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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