Apply the result of obtain a formula for the standard

Chapter 6, Problem 19P

(choose chapter or problem)

Problem 19P

Apply the result of Problem to obtain a formula for the standard deviation of the energy of a system of N identical harmonic oscillators (such as in an Einstein solid), in the high-temperature limit. Divide by the average energy to obtain a measure of the fractional fluctuation in energy. Evaluate this fraction numerically for N = 1, 104 , and 1020. Discuss the results 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