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- Summary:
- I'm trying to show that entropy is a state function based on an analysis of the Carnot cycle and without using advanced mathematics. I'm not satisfied with the presentation in the textbook "University Physics" by Young and Freedman and would like some feedback.

In a (reversible) Carnot cycle the entropy increase of the system during isothermal expansion at temperature T

The mentioned textbook now states that any reversible cyclic process can be constructed from Carnot cycles (towards the end of chapter 20 in the 14th global edition of Young and Freedman.)

The conclusion is that any reversible cyclic process has zero entropy change for the system.

As I see it, this does not show that entropy is a state function.

One would also have to show that the entropy change of the system is zero in any irreversible cyclic process.

Is it okay to simply generalise the argument in the textbook and say that any reversible or irreversible cyclic process can be approximated by (reversible) Carnot processes and therefore the entropy of the system is always unchanged after one complete cycle, no matter whether the process is reversible or irreversible?

_{H}is the same as its decrease during isothermal compression at T_{C}. We can conclude that the entropy change of the system is zero after a complete Carnot cycle.The mentioned textbook now states that any reversible cyclic process can be constructed from Carnot cycles (towards the end of chapter 20 in the 14th global edition of Young and Freedman.)

The conclusion is that any reversible cyclic process has zero entropy change for the system.

As I see it, this does not show that entropy is a state function.

One would also have to show that the entropy change of the system is zero in any irreversible cyclic process.

Is it okay to simply generalise the argument in the textbook and say that any reversible or irreversible cyclic process can be approximated by (reversible) Carnot processes and therefore the entropy of the system is always unchanged after one complete cycle, no matter whether the process is reversible or irreversible?