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Two Carnot engines working in series

This type of question, asked 3 times: 2021 Paper 17, 27 Jul 2022, 28 Jan 2025. All 3 questions below, oldest first.

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  1. Question 1

    2021 Paper 17

    10
    Two Carnot engines A and BB operate in series such that engine AA absorbs heat at T1T_{1} and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T3T_{3}. When workdone in both the cases is equal, the value of TT is:

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  2. Question 2

    27 Jul 2022

    98
    In 1st 1^{\text{st~}} case, Carnot engine operates between temperatures 300 K300\text{ }K and 100 K100\text{ }K. In 2nd 2^{\text{nd~}} case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2nd 2^{\text{nd~}} case) will be:

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  3. Question 3

    28 Jan 2025

    7
    A Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines - engine E1E_{1} works between 473 K to 373 K and engine E2E_{2} works between 373 K to 273 K . If η12\eta_{12}, η1\eta_{1} and η2\eta_{2} are the efficiencies of the engines E,E1E,E_{1} and E2E_{2}, respectively, then

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