Two spherical black bodies of radii ' r₁ ' and ' r₂ ' at temperature ' T₁ ' and ' T₂ ' respectively radiate power in the ratio 1: 2 Then r₁: r₂ is (a) 1/2((T₂)/(T₁))⁴ (b) 1/√(2)((T₂)/(T₁))² (c) 2((T₁)/(T₂))⁴ (d) 2((T₁)/(T₂))²

Answer: (b). P ∝ r² T⁴, so (P₁)/(P₂) = (r₁² T₁⁴)/(r₂² T₂⁴) = 1/2. ((r₁)/(r₂))² = 1/2((T₂)/(T₁))⁴ (r₁)/(r₂) = 1/√(2)((T₂)/(T₁))² So the answer is (b).

Two spherical black bodies of radii ' r₁ ' and ' r₂ ' at temperature… | MHT CET 2023 (11 May, Shift 1)

Q81MHT CET 2023 · 11 MAY · SHIFT 1Medium

Thermal Radiation: Black Body, Stefan & Wien

Two spherical black bodies of radii ' $r_1$ ' and ' $r_2$ ' at temperature ' $T_1$ ' and ' $T_2$ ' respectively radiate power in the ratio $1 : 2$ Then $r_1 : r_2$ is

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Answer: (b)

$P \propto r^2 T^4$ , so $\frac{P_1}{P_2} = \frac{r_1^2 T_1^4}{r_2^2 T_2^4} = \frac{1}{2}$ .
$\left(\frac{r_1}{r_2}\right)^2 = \frac{1}{2}\left(\frac{T_2}{T_1}\right)^4$
$\frac{r_1}{r_2} = \frac{1}{\sqrt{2}}\left(\frac{T_2}{T_1}\right)^2$
So the answer is (b).

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2023 (11 May, Shift 1)

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