therefore, being an ideal gas, which is a model for a thermodynamic system, its efficiency is not dependent on the "ideal gas" considered.

If you want to make an analogy with people, then you must consider "ideal people" evaluated using "ideal grades" and establishing an "ideal IQ". In any case, I think the analogy makes no sense. In the same way I think it makes no sense insisting on dubious flaws of the 2nd law and the Carnot cycle.

I know that doubt is one of the basis of Science (another one is curiosity), but efforts should be "efficiently" directed and invested.

In the textbook, an example is given to calculate the Carnot efficiency using an ideal gas, but it is not stated that the Carnot cycle must use an ideal gas as the working fluid. Any real gas can be used as the working fluid. Take a good look at the book. Wrong understanding affects your thinking.

Bo Miao Yes, the Carnot cycle can be applied to any fluid. When applied to an ideal gas its efficiency does not depend on the "particular" ideal gas employed (because "all ideal gases are all alike", paraphrasing Tolstoy). Using a non-ideal gas, the efficiency will be dependent on the "particular" real gas ("every real gas is real in its own way", Tolstoy again).

What is wrong with this "understanding"?

I just want to say that Carnot efficiency has nothing to do with the working fluid, which goes against common sense and is wrong. My question is very specific, at one point.

Don't list those irrelevant statements here. Don't write anything that doesn't match the book here.

Let's rephrase it in another way:

The Carnot efficiency depends on the properties of the fluid. In the case where the fluid is an ideal gas, the Carnot efficiency is solely a function of the temperatures of the heat source and the heat sink, which is another way to say that it does not depend on the working fluid.

Are the Carnot efficiencies of carbon dioxide and oxygen (using the same heat source) the same? If it's the same, what's the reason? Can a perpetual motion machine prove it?

Please, read carefully: “In the case where the fluid is an ideal gas, the Carnot efficiency is solely a function of the temperatures of the heat source and the heat sink”.

Are carbon dioxide or oxygen ideal gases? No, they are not.

Quoting somebody: “Wrong understanding affects your thinking”.

This will be my last comment in this thread. No more time wasted in useless discussions.

I was chatting with a German PhD earlier, and he shared similar views with you. He even sent a screenshot of a textbook and I pointed out some of his misunderstandings. If everyone asks me to correct it like this, it would be too hard.

As "the German PhD" I can clarify here:

1) The textbook by Planck that I screenshotted demonstrates that for an ideal gas, building on the FIRST law of thermodynamics, you get the Carnot efficiency of n=1-TA/TB. The second law of thermodynamics is not required for that statement.

2) The second law of thermodynamics does not state that this efficiency is also valid for other fluids. It states that there is no real machine operated with a real gas that has a higher efficiency. As I wrote back then, if your textbook claims that you always get n=1-TA/TB independently of the fluid, the author didn't know the correct second law of thermodynamics.

n(ideal gas)=n(CO2)=n(H2)=1-TA/TB---（1）

The inference of the second law of thermodynamics: Carnot efficiency is only related to the temperature of the heat source and not to the working fluid.

Reason for equation (1): Anti perpetual motion machine (this is just a slogan and has no physical meaning).

The above is the content of the book.

*******

I want to clarify that 'Carnot efficiency is not related to the working fluid' is a violation of common sense. Please refer to the first post for details.

You are right, claiming that the Carnot efficiency was not related to the working fluid would be against common sense. That's why the second law of thermodynamics doesn't say that.

I mean, what you do here is great entertainment as always, but is there a point at which you will pick up a decent textbook and find out that the law you are trying to prove wrong doesn't exist in the form you assume it to be?

Jürgen Weippert, Adrian Velazquez-Campoy

>The Carnot efficiency depends on the properties of the fluid. I am sorry to intervene, but this statement is not correct. The main point of the second law is that the Carnot efficiency in a reversible cycle does not depend on the properties of the fluid. There are two ways to show this. First, one can do it as scientists in the 19-th century have done - they have considered two Carnot engines working together. Nowadays one can do it otherwise, one could start with dU = TdS - pdV and show that for a reversible Carnot cycle with any fluid the efficiency is the same.

Evgenii Rudnyi

The point of the second law of thermodynamics is that real efficiencies are lower than that of the ideal Carnot cycle. Only then this would be equivalent to the formulation that for spontaneous processes you have dS≥0. The efficiency can be calculated purely based on the first law.

However, if you could share a more elaborate derivation reference that this results also in the simple expression for a real gas, we could also settle this argument. I would have to admit that I allowed myself to be carried away, but Bo Miao's "counterproofs" against the second law would still be invalid.

Jürgen Weippert

In this case it is important to distinguish reversible and irreversible processes as the inequality in the second law is for irreversible processes only.

The proof for reversible processes from the 19-th century is rather involved. It is done nicely in the books on thermodynamics by Duhem and Poincaré and it could be found in the recent paper below (as Poincaré's Thermodynamics has not been translated into English, it has not been mentioned in this paper)

Norton, John D. "The impossible process: Thermodynamic reversibility." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 55 (2016): 43-61.

