and that this is called the "condition for an exact differential".
Maxwell's equationsSee main: Maxwell's relations
The application of the condition for an
exact differential for functions of two variables that are already known to exist or be actual functions, such as
internal energy U,
enthalpy H,
Helmholtz energy A, and
Gibbs energy G, gives the quick derivation of what are called "Maxwell's equations". [2] In short, applying the results of the condition for an exact differential to the four exact differentials
dU,
dH,
dA, and
dG, gives the following relations as tabulated below to the right:
Potential function
|
| Relation
|
dU = T dS – P dV | hence |  |
dH = T dS + V dP
| hence |  |
dA = –P dV – S dT
| hence |  |
dG = dH – S dT
| hence |  |