Isothermal-isobaric ensemble

Finally, let us look at the ideal gas in the isothermal-isobaric ensemble. The partition function is given by

We change variables to

so that

The enthalpy is given by

which, for the ideal gas, becomes

But recall that the enthalpy is , where E is the average energy. Since E=3NkT/2, we have

This result can also be derived by considering the average volume, given by

But recall the work virial theorem, which states that

where is the instantaneous internal pressure obtained from . Thus, the appropriate form of the ideal gas law is