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Two bodies of same size radiate equally, emissivities in a given ratio: ratio of their temperatures

The same question, asked 4 times: 4 May 2023 S2*, 11 May 2023 S1*, 11 May 2024 S2*, 22 Apr 2025 S2. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S2

    3
    Two bodies 'X' and 'Y' at temperatures 'T1T_1' K and 'T2T_2' K respectively have the same dimensions. If their emissive powers are same, the relation between their temperatures is

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  2. Question 2

    11 May 2023 S1

    4
    Two spheres S1S_1 and S2S_2 have same radii but temperatures T1T_1 and T2T_2 respectively. Their emissive power is same and emissivity in the ratio 1:4. Then the ratio T1:T2T_1 : T_2 is

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  3. Question 3

    11 May 2024 S2

    34
    Two bodies A and B at temperature 'T1T_1'K and 'T2T_2'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 (T1:T2T_1 : T_2) is

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  4. Question 4

    22 Apr 2025 S2

    47
    Two bodies A and B at temperatures ' T1T_{1} ' K and ' T2T_{2} ' K respectively have the same dimensions. Their emissivities are in the ratio 16:1. At T1=xTT_{1}= xT [T=T2T = T_{2}], they radiate the same amount of heat per unit area per unit time. The value of x is

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