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5 March, 03:57

First consider a Carnot engine that operates between a hot reservoir at 58°C and a cold reservoir at - 17°C. In running 24 minutes, this engine absorbs 590 J of heat from the hot reservoir. 1) How much heat does it expel to the cold reservoir?

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  1. 5 March, 06:03
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    Given that,

    Hot reservoir temperature is

    TH = 58°C

    TH = 58 + 273 = 331 K

    Cold reservoir temperature

    TC = - 17°C

    TC = - 17°C + 273 = 256K

    In 24minutes 590 J of heat was removed from hot reservoir

    t = 24mins

    t = 24 * 60 = 1440 seconds

    Then,

    Power is given as

    P = E / t

    P = 590 / 1440

    P = 0.41 W

    Since this removed from the hot reservoir, then, QH = 0.41W

    We want to find heat expelled to the cold reservoir QX

    Efficiency is given as

    η = 1 - TH/TC = 1 - QH/QC

    1 - TH/TC = 1 - QH/QC

    TH/TC = QH/QC

    Make QC subject of formula

    QC = QH * TC / TH

    QC = 0.41 * 256 / 331

    QC = 0.317 W
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