Grand canonical partition function

1.

Hill, Introduction to Statistical Thermodynamics, problem 2-5. What
general thermodynamic principle could be used to justify the second
equality without using statistical thermodynamics?



2.

For the grand canonical ensemble we’ve obtained two expressions for
the pressure:







the grand canonical partition function. Check that the

derivative does not give the first expression exactly.

Nonetheless, the pressure calculated in the two ways agree--at

least to any reasonable accuracy. Why? (HINT: consider what

happens for a large system).



3.

Hill, Introduction to Statistical Thermodynamics, problem 3-1.



4.

Hill, Introduction to Statistical Thermodynamics, problem 3-7.