Problem 6.191

Fig. 6.10 shows heat capacity of a crystal vs temperature in terms of the Debye theory. Here $C_{c l}$ is classical heat capacity, $\Theta$ is the Debye temperature. Using this plot, find: (a) the Debye temperature for silver if at a temperature $T=65 \mathrm{~K}$ its molar heat capacity is equal to $15 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})$ (b) the molar heat capacity of aluminium at $T=80 \mathrm{~K}$ if at $T=250 \mathrm{~K}$ it is equal to $22.4 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K})$ (c) the maximum vibration frequency for copper whose heat capacity at $T=125 \mathrm{~K}$ differs from the classical value by $25 \%$.