Question

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.

Answer 1

`T_(surf) =`3.9°C

Step-by-step explanation:

solution:

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

`Q_(abs) =Q_(em) \\\`

`\alpha Q_(inc)=`εσA
`T^(4) _(surf)`

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

where

`\alpha`=0.2

ε=0.6

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

`Q_(inc)`= 1000 W/m^2

now putting these value in eq 1

`T_(surf) =`3.9°C