Example Problem with Complete Solution

4B-3 : Surface Temperature of a Spacecraft 4 pts
The International Space Station (ISS) absorbs solar radiation and radiates heat into space. At steady-state, the radiation emitted is equal to the solar energy absorbed. 
The surface of the ISS has an emissivity of 0.74 and an absorptivity of 0.25 for solar radiation. Incident solar radiation on the ISS is 1500 W/m2. Determine the surface temperature of the ISS at steady-state.
Read : The key to solving this problem is to recognize that solar radiation is incident on the spacecraft and the spacecraft radiates heat to deep space, which is at an average temperature of 3 K.
Given: Qsun 1500 W/m2 Tspace 3 K
a 0.25 s 5.67E-08 W/m2-K4
e 0.74
Find: Tsurface ??? oC
1 - Incident solar radiation on the spacecraft is uniform.
2 - The spacecraft radiates thermal energy to its surroundings which are at an average temperature of 3 K.
Equations / Data / Solve:
The spacecraft absorbs 30% of the incident radiation from the sun, because:
Eqn 1 Qin 375 W/m2
The space craft radiates to deep space and deep space radiates to the spacecraft as well.
Eqn 2
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 :
Eqn 3
Next, we can combine Eqns 2 and 3 and solve for the surface temperature of the spacecraft.
Eqn 4 Tsurface 307.47 K
Tsurface 34.32 oC
Verify: None of the assumptions can be verified from the data given in the problem statement.
Answers : Tsurface 34 oC