Rate of radiation by a black body is 'R' at temperature 'T'. Another body has same area but emissivity is 0…

Rate of radiation by a black body is 'R' at temperature 'T'. Another body has same area but emissivity is 0.2 and temperature 3 T . Its rate of radiation is
  1. $\quad(162) \mathrm{R}$
  2. $\quad(81) \mathrm{R}$
  3. $\quad(16.2) \mathrm{R}$
  4. $(8.1) \mathrm{R}$

Solution

Rate of radiation for blackbody, $\mathrm{R}=\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\right)_1=\mathrm{eA} \sigma \mathrm{~T}^4=\mathrm{A} \sigma \mathrm{~T}^4 \quad \ldots(\because \mathrm{e}=1)$
For another body, $\begin{aligned} \left(\frac{\mathrm{dQ}}{\mathrm{dt}}\right)_2 & =\mathrm{e}^{\prime} \mathrm{A}^{\prime} \sigma\left(\mathrm{T}^{\prime}\right)^4 \\ & =0.2 \mathrm{~A} \sigma(3 \mathrm{~T})^4 \\ & =16.2 \mathrm{~A} \sigma \mathrm{~T}^4 \\ & =16.2\left(\frac{\mathrm{dQ}}{\mathrm{dt}}\right)_1=16. 2 \mathrm{R} \end{aligned}$

Asked in: MHT CET 2024 (10 May Shift 2)

Practice more Kinetic Theory of Gases and Radiation questions on Aicharya