Question

Why is entropy not a thermodynamic potential in the sense of Legendre transform?

Answer 1

Hey !

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The first law of thermodynamics is a version of the law of conservation of energy, adapted for thermodynamic systems.

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Answer 2

Explanation:

We can formulate thermodynamic theory using entropy S as state function or equivalently using the internal energy U, and U is related with all other thermodynamic potentials via the Legendre transform, and these potentials can also be the state function that represents all possible states of equilibrium of the system. Also in mechanics the Hamiltonian function is too the Legendre transform of the Lagrangian, and we say that the two formulations are equivalent in the sense that they can equally explain the dynamics of the system.