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 $u(\omega )={\frac {k_{B}T}{\pi ^{2}c^{3}}}\omega ^{2}$.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 ____