Figure 7.20 is a plot of (C_{V}(T)) against (T) for a solid, the limiting value (C_{V}(infty)) being

Question:

Figure 7.20 is a plot of $C_{V}(T)$ against $T$ for a solid, the limiting value $C_{V}(\infty)$ being the classical result $3 N k$. Show that the shaded area in the figure, namely
\[
\int_{0}^{\infty}\left\{C_{V}(\infty)-C_{V}(T)ight\} d T
\]
is exactly equal to the zero-point energy of the solid. Interpret the result physically.

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