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?

Respuesta :

Answer with Explanation:

We are given that

Irradiation,G=6300[tex]W/m^2[/tex]

Surface A absorb.[tex]G_A=5600 W/m^2[/tex]

a.[tex]G=\sigma T^4[/tex]

[tex]T^4=\frac{G}{\sigma}[/tex]

[tex]T=(\frac{G}{\sigma})^{\frac{1}{4}}[/tex]

Where [tex]\sigma =5.67\times 10^{-8}[/tex]=Boltzman's constant

[tex]T=(\frac{6300}{5.67\times 10^{-8}})^{\frac{1}{4}}=577.4 K[/tex]

Temperature of surface =577.4 K

b.[tex]E_{in}=E_{out}[/tex]

[tex]E_{emitted}=\sigma E_A T^4[/tex]

[tex]5600=5.67\times 10^{-8}E_A(577.4)^4[/tex]

[tex]E_A=\frac{5600}{5.67\times 10^{-8}\times (577.4)^4}=0.89[/tex]

Hence, the emissivity of  surface =0.89