Question

Parallel rays of light of intensity I=912 Wm$^{-2}$ are incident on a spherical black body kept in surroundings of temperature 300 K . Take Stefan constant $\sigma =5.7 \times 1^{-8} Wm ^{-2} K^{-4}$ and assume that the energy exchange with the surroundings is only through radiation The final steady state temperature of the black body is close to

• A. 330 K
• B. 660 K
• C. 990 K
• D. 1550 K

Answer 1

Answer: (A)

330 K

Answer 2

In steady state Energy incident per second = Energy radiated per second $\therefore \, \, I \pi R^2 =\sigma (T^4 -T_0^4) 4\pi R^2 \, \, \Rightarrow \, \, \, i = \sigma (T^4 -T_0^4)4$ $\Rightarrow \, \, \, \, \, \, T^4 -T_0^4 =40 \times 10^8 \, \, \Rightarrow \, \, \, T^4 -81 \times 10^8 =40 \times 1^8$ $\Rightarrow \, \, \, \, \, T^4 = 121 \times 10^8 \, \, \Rightarrow \, \, \, T=330 K$