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20 June, 22:29

At steady state, a refrigeration cycle operating between hot and cold reservoirs at 300 K and 275 K, respectively, removes energy by heat transfer from the cold reservoir at a rate of 600 kW. (a) If the cycle's coefficient of performance is 4, determine the power input required, in kW. (b) Determine the minimum theoretical power required, in kW, for any such cycle.

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  1. 20 June, 22:55
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    a) Wcycle=150KW

    b) Wcycle=54.55KW

    Explanation:

    Given dа ta:

    Hot reservoir Temp Th=300 K

    Cold reservoir Temp Tc=275 K

    Heat transfer at cold reservoir Qc=600KW

    To find out

    a) Coefficient of performance / beta actual=4

    Cycle power in KW

    b) The minimum theoretical power required Wcycle in KW

    Assumption:

    Constant average values is used.

    Solution:

    a) Actual cycle formula

    Wcycle=Qc:/beta actual

    =600/4

    =150KW

    b) maximum cycle coefficient formula

    B_{max}=Tc: (Th-Tc)

    =275: (300-275)

    =11

    For minimal theoretical power required

    /beta actual=B_{max}=11

    Actual cycle coefficient of performance can be determined by

    /beta actual=Qc:Wcycle

    Wcycle=Qc:/beta actual

    =600/11

    =54.55KW
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