Question

A small surface is placed inside an isothermal enclosure. The enclosure provides an irradiation of 6300 W/m2 . The surface absorbs 5600 W/m2 . After a long time has elapsed (assume steady state): (a) What is the temperature of the surface? (b) What is the emissivity of the surface?

Answer 1

Answer with Explanation:

We are given that

Irradiation,G=6300$W/m^2$

Surface A absorb.$G_A=5600 W/m^2$

a.$G=\sigma T^4$

$T^4=\frac{G}{\sigma}$

$T=(\frac{G}{\sigma})^{\frac{1}{4}}$

Where $\sigma =5.67\times 10^{-8}$=Boltzman's constant

$T=(\frac{6300}{5.67\times 10^{-8}})^{\frac{1}{4}}=577.4 K$

Temperature of surface =577.4 K

b.$E_{in}=E_{out}$

$E_{emitted}=\sigma E_A T^4$

$5600=5.67\times 10^{-8}E_A(577.4)^4$

$E_A=\frac{5600}{5.67\times 10^{-8}\times (577.4)^4}=0.89$

Hence, the emissivity of  surface =0.89