A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ic

Question

A Carnot heat engine uses a hot reservoir consisting of a large amount of boiling water and a cold reservoir consisting of a large tub of ice and water. In 5 minutes of operation of the engine, the heat rejected by the engine melts a mass of ice equal to 3.30×10−2 kg . Throughout this problem use Lf=3.34×105J/kg for the heat of fusion for water.A) During this time, how much work W is performed by the engine?

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Lệ Thu 3 years 2021-08-30T16:47:03+00:00 1 Answers 9 views 0

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    2021-08-30T16:48:08+00:00

    Answer:

    W=4037.36\ J

    Explanation:

    Given:

    mass of ice melted, m=3.3\times10^{-2}\ kg

    time taken by the ice to melt, t=5\ min=300\ s

    latent heat of the ice, L=3.34\times 10^5\ J

    Now the heat rejected by the Carnot engine:

    Q_R=m.L

    Q_R=0.033\times 3.34\times 10^5

    Q_R=11022\ J

    Since we have boiling water as hot reservoir so:

    T_H=373\ K

    The cold reservoir is ice, so:

    T_L=273\ K

    Now the efficiency:

    \eta=1-\frac{T_L}{T_H}

    \eta=1-\frac{273}{373}

    \eta=26.81\%

    Now form the law of energy conservation:

    Heat supplied:

    Q_S-W=Q_R

    where:

    Q_S= heat supplied to the engine

    Q_S-\eta\times Q_S=Q_R

    Q_S(1-\eta)=Q_R

    Q_S=\frac{11022}{1-0.2681}

    Q_S=15059.36\ J

    Now the work done:

    W=Q_S-Q_R

    W=15059.36-11022

    W=4037.36\ J

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