A spacecraft dumps its waste heat through a flat radiator panel of area per face

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 spacecraft dumps its waste heat through a flat radiator panel of area

1.8\,\mathrm{m^2}

per face, held at

310\,\mathrm{K}

and radiating from both faces. The panel is shaded from the Sun and faces deep space, which may be taken as a black enclosure at

3\,\mathrm{K}

. Treat the panel as a black surface. ((a)) Estimate the power the panel rejects. ((b)) An instrument box inside the craft encloses a cavity of

0.25\,\mathrm{L}

310\,\mathrm{K}

. Estimate how many electromagnetic standing-wave modes that cavity holds below

10\,\mathrm{THz}

, counting both polarisations. Two significant figures are enough. Use

\sigma_{\rm SB} = 5.67\times10^{-8}\,\mathrm{W\,m^{-2}\,K^{-4}}

and

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