A cavity is held at

PHYSICS · Multi-part · Fermi University Physics · Quantum Mechanics · Origins of quantum theory · Origins of quantum theory

Thermal Physics, Ch Photons and phonons: blackbody radiation and the heat capacity of solids

Problem

A cavity is held at

T = 300\,\mathrm{K}

. Consider the radiation at the frequency

\nu = 1.00\times10^{12}\,\mathrm{Hz}

(

1.00\,\mathrm{THz}

). ((a)) Evaluate the spectral energy density

u(\nu,T)

from the Planck spectrum, in

\mathrm{J\,m^{-3}\,Hz^{-1}}

. ((b)) Evaluate it from the Rayleigh-Jeans form, in which every mode holds

k_BT

. ((c)) By what percentage does the Rayleigh-Jeans value exceed the Planck value? Take

h = 6.626\times10^{-34}\,\mathrm{J\,s}

k_B = 1.381\times10^{-23}\,\mathrm{J\,K^{-1}}

and

c = 2.998\times10^{8}\,\mathrm{m\,s^{-1}}