Electromagnetic radiation following the Planck distribution...

Electromagnetic radiation following the Planck distribution fills a cavity of volume $V$. Initially $\omega_i$ is the frequency of the maximum of the curve of $u_i(\omega)$, the energy density per unit angular frequency versus $\omega$. If the volume is expanded quasistatically to 2 V , what is the final peak frequency $\omega_f$ of the $u_f(\omega)$ distribution curve? The expansion is adiabatic.

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Key Concepts

Planck Distribution

The Planck distribution describes the spectrum of electromagnetic radiation emitted by a blackbody in thermal equilibrium at a given temperature. It provides the energy density per unit frequency (or angular frequency) and is foundational in quantum theory, explaining how radiation is distributed over different frequencies, including the characteristic peak that shifts with temperature.

Wien's Displacement Law

Wien's displacement law states that the frequency (or wavelength) at which the emission of a blackbody is maximized is directly proportional to the temperature of the blackbody. This implies that as the temperature decreases, the peak of the emission spectrum shifts to lower frequencies, making the law essential in relating changes in thermal conditions to spectral shifts.

Adiabatic Expansion

An adiabatic expansion refers to a process in which a system expands without exchanging heat with its surroundings. In the context of radiation in a cavity, the adiabatic expansion causes the temperature of the radiation field to decrease following a specific scaling law (typically T proportional to V^(-1/3) for three-dimensional radiation in a cavity). This temperature drop, in turn, leads to a shift in the peak frequency of the radiation spectrum as dictated by Wien's displacement law.

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