Two bodies A and B at temperatures ' T₁ ' K and ' T₂ ' K respectively have the same dimensions. Their emissivities are in the ratio 16: 1. At T₁ = xT₂, they radiate the same amount of heat per unit area per unit time. The value of x is (a) 8 (b) 4 (c) 2 (d) 0.5

Answer: (d). Same heat per unit area per unit time: e₁ T₁⁴ = e₂ T₂⁴. ((T₁)/(T₂))⁴ = (e₂)/(e₁) = 1/16 (T₁)/(T₂) = 1/2 ⇒ x = 0.5 So the answer is (d) 0.5.

Two bodies A and B at temperatures ' T₁ ' K and ' T₂ ' K respectively… | MHT CET 2025 (22 Apr, Shift 2)

Q46MHT CET 2025 · 22 APR · SHIFT 2Medium

Thermal Radiation: Black Body, Stefan & Wien

Two bodies A and B at temperatures ' $T_1$ ' K and ' $T_2$ ' K respectively have the same dimensions. Their emissivities are in the ratio $16 : 1$ . At $T_1 = xT_2$ , they radiate the same amount of heat per unit area per unit time. The value of $x$ is

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Answer: (d)

Same heat per unit area per unit time: $e_1 T_1^4 = e_2 T_2^4$ .
$\left(\dfrac{T_1}{T_2}\right)^4 = \dfrac{e_2}{e_1} = \dfrac{1}{16}$
$\dfrac{T_1}{T_2} = \dfrac{1}{2} \Rightarrow x = 0.5$
So the answer is (d) 0.5.

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Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2025 (22 Apr, Shift 2)

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