Question

What is meant by the statement "variation of heat capacity of solids as a function of temperature"?

Hint: This was a phenomenon which the classical phisics wave nature of light could not explain.

Answer 1

Heat capacity of a solid is the amount of heat required to increase its temperature by unity. The temperature depends on the vibrations of the particles of the body. When you give heat to a body, no work being done on/by it, the heat given equals the increase in its internal energy. How does this occur? The net energy of the mechanical particles in the system increases. The potential and kinetic energies both increase. How much which will increase for same amount of heat input, depends on the temperature. And since temperature is the measure of the kinetic energy, the heat capacity comes to vary with temperature.
Now, for an analysis of the exact nature of this variation, you need quantum mechanics. Also, the interactions between these particles being electromagnetic in nature, the emit electromagnetic waves when they oscillate. This is the heat radiation.
Thus, there is no reason why you can expect EM wave theory to explain variation of Heat Capacity of solids with temperature.