Determine the minimum work per unit of heat transfer from the source reservoir that is required to drive a heat pump with thermal energy res

Question

Determine the minimum work per unit of heat transfer from the source reservoir that is required to drive a heat pump with thermal energy reservoirs at 460 K and 540 K.

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Thiên Hương 4 years 2021-09-01T21:10:29+00:00 1 Answers 138 views 0

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  1. ngochoa
    0
    2021-09-01T21:12:11+00:00
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    Answer:

    The minimum work per unit heat transfer will be 0.15.

    Explanation:

    We know the for a heat pump the coefficient of performance (C_{HP}) is given by

    C_{HP} = \dfrac{Q_{H}}{W_{in}}

    where, Q_{H} is the magnitude of heat transfer between cyclic device and    high-temperature medium at temperature T_{H} and W_{in} is the required input and is given by W_{in} = Q_{H} - Q_{L}, Q_{L} being magnitude of heat transfer between cyclic device and low-temperature T_{L}. Therefore, from above equation we can write,

    && \dfrac{Q_{H}}{W_{in}} = \dfrac{Q_{H}}{Q_{H} - Q_{L}} = \dfrac{1}{1 - \dfrac{Q_{L}}{Q_{H}}} = \dfrac{1}{1 - \dfrac{T_{L}}{T_{H}}}

    Given, T_{L} = 460 K and T_{H} = 540 K. So,  the minimum work per unit heat transfer is given by

    \dfrac{W_{in}}{Q_{H}} = \dfrac{T_{H} - T_{L}}{T_{H}} = \dfrac{540 - 460}{540} = 0.15

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