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Engine efficiency rises when the sink temperature is lowered by a given amount: find the source and sink temperatures

The same question, asked 5 times: 15 May 2023 S2*, 21 Apr 2025 S1*, 21 Apr 2025 S2*, 11 Apr 2026 S2*, 17 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    15 May 2023 S2

    37
    Heat engine operating between temperature T1T_1 and T2T_2 has efficiency 16\frac{1}{6}. When T2T_2 is lowered by 62 K, its efficiency increases to 13\frac{1}{3}. Then T1T_1 and T2T_2 respectively are

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  2. Question 2

    21 Apr 2025 S1

    40
    An engine operating between temperatures T1T_{1} and T2T_{2} has efficiency 15\frac{1}{5}. When T2T_{2} is lowered by 45 K , its efficiency becomes 12\frac{1}{2}. Temperatures T1T_{1} and T2T_{2} are respectively

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  3. Question 3

    21 Apr 2025 S2

    21
    A Carnot engine has efficiency 16\frac{1}{6}. It becomes 13\frac{1}{3}, when the temperature of sink is lowered by 57 K . The temperature of the source is

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  4. Question 4

    11 Apr 2026 S2

    116
    Carnot engine operating between temperatures T1T_1 and T2T_2 has efficiency 0.20.2. When T2T_2 is lowered by 4545 K, its efficiency becomes 0.50.5. Temperatures T1T_1 and T2T_2 are respectively

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  5. Question 5

    17 Apr 2026 S2

    114
    A carnot engine having efficiency 16\dfrac{1}{6}, operates between the source temperature THT_H and the sink temperature TCT_C. Its efficiency increases to 13\dfrac{1}{3}, when TCT_C is decreased by 64 K. The temperatures THT_H and TCT_C are repectively

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