Thermodynamics, Statistical Physics, and Quantum Mechanics

212 SOLUTIONS

From (S.4.92.3)

and

SinceVis proportional to

The relativefluctuation isgiven by

4.93 Energy Fluctuation in Canonical Ensemble

(Colorado, Stony Brook)

Firstsolution: For a canonical ensemble:

where On the other hand,

Differentiating(S.4.93.2), we obtain

By inspecting (S.4.93.1)–(S.4.93.3), we find that

Now, the heat capacity at constant volume, is given by