Parallel rays of light of intensity I = 912Wm–2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant s = 5.7 × 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

Engineering

Physics

Radiation

Question

Parallel rays of light of intensity I = 912Wm^–2 are incident on a spherical black body kept in surroundings of temperature 300 K. Take Stefan-Boltzmann constant s = 5.7 × 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

330 K

660 K

990 K

1550 K

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I × πR² = 4πR² σ (T⁴ – 300⁴)

$\frac{912}{4 \times 5.7}$ × 10⁹ + 300⁴ = T⁴

⇒ 4 × 10⁹ + 8.1 × 10⁹ = T⁴

121 × 10⁸ = T⁴

$\sqrt{11} \times 10^{2} = T$

T = 330 K