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Change in Entropy and Entropy as a state function

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Kyriee:
Let's take an isothermic expansion of an ideal gas as example.
In a reversible process, the work done by the system is w=nrT*ln(Vf/Vi). Being the process isothermic, q(absorbed)=w(done), since the difference in energy is 0.
In a reversible process, the work is w=p(Vf-Vi), which is equal to q, since it is also isothermic.
In both cases, the heat absorbed by the enviroment is equal to the heat released by the system. So, in the case which T(enviroment)=T(system), the variation in entropy of the universe is zero? Regardless of the reversible/irreversible nature of the transformation?

If not, can you suggest me a book where to study or understand this basic concept? I've tried Atkins, McQuarrie, youtube videos, but I'm still stuck.

Enthalpy:
Many situations imagined in thermodynamics books and courses aren't completely described. They often forget some elements that provide or absorb work, so for instance "working against the external pressure" isn't all. Missing energy amounts, and resulting logical contradictions, often come from these omitted elements.

And for reversibility, one also must consider other bodies than the gas, vapour... whose behaviour is described. If other components provide heat from a higher temperature or regain it at a lower temperature, a transformation isn't reversible, the entropy increases, but you may not see it at the mentioned body.

In the last example you describe, the pressure of the ideal gas varies (or nothing would happen) so it's not always equal to the outside pressure. A constant outside pressure absorbs work in this process, but more elements are needed to absorb the difference of pressure between the expanded gas and the outer fluid. It can be a piston for instance. This piston absorbs work. Maybe the work converts immediately to kinetic energy, but it's work.

Sidenotes:
"Energy" isn't accurate enough for thermodynamics. You probably meant the internal energy. There are a dozen more.
If the gas expands at constant temperature, it absorbs heat that is lost by something else.

Kyriee:
I'm really sorry but I don't get it, even if your explanations are good and rigorous.
Thank you very much anyways.

Can you please suggest me some sources that you find useful to resolve this issue?

Enthalpy:
I know no clear book for thermodynamics, and I regret it. Yves Rocard maybe, but it's in French.

About the last case you proposed: the hypotheses you make are not consistent, so the reasoning can't bring good conclusions.

The expansion at constant temperature needs a variable pressure. But this expansion shall work against a constant outer pressure. This needs an extra element between the inner and outer fluids, like a piston, which takes or gives work but is absent from your description.

Kyriee:
Thank you!

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