Section-1: Basic and Modified Vapor Compression Cycles
A carnot vapor refrigeration cycle uses R-134a as the working fluid. The refrigerant enters the condenser as saturated vapor at 30oC and leaves as saturated liquid. The evaporator operates at a temperature of -5oC. Determine, in kJ per kg of refrigerant flow, (a) the work input to the compressor, (b) the work developed by the turbine, (c) the heat transfer to the refrigerant passing through the evaporator. (d) What is the coefficient of performance of the cycle? (e) What-if-scenario: How would the answer in part (d) and (c) change if R-134a was replaced with R-12?

Answers: (a) 23.36 kJ/kg , (b) 3.36 kJ/kg , (c) 153.29 kJ/kg , (d) 7.66 , (e) 7.66, 119.43 kJ/kg
 Refrigerant R-22 is the working fluid in a Carnot vapor refrigeration cycle for which the evaporator temperature is 0oC. Saturated vapor enters the condenser at 40oC, and saturated liquid exits at the same temperature. The mass flow rate of refrigerant is 4 kg/min. Determine (a) the rate of heat transfer to the refrigerant passing through the evaporator, in kW, (b) the net power input to the cycle in kW, and (c) the coefficient of performance. (d) What-if-scenario: What would be the answer in part (a) if we change mass flow rate to 1 kg/min? Answers: (a) 9.70 kW , (b) 1.42 kW , (c) 6.83 , (d) 2.43 kW
 A Carnot vapor refrigeration cycle operates between thermal reservoirs at 40oF and 100 oF. For (a) R-12, (b) R-134a, (c) water, (d) R-22, and (e) ammonia as the working fluid, determine the operating pressures in the condenser and evaporator, in lbf/in2, and the coefficient of performance. Answers: (a) 131.83 lbf/in2; 51.64 lbf/in2; 8.3, (b) 138.87 lbf/in2; 49.87 lbf/in2; 8.3, (c) 0.95 lbf/in2; 0.12 lbf/in2; 8.3 (d) 210.54 lbf/in2; 83.15 lbf/in2; 8.3 (e) 211.86 lbf/in2; 73.28 lbf/in2 8.3
 A Carnot vapor refrigeration cycle is used to maintain a cold region at 0oF when the ambient temperature is 75oF. Refrigerant R-134a enters the condenser as saturated vapor at 100 lbf/in2. and leaves as saturated liquid at the same pressure. The evaporator pressure is 20 lbf/in2. The mass flow rate of refrigerant is 12 lbm/s. Calculate (a) the compressor and turbine power, each in Btu/min, and (b) the coefficient of performance. Answers: (a) 9993.44 btu/min ; 1679.28 btu/min , (b) 5.59
 A steady-flow Carnot refrigeration cycle uses refrigerant-134a as the working fluid. The refrigerant changes from saturated vapor to saturated liquid at 30oC in the condenser as it rejects heat. The evaporator pressure is 120 kPa. Show the cycle on T-s diagram relative to saturation lines, determine (a) the coefficient of performance, (b) the amount of heat absorbed from the refrigerated space, and (c) the net work input. Answers: (a) 4.77, (b) 143.26 kW, (c) 30.03 kW
 Refrigerant R-134a enters the condenser of a steady-flow Carnot refrigerator as a saturated vapor at 100 psia, and it leaves as saturated liquid. The heat absorption from the refrigerated space takes place at a pressure of 30 psia and the mass flow rate is 1 kg/s. (a) Show the cycle on a T-s diagram relative to saturation lines, determine (b) the coefficient of performance, (c) the quality at the beginning of the heat-absorption process, and (d) the net work input. Answers: (b) 7.42,(c) 0.22, (d) 20.99 kW,

