An artificial satellite carries electronic equipment that continuously produces of…

PHYSICS · Subjective · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

An artificial satellite carries electronic equipment that continuously produces

4.0\,\text{kW}

of waste heat. To maintain proper functioning, a flat radiator panel on the outside of the satellite must dissipate this energy by thermal radiation. Assume the panel acts as a perfect black surface and is to be maintained at a steady temperature of

320\,\text{K}

. (i) Derive an expression for the minimum surface area

A

of the radiator required to dispose of a steady power

P

at temperature

T

. (ii) Using the expression, calculate the numerical value of

A

needed for

P = 4.0\,\text{kW}

T = 320\,\text{K}

. (iii) If mission constraints later require the operating temperature of the panel to be lowered to

280\,\text{K}

while the waste power remains the same, by what factor must the surface area be increased?

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