Question

A black body radiates heat energy at the rate of $2 \times 10^{5} J / s m ^{2}$ at the temperature of $127^{\circ} C$. Temperature of the black body at which rate of heat radiation $32 \times 10^{5} J / s m ^{2}$, is

• A. 400 K
• B. 600 K
• C. 800 K
• D. 200 K

Answer 1

Answer: (C)

Here, $E_{1}=2 \times 10^{5} J / s m ^{2}$,
$ T_{1}=127^{\circ} C =400 \,K$
and $E_{2}=32 \times 10^{5} J / s m ^{2}$
By Stefan's law, the rate of emission of radiated energy per unit area per unit time is $E=\sigma T^{4}$
$\therefore \frac{E_{2}}{E_{1}}=\frac{T_{2}^{4}}{T_{1}^{4}}$ or
$\frac{T_{2}}{T_{1}}=\left(\frac{E_{2}}{E_{1}}\right)^{1 / 4}=\left(\frac{32 \times 10^{5}}{2 \times 10^{5}}\right)^{1 / 4}=2$
or $T_{2}=2 \times T_{1}=2 \times 400=800\, K$