Five common thermodynamic potentials are:
where T = temperature, S = entropy, p = pressure, V = volume. Ni is the number of particles of type i in the system and μi is the See more

The definitions of the thermodynamic potentials may be differentiated and, along with the first and second laws of thermodynamics, a … See more

Again, define xi and yi to be conjugate pairs, and the yi to be the natural variables of some potential Φ. We may take the "cross differentials" of the state equations, which obey the following relationship:
From these we get the See more

Deriving the Gibbs–Duhem equation from basic thermodynamic state equations is straightforward. Equating any thermodynamic potential definition with its Euler relation expression yields:
$${\displaystyle U=TS-PV+\sum _{i}\mu _{i}N_{i}}$$ See more

For each thermodynamic potential, there are thermodynamic variables that need to be held constant to specify the potential value at a … See more

We can use the above equations to derive some differential definitions of some thermodynamic parameters. If we define Φ to stand for any of … See more

Again, define xi and yi to be conjugate pairs, and the yi to be the natural variables of the internal energy. Since all of the natural variables of … See more