The outer surface of a spacecraft in space has an emissivity of 0.72 and a solar absorptivity of 0.3. If solar radiation is incident on the spacecraft at a rate of 950 W/m2, determine the surface temperature of the spacecraft when the radiation emitted equals the solar energy absorbed.

Explanation:

solar radiation is incident on the spacecraft and the spacecraft radiates heat to deep space, which is at an average temperature of 3 K.

to find

assume that Incident solar radiation on the spacecraft is uniform.      The spacecraft radiates thermal energy to its surroundings which are at an average temperature of 3 K.

The spacecraft absorbs 30% of the incident radiation from the sun, because:

The space craft radiates to deep space and deep space radiates to the spacecraft as well.

When the temperature on the surface of the spacecraft reaches a steady-state value, there will be no net amount of heat transfer to or from the surface :

Next, we can combine Eq 2 & 3 and solve for the surface temperature of the spacecraft.

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