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 2100 W/m^2, determine the surface temperature of the spacecraft when the radiation emitted equals the solar energy absorbed. The surface temperature of the spacecraft when the radiation emitted equals the solar energy absorbed.

Answer 1

Answer:

Explanation:

Given

emmisivity of spacecraft $\epsilon =0.6$

absorptivity $\alpha =0.2$

Solar radiation incident $q_{rad}=2100\ W/m^2$

heat Absorbed by  spacecraft is

$Q_{absorbed}=\alpha A_sq_{rad}$

where $A_s=$Surface area of Sphere

$Q_{absorbed}=0.2\times A_s\times 2100$

$Q_{absorbed}=420A_s$

Radiation emitted by spacecraft

$Q=\epsilon \sigma A_sT^4$

When the radiation emitted equals to the solar energy absorbed

$Q_{absorbed}=Q$

$420A_s=\epsilon \sigma A_sT^4$

$420=0.6\times 5.67\times 10^{-8}\times T^4$

$T_s=3.333\times 100=333.33\ K$