SATHEE: Heat and Thermodynamics 3 Question 5

Heat and Thermodynamics 3 Question 5

5. Parallel rays of light of intensity $I = 912 W m^{- 2}$ are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan constant $σ = 5.7 \times 10^{- 8} W m^{- 2} K^{- 4}$ 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) $660 K$

(d) 1550

Show Answer

Solution:

In steady state

Radiation

Energy incident per second $=$ Energy radiated per second

$\begin{aligned} ∴ I π R^{2} = σ (T^{4} - T_{0}^{4}) 4 π R^{2} \Rightarrow I = σ (T^{4} - T_{0}^{4}) 4 \\ \Rightarrow T^{4} - T_{0}^{4} = 40 \times 10^{8} \Rightarrow T^{4} - 81 \times 10^{8} = 40 \times 10^{8} \\ \Rightarrow T^{4} = 121 \times 10^{8} \Rightarrow T \approx 330 K \end{aligned}$

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Heat and Thermodynamics 3 Question 5

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