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Why do we use the concept of Gibbs's free energy in Ehrenfest's theory of phase transformation ? Why don't we use Helmholtz free energy concept?

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The change in Helmholtz Free Energy (divided -$k_B T$) is the change in entropy of the system $A$ plus environment, assuming the entropy of the environment changes only by exchanging energy with $A$. The Gibbs Free Energy is the entropy of the system plus environment, assuming the entropy of the environment changes only by exchanging energy and volume with the system.

If the phase change doesn't involve a significant change in volume, or very low pressure, then the Helmholtz can be used instead. Biologists often play loose with which Free Energy they're referring to because they deal with small changes in volume and it doesn't matter.

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