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Chapter 5 Thermodynamic potentials

What are the thermodynamic potentials?
Thermodynamic potential or fundamental function is a quantity used to represent the state of a system.
We have four fundamental functions: internal energy U, enthalpy H, Helmholtz free energy F, and Gibbs free energy G.
They are “potential energy” defined as capacity to do work.
Why there are only 4 thermodynamic potentials?
These four potentials provide a comprehensive framework for understanding and analyzing the behavior of thermodynamic systems.
Actually there are not just 4 , there are as many thermodynamic potentials as you want.
The first thermodynamic potential is internal energy and it comes from the first law of thermodynamics.
What are the expressions for the four thermodynamic potentials?
E=E(S,V);H=H(S,P);F=F(T,V).
In this list of pairs of four arguments, only one pair is missing: {T,P}.
The thermodynamic function of this pair, which gives the two remaining variables (S and V) by simple differentiation, is called the Gibbs energy (or sometimes the “Gibbs free energy”): G=G(T,P).
It follows that the total pressure p = Σ_i p_i and p_i/p = x_i (for ideal gases).
In words: The chemical potential of gas number i in a mixture of gases at a certain temperature T and pressure p is equal to the chemical potential of this gas in the pure phase at p and T plus RT· lnx_i.

What are the thermodynamic potentials?