Question

Compare the rates of emission of heat by a blackbody maintained at 727 ºC and at 227ºC, if the blackbodies are surrounded by an enclosure (black) at 27 ºC. What would be the ratio of their rates of loss of heat ? 

Answer 1

Given: T₁ = 273 + 727 = 1000 K, T₂ = 273 + 227 = 500 K, T₀ = 273 + 27 = 300 K

i) The rate of emission of heat,

dQ/dt = σAT⁴

we assume that the surface area A is the same for the two bodies.

\(\frac{(dQ/dt)_1}{(dQ/dt)_2}\) = \(\frac{T_1^4}{T_2^4}\)

= \((\frac{T_1}{T_2})^4\)

=\((\frac{1000}{500})^4\) = 2⁴ = 16

i) The rate of loss of heat,

dQ'/dt = σA( T⁴ - T₀⁴ )

\(\frac{(dQ'/dt)_1}{(dQ/dt)_2}\) = \(\frac{T_1^4-T_0^4}{T_2^4-T_0^4}\)

= \(\frac{10^{12}-81×10^8}{625×10^8-81×10^8}\)

= 18.23