A refrigerator uses R-12 as the working fluid and operates on an ideal vapor compression refrigeration cycle between 0.15 MPa and 1 MPa. If the mass flow rate is 0.04 kg/s, determine (a) the tonnage of the system, (b) compressor power, and (c) the COP. (d) What-if-scenario: How would the answer in part (c) change if R-12 was replaced with R-134a, a more Environmentally benign refrigerant?
Answers: (a) 1.165 tons, (b) 1.36 kW, (c) 3.01, (d) 3.33
 A refrigerator uses R-134a as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.15 and 1 MPa. For a cooling load of 10 kW, determine the mass flow rate of the refrigerant through the evaporator. Answers: 0.0938 kg/s
 Refrigerant R-134a enters the compressor of an ideal vapor-compression refrigeration system as saturated vapor at -10oC and leaves the condenser as saturated liquid at 35oC. For a cooling capacity of 20 kW, determine (a) the mass flow rate, (b) the compressor power in kW, and (c) the coefficient of performance. Answers: (a) 0.1397 kg/s, (b) 4.31 kW , (c) 4.64
 A refrigerator uses R-12 as the working fluid and operates on an ideal vapor-compression refrigeration cycle between 0.15 and 0.8 MPa. The mass flow rate of the refrigerant is 0.04 kg/s. (a) Show the cycle on a T-s diagram with respect to saturation lines. Determine (b) the rate of heat removal from the refrigerated space and the power input to the compressor, (c) the rate of heat rejection to the environment, and (d) the coefficient of performance. (e) What-if-scenario: How would the answer in part (b) change if the mass flow rate was doubled?. Answers: (b) 4.45 kW ; 1.19 kW, (c) 5.64 kW (d) 3.76 (e) 8.91 kW ; 2.37 kW
 An ideal vapor-compression refrigeration cycle operates at steady state with Refrigerant R-134a as the working fluid. Saturated vapor enters the compressor at -5oC, and saturated liquid leaves the condenser at 35oC. The mass flow rate of refrigerant is 5 kg/min. Determine (a) the compressor power in kW, (b) the refrigerating capacity, in tons, and (c) the coefficient of performance. (d) What-if-scenario: How would the COP change if the condenser operated at 50 oC? Answers: (a) 2.04kW, (b) 3.61 ton, (c) 6.22, (d) 4.05
 A large refrigeration plant is to be maintained at -18oC, and it requires refrigeration at a rate of 200 kW. The condenser of the plant is to be cooled by liquid water, which experiences a temperature rise of 8oC as it flows over the coils of the condenser. Assuming the plant operates on the ideal vapor-compression cycle using refrigerant-134a between the pressure limits of 120 and 700 kPa, determine (a) the mass flow rate of the refrigerant, (b) the power input to the compressor, and (c) the mass flow rate of cooling water. Image of a Refrigeration plant Answers: (a) 1.36 kg/s , (b) 49.65 kW , (c) 7.41 kg/s
 An ideal vapor-compression refrigeration system operates at steady state with Refrigerant R-12 as the working fluid. Superheated vapor enters the compressor at 25 lbf/in2, 10oF, and saturated liquid leaves the condenser at 200 lbf/in2. The refrigeration capacity is 5 tons. Determine (a) the compressor power in horsepower, (b) the rate of heat transfer from the working fluid passing through the condenser, in Btu/min, and (c) the coefficient of performance. (d) What-if-scenario: How would the compressor power change if the refrigeration capacity was 10 tons? Answers: (a) 9.76 hp , (b) 1413.88 btu/min, (c) 2.41, (d) 19.52 hp
 Refrigerant R-12 enters the compressor of an ideal vapor-compression refrigeration system as saturated vapor at -10oC with a volumetric flow rate of 1 m3/min. The refrigerant leaves the condenser at 35oC, 10 bar. Determine (a) the compressor power, in kW, (b) the refrigerating capacity in tons, and (c) the coefficient of performance. Answers: (a) 5.9 kW , (b) 7.01 ton , (c) 4.17
 A refrigerator uses R-134a as the working fluid and operates on an ideal vapor compression refrigeration cycle between 0.15 MPa and 1 MPa. If the mass flow rate is 1 kg/s, determine (a) the net power necessary to run the system, and (b) COP. (c) What-if-scenario: How would the answer in (b) change if the expansion valve was replaced with an isentropic turbine? Answers: (a) 39.63 kW, (b) 3.33, (c) 4.50
 A vapor-compression refrigeration system, using ammonia as the working fluid, has evaporator and condenser pressures of 1 and 14 bar, respectively. The refrigerant passes through each heat exchanger with a negligible pressure drop. At the inlet and exit of the compressor, the temperature are -12oC and 210oC, respectively. The heat transfer rate from the working fluid passing through the condenser is 15 kW, and liquid exits at 12 bar, 28oC. If the compressor operates adiabatically, determine (a) the compressor power input in kW, and (b) the coefficient of performance.(c) What-if-scenario: How would the compressor power change if the condenser temperature rose to 250oC ? Answers: (a) 4.44 kW , (b) 2.37 , (c) 5.40 kW
 A vapor-compression refrigeration system, with a capacity of 15 tons has superheated Refrigerant R-134a vapor entering the compressor at 15oC, 4 bar, and exiting at 12 bar. The compression process can be taken as polytropic, with n = 1.01. At the condenser exit, the pressure is 11.6 bar, and the temperature is 44oC. The condenser is water-cooled, with water entering at 20oC and leaving at 30oC with a negligible change in pressure. Heat transfer from the outside of the condenser can be neglected. Determine (a) the compressor power input in kW, (b) the coefficient of performance, and (c) the irreversibility rate of the condenser, in kW, for T0 = 20oC. Answers: (a) 26.09 kW , (b) 2.02 , (c) 0.00604 kW/K
 An ideal vapor-compression refrigeration cycle, with ammonia as the working fluid, has an evaporator temperature of -25oC and a condenser pressure of 20 bar. Saturated vapor enters the compressor, and saturated liquid exits the condenser. The mass flow rate of the refrigerant is 3 kg/min. Determine (a) the coefficient of performance, and (b) the refrigerating capacity, in tons. (c) What-if-scenario: How would the COP change if the evaporator temperature was -40oC? Answers: (a) 2.59, (b) 15.11 ton, (c) 1.87
 Consider a 500 kJ/min refrigeration system that operates on an ideal vapor-compression refrigeration cycle with refrigerant-134a as the working fluid. The refrigerant enters the compressor as saturated vapor at 150 kPa and is compressed to 800 kPa. (a) Show the cycle on a T-s diagram with respect to saturation lines, and determine (b) the quality of the refrigerant at the end of the throttling process, (c) the coefficient of performance, and (d) the power input to the compressor. (e) What-if-scenario: How would the answers change if R-12 was the working fluid. Answers: (b) 0.31553 , (c) 0.24 , (d) 34.83 kW , (e) 0.30825 ; 0.28 ; 29.64 kW
 Refrigerant R-12 enters the compressor of a refrigerator as super-heated vapor at 0.14 MPa and -20oC at a rate of 0.04 kg/s, and leaves at 0.7 MPa and 50oC. The refrigerant is cooled in the condenser to 24 oC and 0.65 MPa, and is throttled to 0.15 MPa. Disregarding any heat transfer and pressure drops in the connecting lines between the components, (a) show the cycle on a T-s diagram with respect to saturation lines, determine (b) the rate of heat removal from the refrigerated space and the power input to the compressor,(c) the isentropic efficiency of the compressor, and (d) the COP of the refrigerator. Image of a Refrigerant circuit Answers: (b) 4.81 ; 1.43 , (c) 79.7% , (d) 3.35
 Refrigerant R-12 enters the compressor of a refrigerator at 140 kPa and -10oC at a rate of 0.3 m3/min and leaves at 1 MPa. The compression is isentropic. The refrigerant enters the throttling valve at 0.95 MPa and 30oC and leaves the evaporator as saturated vapor at -18.5oC. (a) Show the cycle on a T-s diagram with respect to saturation lines, and determine (b) the power input to the compressor, (c) the rate of heat removal from the refrigerated space, and (d) the pressure drop and rate of heat gain in the line between the evaporator and condenser. Answers: (b) 1.5 kW, (c) 6.06 kW, (d) 20 kPa ; 0.23 kW

