Tru Physics

Problem 7.6 (Schroeder’s Intro to Thermal Physics)

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Problem 7.6

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

\overline{N} = \dfrac{kT}{Z} \dfrac{\partial Z}{\partial \mu}

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

\overline{N^2} = \dfrac{(kT)^2}{Z} \dfrac{\partial^2 Z}{\partial \mu^2} .

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

\sigma_N = \sqrt{kT(\partial \overline{N} / \partial \mu)} ,

in analogy with Problem 6.18. Finally, apply this formula to an ideal gas, to obtain a simple expression for \sigma_N in terms of N. Discuss your result briefly.

Solution:

Problem 7.6 (Schroeder's Intro to Thermal Physics) 1 of 2
Problem 7.6 (Schroeder's Intro to Thermal Physics) 2 of 2

Problem 7.6 Solution (Download)

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