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-Boltzmann constant σ=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

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-Boltzmann constant σ=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 (A) 330 K (B) 660 K (C) 990 K (D) 1550 K

Tardigrade Admin · Accepted Answer

Rate of radiation energy lost by the sphere = Rate of radiation energy incident on it ⇒ σ × 4 π r2[T4-(300)4]=912 × π r2 ⇒ T=√11 × 102 ≈ 330 K

330 K

660 K

990 K

1550 K

Rate of radiation energy lost by the sphere = Rate of radiation energy incident on it ⇒σ×4πr2[T4−(300)4]=912×πr2 ⇒T=11​×102≈330K

Rate of radiation energy lost by the sphere
$=$ Rate of radiation energy incident on it
$\Rightarrow σ \times 4 π r^{2} [T^{4} - (300)^{4}] = 912 \times π r^{2}$
$\Rightarrow T = 11 \times 1 0^{2} \approx 330 K$