A vapor-compression refrigeration system circulates R-134a at a rate of 10 kg/min. The refrigerant enters the compressor at -10oC, 1.2 bar, and exits at 7 bar. The isentropic compressor efficiency is 68%. There are no significant pressure drops as the refrigerant flows through the condenser and evaporator. The refrigerant leaves the condenser at 7 bar, 24oC. Ignoring the heat transfer between the compressor and its surroundings, determine (a) the coefficient of performance, (b) the refrigerating capacity in tons, and (c) the irreversibility rates of the compressor and expansion valve each in kW for an ambient temperature of 20oC.

Answers:
(a) 2.83 , (b) 7.65 ton , (c) 2.704 kW; 1.107 kW
 A vapor-compression refrigeration system for a household refrigerator has a refrigerating capacity of 1500 Btu/h and uses R-12 as the refrigerant. The refrigerant enters the evaporator at 21.422 lbf/in2 and exits at 5 oF. The isentropic compressor efficiency is 70%. The refrigerant condenses at 122.95 lbf/in2 and exits the condenser subcooled at 90oF . There are no significant pressure drops in the flows through the evaporator and condenser. Determine (a) the mass flow rate of refrigerant in lb/min, (b) the compressor power input in horsepower, and (c) the coefficient of performance. Answers: (a) 30.34 lb/min, (b) 13.92 hp , (c) 2.54 ,

The refrigerator-freezer unit, shown in the schematic below, uses R-134a as the working fluid and operates on an ideal vapor-compression cycle. The temperature in the condenser, refrigerator, and freezer are 25°C, 25°C, and -20°C respectively. The mass flow rate of the refrigerant is 0.1 kg/s. If the refrigerant quality at the refrigerator exit is 0.4, determine the rate of heat removal from (a) the refrigerator, and (b) freezer. Also, determine (c) the compressor power input and (d) the COP of the unit.

