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30 August, 01:19

A Carnot heat engine operates between 1000 deg F and 50 deg F, producing 120 BTU of work. What is the heat input to the engine?

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  1. 30 August, 01:49
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    184.6 BTU

    Explanation:

    The thermal efficiency for a Carnot cycle follows this equation:

    η = 1 - T2/T1

    Where

    η: thermal efficiency

    T1: temperature of the heat source

    T2: temperature of the heat sink

    These temperatures must be in absolute scale:

    1000 F = 1460 R

    50 F = 510 R

    Then

    η = 1 - 510/1460 = 0.65

    We also know that for any heat engine:

    η = L / Q1

    Where

    L: useful work

    Q1: heat taken from the source

    Rearranging:

    Q1 = L / η

    Q1 = 120 / 0.65 = 184.6 BTU
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