Heat and Thermodynamics 3 Question 5
5. 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 $\sigma=5.7 \times 10^{-8} Wm^{-2} K^{-4}$ 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
(2014 Main)
(a) $330 K$
(b) $660 K$
(c) $990 K$
(d) 1550
Show Answer
Solution:
- In steady state
Radiation
Energy incident per second $=$ Energy radiated per second
$$ \begin{aligned} & \therefore I \pi R^{2}=\sigma\left(T^{4}-T _0^{4}\right) 4 \pi R^{2} \Rightarrow I=\sigma\left(T^{4}-T _0^{4}\right) 4 \\ & \Rightarrow \quad T^{4}-T _0^{4}=40 \times 10^{8} \Rightarrow T^{4}-81 \times 10^{8}=40 \times 10^{8} \\ & \Rightarrow \quad T^{4}=121 \times 10^{8} \Rightarrow T \approx 330 K \end{aligned} $$