Answers:
(a) 4.68 kW , (b) 10.46 kw, (c) 3.33 kW, (d) 4.55

Refrigerant 134a is the working fluid in a vapor-compression refrigeration system with two evaporators. The system uses only one compressor. Saturated liquid leaves the condenser at 11 bar, one part of liquid is throttled to 3 bar, second part is throttled to the second evaporator temperature of -15oC. Vapor leaving the first evaporator as saturated vapor and is throttled to the pressure of the second evaporator. The refrigerating capacity in the first evaporator 1 ton, in second is 2 tons. Determine (a) the mass flow rates through each evaporator, (b) the compressor power input, (c) the heat transfer from the refrigerant passing through the condenser. All processes of the working fluid are internally reversible, except for the expansion through each valve. The compressor and valves operate adiabatically. Kinetic and potential energy effects are negligible. (d) What-if-scenario: How would the answer in (b) change if the entire cooling capacity of the first evaporator was shifted to the second?

Answers:
(a) 1.53 kg/min ; 3.29 kg/min , (b) 3.24 kW , (c) 13.79 kW, (d) 3.26 kW

An ideal vapor-compression cycle uses R-134a as a working fluid between 0.1 and 1.5 MPa. The refrigerant leaves the condenser at 30oC and the heat exchanger at 10oC. The refrigerant is then throttled to the evaporator pressure. Refrigerant leaves the evaporator as a saturated vapor and goes to the heat exchanger. The mass flow rate is 1 kg/s. Determine (a) the rate of heat removal from the refrigerated space per unit of the mass flow, and (b) COP. (c) What-if-scenario: How would the answers change if the heat exchanger was removed?

Answers:
(a) 167.5 kW , (b) 2.52 , (c) 139.6 kW, 2.45
 Repeat problem with R-12 as the working fluid. Answers:(a) 128 kW , (b) 2.27 , (c) 109 kW, 2.24

Consider a two-stage R-12 refrigeration system operating between 0.15 MPa and 1 MPa. The refrigerant leaves the condenser as saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. The vapor from the flash chamber is mixed with the refrigerant leaving the low-pressure compressor and the mixture is compressed by the high-pressure compressor to the condenser pressure. The liquid in the flash chamber is throttled to the evaporator pressure where the cooling load is handled through evaporation. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of refrigerant that evaporates in the flash chamber, (b) the cooling load, and (c) the COP. (d) What-if-scenario: How would the answer in (c) change if the intermediate pressure was changed to 0.8 MPa?

Answers:
(a) 0.2215 kg/s , (b) 29.9 tons, (c) 3.49, (d) 3.18
 Repeat problem with R-134a as the working fluid. Answers:(a) 0.2278 kg/s , (b) 38.6 tons, (c) 3.88, (d) 3.60
 Consider an ideal two-stage refrigeration system (see Fig. ) that uses R-12 as the working fluid. Saturated liquid leaves the condenser at 40oC and is throttled to -20oC. The liquid and vapor at this temperature are separated, and the liquid is throttled to the evaporator temperature, -70oC. Vapor leaving the evaporator is compressed to the saturation pressure corresponding to -20oC, after which it is mixed with vapor leaving the flash chamber. Determine the coefficient of performance of the system. (b) What-if-scenario: How would the result change if the flash chamber was removed with the entire flow directed to the second expansion valve? Answers: (a) 1.43 , (b) 1.03
 Consider a two-stage compression refrigeration system (see Fig. ) operating between the pressure limits of 1.2 and 0.08 MPa. The working fluid is R-12. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.4 MPa. Part of the refrigerant evaporates during this flashing process, and this vapor is mixed with the refrigerant leaving the low-pressure compressor. The mixture is then compressed to the condenser to the condenser pressure by the high-pressure compressor. The liquid in the flash chamber is throttled to the evaporator pressure, and it cools the refrigerated space as it vaporizes in the evaporator. Assuming the refrigerant leaves the evaporator as saturated vapor and both compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the amount of heat removed from the refrigerated space and the compressor work per unit mass of refrigerant flowing through the condenser, and (c) the coefficient of performance.(d) What-if-scenario: How would the answer change if R-134a was used instead? Answers: (a) 0.2701, (b) 93.55 kW ; 40.93 kW, (c) 2.28, (d) 0.2826 ; 119.80 kW ; 47.22 kW ; 2.54

A two-stage compression refrigeration system operates between the pressure limits of 1 and 0.12 MPa. The refrigerant leaves the condenser as a saturated liquid and is throttled to a flash chamber operating at 0.7 MPa. The refrigerant leaving the low-pressure compressor at 0.7 MPa is also routed to the flash chamber. The vapor in the flash chamber is then compressed to the condenser pressure by the high-pressure compressor, and the liquid is throttled to the evaporator pressure. Assuming the refrigerant leaves the evaporator as saturated vapor and both the compressors are isentropic, determine (a) the fraction of the refrigerant that evaporates as it is throttled to the flash chamber, (b) the rate of heat removed from the refrigerated space for a mass flow rate of 1 kg/s through the condenser, and (c) the coefficient of performance.(d) What-if-scenario: Do a parametric study of how the COP changes with the flash chamber pressure as it increases from 0.5 kPa to 0.9 kPa.

