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My professor asked me this and I haven't been able to find an answer. I know that entropy is constant in reversible processes like an adiabatic one, but in that case, the internal energy is also conserved.

Any ideas?

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    $\begingroup$ All adiabatic reversible processes have zero change in entropy, but their internal energy changes if work is done. $\endgroup$ Apr 11, 2023 at 10:41

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For an adiabatic and reversible transformation (for example the adiabatic compression of a gas), the entropy of the system does not change while it receives work: its internal energy changes.

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I know that entropy is constant in reversible processes like an adiabatic one, but in that case, the internal energy is also conserved.

You sure about that?

What about a system doing reversible work?

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The fundamental thermodynamic identity is $$ dU=TdS - pdV, $$ which can be also written in terms of enthalpy as $$ dH=TdS+Vdp. $$ These relations readily suggest that we can change the internal energy by changing volume and/or pressure without changing entropy ($dS=0$), although in order to keep entropy constant these might have to be changed in a specific way.

More generally, reversible thermodynamic processes are the processes that do not result in total entropy change of the system with its environment (since otherwise, they would not be reversible - if entropy increased, reversibility would require decreasing it to return to the initial state.)

In this context it is worth mentioning that Gibbs' definition of entropy ("Gibbs I") was explicitly designed in such a way as to reflect the arrow of time, i.e., irreversible direction of evolution of thermodynamic systems. While there exist alternative definitions of entropy, they can be shown to be equivalent to this definition in thermodynamic context (see Is information entropy the same as thermodynamic entropy?)

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