Quantum Mechanics/Blackbody Radiation

Black-body radiation is the thermal electromagnetic radiation within or surrounding a body in thermodynamic equilibrium with its environment, or emitted by a black body (an opaque and non-reflective body). It has a specific spectrum and intensity that depends only on the body's temperature, which is assumed for the sake of calculations and theory to be uniform and constant.

Considering a cavity at temperature $$T$$ in radiation equilibrium, the volume of the cavity is $$V=L^3$$, the energy density (energy per unit volume and frequency) $$u(\omega)$$. Here $$u(\omega)\mathrm{d}\omega$$expresses the energy per unit volume in the interval$$ [\omega,\omega+\mathrm{d}\omega]$$. Classically, the situation is described by the Rayleigh–Jeans law $$u(\omega)=\frac{k_BT}{\pi^2c^3}\omega^2$$.One can easily make this plausible by considering standing plane waves in a cavity with reflecting metal walls. Where L is defined as ____ and Where u($$\omega$$) is defined as ____ and Where k is defined as ____ and Where B is defined as ____ and Where c is defined as ____ and Where $$\omega$$ is defined as ____