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)

$\frac{R}{16}$

Answer 2

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, $E_{1}=R,\, T_{1}=273^{\circ} C$ $=273+273=546\, K$ $T_{2}=0^{\circ} C =273\, K$ $\therefore \frac{E_{1}}{E_{2}} =\frac{T_{1}^{4}}{T_{2}^{4}}$ $\Rightarrow E_{2} =\frac{T_{2}^{4}}{T_{1}^{4}} E_{1}$ $\Rightarrow E_{2} =\frac{(273)^{4}}{(546)^{4}} R$ $\therefore E_{2}=\frac{R}{16}$