[UPSC CSE 2020] Black Body Radiation (Q441, 20M)

A historic failure of Classical Physics is its inability to describe the electromagnetic radiation emitted from a black body. Consider a simple model for an ideal black body consisting of a cubic cavity of side L with a small hole on one side. Assuming the classical equipartition of energy, derive an expression for the average energy per unit volume and unit frequency range. In what way does this result deviate from actual observation? What is this law called?

Repeat the calculations now using quantum idea to obtain an expression that properly accounts for the observed spectral distribution. Find the temperature dependence of the total power emitted from the hole.