s. The maximum absolute temperature in the cycle is 1.15 times the minimum absolute temperature, and the net power input to the cycle is 5 kW. If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, determine the ratio of the maximum to minimum pressures in the cycle

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Consider a Carnot heat pump cycle executed in a steady-flow system in the saturated mixture region using R-134a flowing at a rate of 0.264 kg/s. The maximum absolute temperature in the cycle is 1.15 times the minimum absolute temperature, and the net power input to the cycle is 5 kW. If the refrigerant changes from saturated vapor to saturated liquid during the heat rejection process, determine the ratio of the maximum to minimum pressures in the cycle.

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  • Limosa


    Answer:

    7.15

    Explanation:

    Firstly, the COP of such heat pump must be measured that is,

                  COP_{HP}=\frac{T_H}{T_H-T_L}

    Therefore, the temperature relationship, T_H=1.15\;T_L

    Then, we should apply the values in the COP.

                               =\frac{1.15\;T_L}{1.15-1}

                               =7.67

    The number of heat rejected by the heat pump must then be calculated.

                       Q_H=COP_{HP}\times W_{nst}

                              =7.67\times5=38.35

    We must then calculate the refrigerant mass flow rate.

                       m=0.264\;kg/s

                       q_H=\frac{Q_H}{m}

                             =\frac{38.35}{0.264}=145.27

    The h_g value is 145.27 and therefore the hot reservoir temperature is 64° C.

    The pressure at 64 ° C is thus 1849.36 kPa by interpolation.

    And, the lowest reservoir temperature must be calculated.

                       T_L=\frac{T_H}{1.15}

                            =\frac{64+273}{1.15}=293.04

                            =19.89\°C

    the lowest reservoir temperature = 258.703  kpa                    

    So, the pressure ratio should be = 7.15