>The efficiency can be calculated purely based on the first law.

This is a common misunderstanding. The problem along this way is a derivative (dU/dV)_T as it is needed for the calculation. This derivative is given by the second law:

(dU/dV)_T = p(dp/dT)_V - p

For the ideal gas it is zero, for other fluids it is not zero. But if you use this derivative in the calculation, you should obtain the same efficiency for any fluid in the reversible Carnot cycle.

I should confess that I do not remember where this has been done this way, sorry. But it must work, otherwise one could create a perpetuum mobile of the second kind.

n(ideal gas)=n(CO2)=n(H2)=1- TA/TB--- （1）

This formula is not supported by experiments. Scientists use the piecing together method to process experimental data. Please refer to the attached figure (the correctness of the formula must meet the requirements of prediction and experimental consistency)

The actions of scientists indicate that formula (1) is incorrect.

Anti perpetual motion machine===》n(ideal gas)=n(CO2)=n(H2)=1-TA/TB

This is a very foolish deduction，‘Anti perpetual motion machine’ is just a slogan and has no physical meaning).

All heat engines (including Carnot engines) can be calculated using the following three formulas:

dE=dQ+PdV

E=E(V,T)

P=P(V,T)

Evgenii Rudnyi

Thank you for the references, I will have a closer look at it.

Bo Miao

Of course the efficiency is calculated from the energy conservation, but as long as you don't construct a machine more efficient than Carnot, which would be the perpetuum mobile 2nd order, the second law is not in trouble.

What I mean is that all calculations of thermal work conversion can be done using the first law of thermodynamics, without the need for the second law of thermodynamics.

All heat engines (including Carnot engines) can be calculated using the following three formulas:

dE=dQ+PdV

E=E(V,T)

P=P(V,T)

>E=E(V,T)

That is exactly the problem as where you take the derivative (dE/dV)_T from? The first law does not give you this. You have it by the second law only.

E=E(V,T)

P=P(V,T)

Experimental testing yielded E and P values

Scientists are just piecing together experimental data using the second law of thermodynamics (see image for details), which is illegal. And the data pieced together does not match the experiment.

This two equations are connected to each other:

(dE/dV)_T = p(dp/dT)_V - p

This is the main point of the Second Law.

The fact that scientists pieced together experimental data using the second law of thermodynamics (see attached figure) implies a fact that the formula you wrote is incorrect and does not match the experiment. I don't like you piling up knowledge that has nothing to do with the actual issues being discussed.

Assembling data is not allowed for basic science, it can only be predicted and verified. The second law of thermodynamics is no exception,

Could you please cite a scientific paper where it has been experimentally shown that the equation I have written is incorrect?

1. Your formula is derived from the inverse perpetual motion machine. Is that correct? If the formula you write is correct, scientists will not piece together data. 3. You are like a bulldozer, pushing knowledge over. And without the ability to discern, they also learn from others' things. It's really sad!

What I am talking about is the discipline that natural sciences must follow: 1) Carnot efficiency has nothing to do with the working fluid, which violates common sense. See the first post for details. 2) Basic science can only engage in data prediction and verification, not data assembly, as shown in the picture. You need to break free from the second law of thermodynamics and approach problems from the perspective of natural science.

I see this has escalated overnight quite a bit.

Let us go back to the original sources of what the second law says.

First one is Clausius, his original words are:

"Es gibt keine Zustandsänderung, deren einziges Ergebnis die Übertragung von Wärme von einem Körper niederer auf einen Körper höherer Temperatur ist."

Translation: There is no change of states whose sole result is the transfer of warmth from one entity of low to an entity of high temperature.

Kelvin:

"It is impossible for any device that operates on a cycle to receive heat from a single reservoir and produce only a net amount of work."

Planck suggested to refer to such a non-existing device as a perpetuum mobile of second order.

Concluding from this in a strict manner, the second law only has failed if a transfer of warmth from a low-temperature to a high-temperature entity has been observed experimentally or if a device producing only work has been built - not simulated, built. But let's expand this to a less narrow-minded scale:

Neither of these formulations provide an equation of any kind, both of them provide process ranges and ranges in mathematics are specified by inequations, therefore any mathematical reformulation of the second law must also be an inequation. An expression equating a quantity to another, e.g. an efficiency to an expression, may be a threshold, but not a reformulation of the law.

A straightforward related statement is Clausius' theorem of entropy increase:

"Bei jedem natürlichen Vorgang nimmt die Entropie zu."

Translation: in any natural process, entropy will increase.

Mathematically spoken, we have dS≥0.

Transferring this to the Carnot cycle, the ideal cycle has dS=0 and therefore the ideal Carnot cycle constitutes a theoretical optimum of efficiency. Therefore, from the second law we can conclude that no other cycle will beat the efficiency of Carnot.

Bo Miao

So your answers confirms that you cannot cite scientific papers that support your point. Thank you, now everything is quite clear.