A spherical interplanetary probe of 05 meters in diameter co

A spherical interplanetary probe of 0.5 meters in diameter contains electronics that dissipate 150 W continuously, and at a steady rate. If the probe surface has an emissivity of 0.8, and the probe does not receive any radiation from other surfaces, such as the sun, then what is its surface temperature?

Solution

Here ,

diameter , d = 0.5/2 = 0.25 m

Power , P = 150 W

emissivity , e = 0.8

let the surface temperture is T

Power = sigma * e * A * T^4

150 = 5.6703 *10^-8 * 4*pi *0.25^2 * 0.8 * T^4

solving for T

T = 255 K

the temperature of the surface is 255 K