Question 2.165: Radiation pressure. One may think of radiation as a gas of p...
Radiation pressure.
One may think of radiation as a gas of photons and apply many of the results from kinetic theory and thermodynamics to the radiation gas.
(a) Prove that the pressure exerted by an isotropic radiation field of energy density u on a perfectly reflecting wall is p = u/3.
(b) Blackbody radiation is radiation contained in, and in equilibrium with, a cavity whose walls are at a fixed temperature T. Use thermodynamic arguments to show that the energy density of blackbody radiation depends only on T and is independent of the size of the cavity and the material making up the walls.
(c) From (a) and (b) one concludes that for blackbody radiation the pressure depends only on the temperature, p = p(T), and the internal energy U is given by U = 3p(T)V where V is the volume of the cavity.
Using these two facts about the gas, derive the functional form of p(T), up to an unspecified multiplicative constant, from purely thermodynamic reasoning.
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