Thermodynamic Potentials
Since the dimensionless heat capacity at constant pressure is a constant we can express the entropy in what will prove to be a more convenient form:
where is now the undetermined constant. The chemical potential of the ideal gas is calculated from the corresponding equation of state (see thermodynamic potential):
where G is the Gibbs free energy and is equal to so that:
The thermodynamic potentials for an ideal gas can now be written as functions of T, V, and N as:
The most informative way of writing the potentials is in terms of their natural variables, since each of these equations can be used to derive all of the other thermodynamic variables of the system. In terms of their natural variables, the thermodynamic potentials of a single-species ideal gas are:
In statistical mechanics, the relationship between the Helmholtz free energy and the partition function is fundamental, and is used to calculate the thermodynamic properties of matters; see configuration integral for more details.
Read more about this topic: Ideal Gas