Two spherical black bodies of radii ' R₁ ' and ' R₂ ' and with surface temperature ' T₁ ' and ' T₂ ' respectively radiate the same power. The ratio of ' R₁ ' to ' R₂ ' will be (a) ((T₂)/(T₁))⁴ (b) ((T₂)/(T₁))² (c) ((T₁)/(T₂))⁴ (d) ((T₁)/(T₂))²

Answer: (b). Power P = 4π R² σ T⁴; equal power gives R₁² T₁⁴ = R₂² T₂⁴. (R₁)/(R₂) = ((T₂)/(T₁))² So the answer is (b).

Two spherical black bodies of radii ' R₁ ' and ' R₂ ' and with… | MHT CET 2024 (3 May, Shift 1)

Q65MHT CET 2024 · 3 MAY · SHIFT 1Medium

Thermal Radiation: Black Body, Stefan & Wien

Two spherical black bodies of radii ' $R_1$ ' and ' $R_2$ ' and with surface temperature ' $T_1$ ' and ' $T_2$ ' respectively radiate the same power. The ratio of ' $R_1$ ' to ' $R_2$ ' will be

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Answer: (b)

Power $P = 4\pi R^2 \sigma T^4$ ; equal power gives $R_1^2 T_1^4 = R_2^2 T_2^4$ .
$\dfrac{R_1}{R_2} = \left(\dfrac{T_2}{T_1}\right)^2$
So the answer is (b).

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2024 (3 May, Shift 1)

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