Two spheres S₁ and S₂ have same radii but temperatures T₁ and T₂ respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio T₁: T₂ is (a) 2: 1 (b) √(2): 1 (c) 1: √(2) (d) 1: 2

Answer: (b). Same emissive power: e₁ T₁⁴ = e₂ T₂⁴. ((T₁)/(T₂))⁴ = (e₂)/(e₁) = 4 (T₁)/(T₂) = 41/4 = √(2) So the answer is (b) √(2): 1.

Two spheres S₁ and S₂ have same radii but temperatures T₁ and T₂… | MHT CET 2024 (11 May, Shift 1)

Q60MHT CET 2024 · 11 MAY · SHIFT 1Medium

Thermal Radiation: Black Body, Stefan & Wien

Two spheres $S_1$ and $S_2$ have same radii but temperatures $T_1$ and $T_2$ respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio $T_1 : T_2$ is

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Answer: (b)

Same emissive power: $e_1 T_1^4 = e_2 T_2^4$ .
$\left(\dfrac{T_1}{T_2}\right)^4 = \dfrac{e_2}{e_1} = 4$
$\dfrac{T_1}{T_2} = 4^{1/4} = \sqrt{2}$
So the answer is (b) $\sqrt{2} : 1$ .

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