Answers:
(a) 0.1055, (b) 131.98 kW, (c) 3.27, (d) The COP falls from 3.43 to 3.03
 Consider a two-stage cascade refrigeration system operating between the pressure limits of 2 and 0.05 MPa. Each stage operates on the ideal vapor-compression refrigeration cycle with R-134a as the working fluid. Heat rejection from the lower cycle to the upper cycle takes place in an adiabatic counterflow heat exchanger where both streams enter at about 0.5 MPa. If the mass flow rate of the refrigerant through the upper cycle is 0.25 kg/s, determine (a) the mass flow rate of the refrigerant through the lower cycle, (b) the rate of heat removal from the refrigerated space and the power input to the compressor in lower cycle, and (c) the coefficient of performance of this cascade refrigerator.(d) What-if-scenario: How would the COP change if the heat exchanger pressure was 0.4 MPa, 0.7 MPa. Answers: (a) 0.135 kg/s , (b) 20.42 kW ; 6.36 kW , (c) 1.51 , (d) 1.49 ; 1.50
 Consider a two-stage cascade refrigeration system operating between the -80oC and 80oC. Each stage operates on the ideal vapor-compression refrigeration cycle. Upper cycle use R-12 as working fluid, lower cycle use R-13. In the lower cycle refrigerant condenses at 0oC, in the upper cycle refrigerant evaporates at -5oC. If the mass flow rate in the lower cycle is 1 kg/s, determine (a) the mass flow rate through the upper cycle, (b) the amount of heat removed from the refrigerated space, (c) COP. (d) What-if-scenario: What would be with COP if we consider one-stage ideal vapor-compression system between -80oC and 80oC with R-13 as a working fluid Answers: (a) 1.78 kg/s , (b) 66.75 kW , (c) 1.32 , (d) COP doesn't exist

Consider a two-stage cascade refrigeration system operating between 0.1 MPa and 1 MPa. Each stage operates on the ideal cycle with R-134a as the working fluid. Heat rejection from the lower to the upper cycle occurs at about 0.4 MPa. If the mass flow rate in the upper cycle is 0.1 kg/s. Determine (a) the mass flow rate through the lower cycle, (b) the COP. (c) What-if-scenario: How would the answer in (b) change if the intermediate pressure was changed to 0.6 MPa?

Answers: (a) 0.075 kg/s , (b) 3.15 , (c) 3.05

 Consider a two-stage cascade refrigeration system operating between the -60oC and 50oC. Each stage operates on the ideal vapor-compression refrigeration cycle. Upper cycle use R-134a as working fluid, lower cycle use R-22. In the lower cycle refrigerant condenses at 10oC, in the upper cycle refrigerant evaporates at 0oC. If the mass flow rate in the upper cycle is 0.5 kg/s, determine (a) the mass flow rate through the lower cycle, (b) the rate of cooling in tons, (c) the coefficient of performance. (d) the compressor power input in kW. Answers: (a) 0.26 kg/s ,(b) 12.49 ton ,(c) 1.25 ,(d) 34.99 kW

