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MHT CET 2023 (11 May, Shift 2) · Thermal Radiation: Black Body, Stefan & Wien

Thermal Radiation: Black Body, Stefan & Wien question from MHT CET 2023 (11 May, Shift 2)

Q75MHT CET 2023 · 11 MAY · SHIFT 2Medium

Thermal Radiation: Black Body, Stefan & Wien

Two bodies $A$ and $B$ at temperatures ' $T_1$ ' $\text{K}$ and ' $T_2$ ' $\text{K}$ respectively have the same dimensions. Their emissivities are in the ratio $1 : 3$ . If they radiate the same amount of heat per unit area per unit time, then the ratio of their temperatures $(T_1 : T_2)$ is

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Answer: (b)

Same heat per unit area per unit time: $e_1 T_1^4 = e_2 T_2^4$ .
$\left(\dfrac{T_1}{T_2}\right)^4 = \dfrac{e_2}{e_1} = 3$
$\dfrac{T_1}{T_2} = 3^{1/4}$
So the answer is (b) $3^{1/4} : 1$ .

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