Isobaric-Isothermal Ensemble

In this ensemble a certain number of molecules are kept inside a container in which it is allowed to interact with a heat reservoir of infinite pressure and temperature. It should be noted that this ensemble has a lot of significance. In most of the chemical engineering problems we observe phenomena which are at constant temperature and pressure. Let us represent the partition function by

In the same manner the probability of a microstate in isobaric-isothermal system is

It follows that

The other thermodynamic properties may be derived in a similar manner as that of canonical partition function and is thus left to the students. The entropy term obtained is given as

γ  is a constant which is a function of the reservoir. Similarly the expression for CP is