Thermodynamics A space probe that has travelled very far from the Earth and Sun

Question

Thermodynamics

A space probe that has travelled very far from the Earth and Sun and is now in deep space. It has a 100 W thermal energy source. The surface of the probe is perfectly black and has an area of 6.0 m^2. The power source is internal to the space probe. What is the (steady state) temperature of the space probe as described above? What is the temperature of the space probe if a thin thermal shield (also black) surrounds the space probe? The shield is attached close to the probe's surface by a number of thermally insulating supports. Between the shield and the probe's surface is a vacuum.

Explanation / Answer

a) Q = sigma*A*T^4

where sigma = bolzman constant

A = area , T = temperature in kelvin

100 = 5.67*10^-8*6*T^4

T = 130.93 K

the steady state temperature of the space probe is 130.93 K

b) for the second part

2*Q = sigma*A*T^4

2*100 = 5.67*10^-8*6*T^4

T = 155.71 K

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