The International
Space Station (ISS) absorbs solar radiation and radiates heat into space. At steadystate, 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/m^{2}. Determine the surface temperature of the ISS
at steadystate. 





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. 







Diagram: 


Given: 
Q_{sun} 
1500 
W/m^{2} 

T_{space} 
3 
K 


a 
0.25 


s 
5.67E08 
W/m^{2}K^{4} 


e 
0.74 







Find: 
T_{surface} 
??? 
^{o}C 


Assumptions: 


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 

Q_{in} 
375 
W/m^{2} 



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
steadystate 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 

T_{surface} 
307.47 
K 



T_{surface} 
34.32 
^{o}C 










^{} 

Verify: 
None of the
assumptions can be verified from the data given in the problem statement. 












Answers : 
T_{surface} 
34 
^{o}C 

