Section-2: Gas Refrigeration Cycles

In a gas refrigeration system air enters the compressor at 10oC and 50 kPa and the turbine at 50oC and 250 kPa. The mass flow rate is 0.08 kg/s. Assuming variable specific heat, determine (a) the rate of cooling, (b) the net power input, and (c) the COP. (d) What-if-scenario: How would the COP changes if the compressor inlet temperature was 15oC?
Answers: (a) 6.35 , (b) 3.7 kW, (c) 1.72, (d) 1.71
 Air enters the compressor of an perfect-gas refrigeration cycle at 45oF and 10 psia and the turbine at 120oF and 30 psia. The mass flow rate of air through the cycle is 0.5 lbm/s. Determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance. Answers: (a) 584.56 Btu/min , (b) 215.79 Btu/min , (c) 2.70
 Air enters the compressor of a perfect-gas refrigeration cycle at 15oC and 50 kPa and the turbine at 50 oC and 300 kPa. The mass flow rate through the cycle is 0.25 kg/s. Assuming variable specific heats for air (IG model), determine (a) the rate of refrigeration, (b) the net power input, and (c) the coefficient of performance.(d) What-if-scenario: How would the COP change if the IG model was used for air? Answers: (a) 23.72 kW , (b) 15.88 kW , (c) 1.49 , (d) 1.50
 Air enters the compressor of an ideal Brayton refrigeration cycle at 200 kPa, 270 K, with a volumetric flow rate of 1 m3/s, and is compressed to 600 kPa. The temperature at the turbine inlet is 330 K. Treating air as a perfect gas, determine (a) the net power input in kW, (b) the refrigeration capacity in kW and tons, and (c) the coefficient of performance. (d) What-if-scenario: How would the COP change if a reversible cycle could be operated between the highest and lowest temperatures of the cycle? Answers: (a) 27.70 kW, (b) 75.05 kW ; 21.34 ton, (c) 2.7, (d) 1.87
 An ideal-gas refrigeration cycle using air as the working fluid to maintain a refrigerated space at -30oC while rejecting heat to the surrounding medium at 30 oC. If the pressure ratio of the compressor is 4, determine (a) the maximum and minimum temperatures in the cycle, (b) the coefficient of performance, and (c) the rate of refrigeration for a mass flow rate of 0.05 kg/s.(d) What-if-scenario: How would the COP change if the PG model was used for air? Answers: (a) 87.99 oC ; -69.22 oC , (b) 2.057 , (c) 1.97 kW, (d) 2.055
 An ideal Brayton refrigeration cycle has a compressor pressure ratio of 6. At the compressor inlet, the pressure and temperature of the entering air are 55 lbf/in2. and 600oR. The temperature at the exit of the turbine is 370oR. For a refrigerating capacity of 15 tons, determine (a) the net power input, in Btu/min, (b) the coefficient of performance, and (c) the specific volumes of the air at the compressor and turbine inlets, each in ft3/lb. Answers: (a) 1983.51 Btu/min , (b) 1.51 , (c) 4.04064 ft3/lb ; 0.69294 ft3/lb
 Air enters the compressor of an ideal Brayton refrigeration cycle at 120 kPa, 275 K. The compressor pressure ratio is 3, and the temperature at the turbine inlet is 325 K. Treating air as a perfect gas, determine (a) the net work input, per unit mass of air flow, in kJ/kg, (b) the refrigeration capacity per unit mass of air flow in kJ/kg, and (c) the coefficient of performance.(d) What-if-scenario: How would the COP change if the IG model was used for air? Answers: (a) 13.94 kJ/kg , (b) 37.76 kJ/kg , (c) 2.71 , (d) 2.72

A gas refrigeration system uses helium as the working fluid and operates with a pressure ratio of 3.5. The temperature of the He is -10oC at the compressor inlet and 50oC at the turbine inlet. Assuming adiabatic efficiencies of 80% for the compressor and the turbine, determine (a) the minimum temperature of the cycle, (b) mass flow rate for a refrigeration rate of 1 ton, and (c) the COP. (d) What-if-scenario: How would the answer in (c) change if the adiabatic efficiencies was to increase to 85%?

Answers:
(a) -51.89 oC , (b) 0.016 kg/s, (c) 0.37, (d) 0.52
 In problem consider that the compressor and turbine each has an isentropic efficiency of 85%. Determine for the modified cycle (a) the mass flow rate of air, in lb/s, and (b) the coefficient of performance. (c) What-if-scenario: Do a parametric study of how the COP would change if the isentropic efficiency varied from 50% to 100%. Answers: (a) 0.906 lb/s , (b) 0.35, (c) the COP rises from 0.25 to 1.51
 In consider that the compressor and turbine have isentropic efficiencies of 80 and 90% respectively. Determine for the modified cycle (a) the coefficient of performance, and (b) the irreversibility rates, per unit mass of air flow, in the compressor and turbine, each in kJ/kg, for T0 = 300 K. Answers: (a) 0.6 , (b) 0.06546 kJ/kg.K ; 0.03638 kJ/kg.K
 A gas refrigeration cycle with a pressure ratio of 3 uses helium as the working fluid. The temperature of the helium is -15oC at the compressor inlet at 50oC at the turbine inlet. Assuming adiabatic efficiencies of 85% for both the turbine and the compressor, determine (a) the minimum temperature in the cycle, (b) the coefficient of performance, and (c) the mass flow rate of the helium for a refrigeration rate of 10 kW. (d) What-if-scenario: How would the COP change if the turbine inlet temperature was increased to 60oC? Answers: (a) -47.67 oC , (b) 0.46, (c) 0.0589 kg/s, (d) 0.38

A gas refrigeration system using air as the working fluid has a pressure ratio of 4. Air enters the compressor at -7oC. The high-pressure air is cooled to 30oC by rejecting heat to the surroundings. It is further cooled to -15oC by regenerative cooling before it enters the turbine. Assuming both the turbine and the compressor to be isentropic and using the PG model for air, determine (a) the lowest temperature that can be obtained by this cycle, (b) the coefficient of performance of the cycle, and (c) the mass flow rate of air for a refrigeration rate of 12 kW. (d) What-if-scenario: How would the COP change if the pressure ratio was 5?

