Question

A spherical interplanetary probe of 0.5-m diameter contains electronics that dissipate 150 W. If the probe surface has an emissivity of 0.8 and the probe does not receive radiation from other surfaces, as, for example, from the sun, what is its surface temperature?

Answer 1

Answer:254.7 K

Explanation:

Given

diameter(d)=0.5 m

Energy dissipate$(E_g)$=150 w

emissivity$(\epsilon )$=0.8

According to conservation of Energy Energy generation and energy dissipation at any instant is given by

$-E_{out}+E_g=0$

$E_g=\epsilon A_s\sigma T^4$

$T=\frac{E_g}{\epsilon A_s\simga }^{\frac{1}{4}}$

$T=(\frac{150}{0.8\pi (0.5)^2\times 5.67\times 10^{-8}})^{\frac{1}{4}}$

T=254.7 K