Thermodynamics

622 | Thermodynamics(In practice, the working fluid of the lower cycle is at a higher pressure andtemperature in the heat exchanger for effective heat transfer.) If the mass flowrate of the refrigerant through the upper cycle is 0.05 kg/s, determine (a) themass flow rate of the refrigerant through the lower cycle, (b) the rate of heatremoval from the refrigerated space and the power input to the compressor,and (c) the coefficient of performance of this cascade refrigerator.Solution A cascade refrigeration system operating between the specifiedpressure limits is considered. The mass flow rate of the refrigerant throughthe lower cycle, the rate of refrigeration, the power input, and the COP are tobe determined.Assumptions 1 Steady operating conditions exist. 2 Kinetic and potentialenergy changes are negligible. 3 The heat exchanger is adiabatic.Properties The enthalpies of the refrigerant at all eight states are determinedfrom the refrigerant tables and are indicated on the T-s diagram.Analysis The T-s diagram of the refrigeration cycle is shown in Fig. 11–11.The topping cycle is labeled cycle A and the bottoming one, cycle B. Forboth cycles, the refrigerant leaves the condenser as a saturated liquid andenters the compressor as saturated vapor.(a) The mass flow rate of the refrigerant through the lower cycle is determinedfrom the steady-flow energy balance on the adiabatic heat exchanger,E # out E # in ¡ m # Ah 5 m # Bh 3 m # Ah 8 m # Bh 2m # A 1h 5 h 8 2 m # B 1h 2 h 3 210.05 kg>s231251.88 95.472 kJ>kg4 m # B31255.93 55.162 kJ>kg4m # B 0.0390 kg/s(b) The rate of heat removal by a cascade cycle is the rate of heat absorptionin the evaporator of the lowest stage. The power input to a cascade cycle isthe sum of the power inputs to all of the compressors:Q # L m # B 1h 1 h 4 2 10.0390 kg>s231239.16 55.162 kJ>kg4 7.18 kWW # in W # comp I,in W # comp II,in m # A 1h 6 h 5 2 m # B 1h 2 h 1 2TFIGURE 11–11T-s diagram of the cascaderefrigeration cycle described inExample 11–3.h 3 = 55.16h 7 = 95.476h 6 = 270.92 kJ/kg72 h 2 = 255.930.8 MPaA380.32 MPa 5h 8 = 95.47h 5 = 251.88B0.14 MPah 1 = 239.1641h 4 = 55.16s