Answers:
(a) -99.49oC , (b) 1.055 , (c) 0.253kg/s, (d) 1.055
 In problem evaluate the effect of regeneration on the COP by changing the turbine inlet temperature to (a) -10°C, (b) 0°C, (c) 10°C, and (d) 20°C. Answers: (a) 1.133 , (b) 1.307, (c) 1.512, (d) 1.757

Section-3: Heat Pump Systems

A heat pump which operates on the ideal vapor-compression cycle with R-12 is used to heat water from 5 to 30oC at a rate of 0.2 kg/s. The condenser and evaporator pressures are 0.8 and 0.2 MPa respectively. Determine (a) the power input to the heat pump and (b) the COP of the heat pump.(c) What-if-scenario: Could we heat the water if R-12 was replaced with R-22?

Answers:
(a) 3.68 kW, (b) 5.67 , (c) No.
 Ammonia is the working fluid in a vapor-compression heat pump system with a heating capacity of 25,000 Btu/h. The condenser operates at 250 lbf/in2., and the evaporator temperature is -10oF. The refrigerant is a saturated vapor at the evaporator exit and a liquid is 100oF at the condenser exit. Pressure drops in the flows through the evaporator and condenser are negligible. The compression process is adiabatic, and the temperature at the compressor exit is 400 oF. Determine (a) the mass flow rate of refrigerant, in lb/min, (b) the compressor power input in horsepower, (c) the isentropic compressor efficiency, and (d) the coefficient of performance. Answers: (a) 0.6 lb/min , (b) 3.15 hp , (c) 0.74 , (d) 3.12
 A small heat pump unit is used to heat water for hot-water supply. Assume that the unit uses R-22 and operates on the ideal refrigeration cycle. the evaporator temperature is 0oC and condenser temperature is 50oC. If the amount of hot water needed is 0.1 kg/s, determine the amount of energy saved by using the heat pump instead of directly heating the water from 0oC to 50oC. Answers: 16.03 kW
 An ideal vapor-compression heat pump cycle with Refrigerant R-134a as the working fluid provides 10 kW to maintain a building at 22oC when the outside temperature is 5oC. Saturated liquid leaves the condenser. Calculate (a) the power input to the compressor in kW, (b) the coefficient of performance, and (c) the coefficient of performance of a reversible heat pump cycle operating between thermal reservoirs at 22oC and 5oC.(d) What-if-scenario: How would the answers in part (b) and (c) change if the outside temperature was 0 oC? Answers: (a) 0.63 kW , (b) 14.94 , (c) 15.94 , (d) 11.13 ; 12.13
 A heat pump which operates on the ideal vapor-compression cycle with R-12 is used to heat the house and maintain it at 20oC using underground water at oC as the heat source. The house is losing heat at a rate of 90,000 kJ/h. The evaporator and condenser pressures are 0.35 and 0.8 MPa respectively. Determine (a)the power input to the heat pump.(b) What-if-scenario: If an electric resistance heater is used instead of heat pump, calculate the increase in electric power input. Answers: (a) 1.68 kW , (b) 23.32 kW
 A vapor-compression heat pump system uses Refrigerant R-134a as the working fluid. The refrigerant enters the compressor at 2.4 bar, 0oC, with a volumetric flow rate of 0.8 m3/min. Compression is adiabatic to 10 bar, 50oC, and saturated liquid exits the condenser at 9 bar. Determine (a) the power input to the compressor in kW, (b) the heating capacity of the system in kW and tons, (c) the coefficient of performance, and (d) the isentropic compressor efficiency.(e) What-if-scenario: How would the COP change if the refrigerant temperature at the compressor exit was 70oC? Answers: (a) 1.85 kW , (b) 27.1kW ; 7.71 ton , (c) 5.59 , (d) 0.97 , (e) 2.75
 The refrigerant R-22 is used as the working fluid in a conventional heat pump cycle. Saturated vapor enters the compressor of this unit at 15 oC; its exit temperature from the compressor is measured and found to be 90oC. If the isentropic efficiency of the compressor is estimated to be 75%, (a) what is the coefficient of performance of the heating pump. (b) What-if-scenario: How would the coefficient of performance change if the the isentropic compressor efficiency changed to 65% Answers: (a) 3.77 , (b) 3.40
 A vapor-compression heat pump with a heating capacity of 500 kJ/min is driven by a power cycle with a thermal efficiency of 25%. For the heat pump, Refrigerant 134a is compressed from saturated vapor at -10oC to the condenser pressure of 10 bar. The isentropic compressor efficiency of 85%. Liquid enters the expansion valve at 9.6 bar, 34oC. For the power cycle, 90% of the heat rejected is transferred to the heated space. Determine (a) the power input to the heat pump compressor in kW, and (b) evaluate the ratio of total rate at which heat is delivered to the heated space to the rate of heat input to the power cycle. Answers: (a) 1.84 kW , (b) 2.32
 A heat pump using R-12 heats a house by using underground water at 8oC as the heat source. The house is losing heat at a rate of 30,000 kJ/h. The refrigerant enters the compressor at 250 kPa and -2oC and it leaves at 1.2 MPa and 70oC. The refrigerant leaves the condenser at 30oC. Determine (a) the power input to the heat pump, (b) the rate of heat absorption from the water. (c) What-if-scenario: If an electric resistance heater is used instead of heat pump, calculate the increase in electric power input. Answers: (a) 1.85 kW , (b) 6.48 kW , (c) 6.48 kW

