11-52 11-66 A two-stage cascade refrigeration cycle with a flash chamber with refrigerant-134a as the working fluid is considered. The mass flow rate of the refrigerant through the high-pressure compressor, the rate of refrigeration, the COP are to be determined. Also, the rate of refrigeration and the COP are to be determined if this refrigerator operated on a single-stage vapor-compression cycle under similar conditions. Assumptions 1 Steady operating conditions exist. 2 Kinetic and potential energy changes are negligible. Analysis (a) From the refrigerant-134a tables (Tables A-11 through A-13) h1 h g @ 10C 244.51 kJ/kg s1 s g @ 10C 0.9377 kJ/kg.K P2 450 kPa h2 s 261.07 kJ/kg s 2 s1 C 0.86 h2 s h1 h2 h1 261.07 244.51 h2 263.76 kJ/kg h2 244.51 T 1.6 MPa 4s 4 5 A 7 6 9 B 3 −10C 8 h3 h g @ 450 kPa 257.53 kJ/kg 2s 2 0.45 MPa 1 s h5 h f @ 1600 kPa 135.93 kJ/kg h6 h5 135.93 kJ/kg h7 h f @ 450 kPa 68.81 kJ/kg h8 h7 68.81 kJ/kg h6 135.93 kJ/kg x 6 0.3557 P6 450 kPa The mass flow rate of the refrigerant through the high pressure compressor is determined from a mass balance on the flash chamber m m 7 0.11 kg/s 0.1707 kg/s 1 x 6 1 0.3557 Also, m 3 m m 7 0.1707 0.11 0.06072 kg/s (b) The enthalpy at state 9 is determined from an energy balance on the mixing chamber: m h9 m 7 h2 m 3 h3 (0.1707 kg/s)h9 (0.11 kg/s)(263.76 kJ/kg) (0.06072 kg/s)(257.53 kJ/kg) h9 261.54 kJ/kg Then, P9 450 kPa s 9 0.9393 kJ/kg h9 261.54 kJ/kg P4 1600 kPa h4 s 288.41 kJ/kg s 4 s9 C 0.86 h4 s h9 h4 h9 288.41 261.54 h4 292.78 kJ/kg h4 261.54 PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission. 11-53 The rate of heat removal from the refrigerated space is Q L m 7 (h1 h8 ) (0.11 kg/s)(244.51 68.81)kJ/kg 19.33 kW (c) The power input and the COP are W in m 7 (h2 h1 ) m (h4 h9 ) (0.11 kg/s)(263.76 244.51)kJ/kg (0.1707 kg/s)(292.78 261.54)kJ/kg 7.45 kW COP Q L 19.33 2.59 7.45 W in (d) If this refrigerator operated on a single-stage cycle between the same pressure limits, we would have h1 h g @ 10C 244.51 kJ/kg s1 s g @ 10C 0.9377 kJ/kg.K P2 1600 kPa h2 s 287.85 kJ/kg s 2 s1 h h1 C 2s h2 h1 2 T · QH 2s · Win 1.6 MPa 3 287.85 244.51 0.86 h2 294.90 kJ/kg h2 244.51 −10C 4 · QL 1 s h3 h f @ 1600 kPa 135.93 kJ/kg h4 h3 135.93 kJ/kg Q L m (h1 h4 ) (0.1707 kg/s)(244.51 135.93)kJ/kg 18.54 kW W in m (h2 h1 ) (0.1707 kg/s)(294.90 244.51)kJ/kg 8.60 kW COP Q L 18.54 2.16 8.60 W in Discussion The cooling load decreases by 4.1% while the COP decreases by 16.6% when the cycle operates on the singlestage vapor-compression cycle. PROPRIETARY MATERIAL. © 2011 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and educators for course preparation. If you are a student using this Manual, you are using it without permission.