A thermodynamic potential (or more accurately, a thermodynamic potential energy) is a scalar quantity … See more

For each thermodynamic potential, there are thermodynamic variables that need to be held constant to specify the potential value at a thermodynamical equilibrium state, such as independent variables for a mathematic… See more

The definitions of the thermodynamic potentials may be differentiated and, along with the first and second laws of thermodynamics, a set of differential equations known as the fundamental equations f… 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 the thermodynamic potentials, then the above equations are of the form: … 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 thes… 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 the internal energy U are extensive quantities
it follows from … 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:
Differentiati… See more