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The outer surface of a spacecraft in space has an emissivity of 0.6 and an absorptivity of 0.2 for solar radiation. If solar radiation is incident on the spacecraft at a rate of 1000 W/m2 , determine the surface temperature of the spacecraft when the radiation emitted equals the solar energy absorbed.

Respuesta :

Hashirriaz830

Answer:

[tex]T_{surf} =[/tex]3.9°C

Explanation:

solution:

we express the surface temperature from the quality of the emitted and absorbed heat rates:

[tex]Q_{abs} =Q_{em} \\\[/tex]

[tex]\alpha Q_{inc}=[/tex]εσA[tex]T^{4} _{surf}[/tex]

[tex]T_{surf} =[/tex][tex]\sqrt[4]{}[/tex][tex]\alpha[/tex]/εσ*[tex]\frac{Q_{inc} }{A}[/tex]........................(1)

where

[tex]\alpha[/tex]=0.2

ε=0.6

A=5.67*10^-8 W/m^2K^4

[tex]Q_{inc}[/tex]= 1000 W/m^2

now putting these value in eq 1

[tex]T_{surf} =[/tex]3.9°C

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