Show that when a system is in thermal and diffusive

Chapter 7, Problem 6P

(choose chapter or problem)

Problem 6P

Show that when a system is in thermal and diffusive equilibrium with a reservoir, the average number of particles in the system is

where the partial derivative is taken at fixed temperature and volume. Show also that the mean square number of particles is

Use these results to show that the standard deviation of N is

in analogy with Problem Finally, apply this formula to an ideal gas, to obtain a Simple expression for σN in terms of . Discuss your result briefly.

Problem:

Prove that, for any system in equilibrium with a reservoir at temperature T, the average value of E2 is

Then use this result and the results of the previous two problems to derive a formula for σE in terms of the heat capacity,  You should find