Question

At $273^{\circ} C, $ the emissive power of a perfect black body is R. What is its value at $ 0^{\circ} C, $ ?

• A. $ \frac{R}{4} $
• B. $ \frac{R}{16} $
• C. $ \frac{R}{2} $
• D. None of the above

Answer 1

Answer: (B)

From Stefans law, the total radiant energy emitted per second per unit surface area of a black body is proportional t6 the fourth power of the absolute temperature (T) of the body.
$\therefore E=\sigma T^{4}$
where, $\sigma$ is Stefan's constant.
Given, $E_{1}=R,\, T_{1}=273^{\circ} C$
$=273+273=546\, K$
$T_{2}=0^{\circ} C =273\, K$
$\therefore \frac{E_{1}}{E_{2}} =\frac{T_{1}^{4}}{T_{2}^{4}}$
$\Rightarrow E_{2} =\frac{T_{2}^{4}}{T_{1}^{4}} E_{1}$
$\Rightarrow E_{2} =\frac{(273)^{4}}{(546)^{4}} R$
$\therefore E_{2}=\frac{R}{16}$