In an actual refrigeration cycle, heating pump using R-12 as the working fluid, the refrigerant flow rate is 0.1 kg/s. Vapor enters the compressor at 200 kPa, -5oC, and leaves at 1.5 MPa, 90oC. The power input to the compressor is measured and found be 2.6 kW. The refrigerant enters the expansion valve at 1.2 MPa, 40oC and leaves the evaporator at 200 kPa, -12oC. Determine (a) the irreversibility during the compression process, (b) the refrigeration capacity, (c) COP of the heating pump

Answers:
(a) -0.00441 kW/K , (b) 12.97 kW , (c) 6.15

Section-4: Exergy Analysis of Refrigeration and Heat Pump Cycles

A refrigerator uses R-134a as the working fluid and operates on an ideal vapor compression refrigeration cycle between 0.15 MPa and 1 MPa. A temperature difference of 5°C is maintained for effective heat exchange between the refrigerant and its surroundings at the evaporator and condenser. The atmospheric conditions are 100 kPa and 25°C. If the mass flow rate is 0.04 kg/s, (a) perform an exergy inventory on a rate (kW) basis for the entire cycle complete with an exergy flow diagram. Determine the (b) exergetic efficiency and (c) COP of the system. (d) Identify the device with the highest rate of exergy destruction.

Answers:
(b) 62.66%, (c) 3.33,

A vapor-compression refrigeration system circulates R-134a at a rate of 10 kg/min. The refrigerant enters the compressor at -10oC, 1.2 bar, and exits at 7 bar. The isentropic efficiency of the adiabatic compressor is 68%. There are no significant pressure drops as the refrigerant flows through the condenser and evaporator. The refrigerant leaves the condenser at 7 bar, 24oC. A temperature difference of 5°C is maintained for effective heat exchange between the refrigerant and its surroundings at the evaporator and condenser. The atmospheric conditions are 100 kPa and 25°C. (a) Perform an exergy inventory on a rate (kW) basis for the entire cycle complete with an exergy flow diagram. Determine the (b) exergetic efficiency and (c) COP of the system. (d) Identify the device with the highest rate of exergy destruction.

Answers:
(b) 60.53%, (c) 2.83

An ideal vapor-compression cycle uses R-134a as a working fluid between 0.1 and 1.5 MPa. The refrigerant leaves the condenser at 30oC and the heat exchanger at 10oC. The refrigerant is then throttled to the evaporator pressure. Refrigerant leaves the evaporator as a saturated vapor and goes to the heat exchanger. The mass flow rate is 1 kg/s. A temperature difference of 5°C is maintained for effective heat exchange between the refrigerant and its surroundings at the evaporator and condenser. The atmospheric conditions are 100 kPa and 25°C. (a) Perform an exergy inventory on a rate (kW) basis for the entire cycle complete with an exergy flow diagram. Determine the (b) the cooling capacity, (c) exergetic efficiency, and (d) COP of the system.

Answers:
(b) 167.5 kW , (c) 59.0%, (d) 2.52

 Repeat problem with the heat exchanger removed. Answers: (b) 139.57 kW , (c) 57.46%, (d) 2.45

A heat pump which operates on the ideal vapor-compression cycle with R-134a is used to transfer heat at a rate of 20 kW to a space maintained at 50oC from outside atmosphere at 0oC. A temperature difference of 5°C is maintained for effective heat exchange between the refrigerant and its surroundings at the evaporator and condenser. The atmospheric conditions are 100 kPa and 0°C. (a) Perform an exergy inventory on a rate (kW) basis for the entire cycle complete with an exergy flow diagram. Determine the (b) the power consumption rate, (c) the exergetic efficiency, and (d) the COP of the system.

Answers:
(b) 4.91 kW, (c) 62.93%, (d) 4.06

 Repeat problem with the outside atmosphere at 100 kPa, -5°C. Answers: (b) 5.42 kW, (c) 57.08%, (d) 3.69

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