Problem 1:
Assume two phases to be in equilibrium namely p and q. Compute the Grand Canonical partition function of the total system.

Solution

The total  number of moles of the system is :

Now writing the total partition function as the product of two individual partition function we get

 

"The write up for this portion has been adapted from the book titled "An Introduction to Applied Statistical Thermodynamics” authored by Stanley I Sandler and published by Wiley,Hoboken,NJ,2010"