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 (c) change if R-12 were replaced with R-134a, a more Environmentally benign refrigerant? [Manual Solution] [TEST Solution] Click on the image to animate!
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 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 were replaced with an isentropic turbine? [Manual Solution] [TEST Solution]
Answers: (a) 79.2 kW, (b) 5, (c) 5.94

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. What-if-scenario: How would the answer in part (b) change if the mass flow rate were doubled?. [Manual Solution] [TEST Solution]

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. What-if-scenario: (e) How would the answers change if R-12 were the working fluid. [Manual Solution] [TEST Solution]

Refrigerant-134a enters the compressor of a refrigerator as super-heated vapor at 0.14 MPa and -10oC at a rate of 0.15 kg/s, and leaves at 0.7 MPa and 50oC. The refrigerant is cooled in the condenser to 24oC 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. [Manual Solution] [TEST Solution]

Refrigerant R-134a 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 isentropic efficiency of the compressor is 78%. 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. [Manual Solution] [TEST Solution]

An ideal vapor-compression refrigeration cycle operates at steady state with Refrigerant R-134a as the working fluid. Saturated vapor enters the compressor at -10oC, and saturated liquid leaves the condenser at 30oC. 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. What-if-scenario: (d) How would the COP change if the condenser operated at 40oC? [Manual Solution] [TEST Solution]

A large refrigeration plant is to be maintained at -15oC, and it requires refrigeration at a rate of 150 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. [Manual Solution] [TEST Solution]

An ideal vapor-compression refrigeration system operates at steady state with Refrigerant R-134a as the working fluid. Superheated vapor enters the compressor at 30 lbf/in2., 15oF, and saturated liquid leaves the condenser at 150 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. What-if-scenario: (e) How would the compressor power change if the refrigeration capacity were 10 tons? [Manual Solution] [TEST Solution]

Refrigerant R-134a enters the compressor of an ideal vapor-compression refrigeration system as saturated vapor at -15oC 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. [Manual Solution] [TEST Solution]

An ideal vapor-compression refrigeration cycle, with ammonia as the working fluid, has an evaporator temperature of -20oC and a condenser pressure of 15 bar. Saturated vapor enters the compressor, and saturated liquid exits the condenser. The mass flow rate of the refrigerant is 5 kg/min. Determine (a) the coefficient of performance, and (b) the refrigerating capacity, in tons. What-if-scenario: (c) How would the COP change if the evaporator temperature were -30oC? [Manual Solution] [TEST Solution]

A vapor-compression refrigeration system circulates R-134a at a rate of 5 kg/min. The refrigerant enters the compressor at -10oC, 1.4 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, (c) the irreversibility rates of the compressor and expansion valve each in kW. [Manual Solution] [TEST Solution]

A vapor-compression refrigeration system, using ammonia as the working fluid, has evaporator and condenser pressures of 3 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 -10oC and 140oC, 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. What-if-scenario: (c) How would the compressor power change if the condenser pressure rose to 20 bar? [Manual Solution] [TEST Solution]

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 power input and the heat transfer rate for the compressor, each in kW, (b) the coefficient of performance, and (c) the irreversibility rate of the condenser, in kW, for T0 = 20oC. [Manual Solution] [TEST Solution]

A vapor-compression refrigeration system for a household refrigerator has a refrigerating capacity of 1500 Btu/h and uses R-134a as the refrigerant. The refrigerant enters the evaporator at -10oF and exits at 0oF. The isentropic compressor efficiency is 80%. The refrigerant condenses at 95oF and exits the condenser subcooled at 90oF . There are no significant pressure drops in the flows through the evaporator and condenser. Determine the (a) evaporator and (b) condenser pressures, each in lbf/in2, (c) the mass flow rate of refrigerant in lb/min, (d) the compressor power input in horsepower, and (e) the coefficient of performance. What-if-scenario: (c) How would the COP change if the refrigerant were R-134a instead? [Manual Solution] [TEST Solution]

A carnot vapor refrigeration cycle uses R-134a as the working fluid. The refrigerant enters the condenser as saturated vapor at 30 0C and leaves as saturated liquid. The evaporator operates at a temperature of -10oC. 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. What is the coefficient of performance of the cycle? [Manual Solution] [TEST Solution]

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. [Manual Solution] [TEST Solution]

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. [Manual Solution] [TEST Solution]

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 lb/min. Calculte (a) the compressor and turbine power, each in Btu/min, and (b) the coefficient of performance. [Manual Solution] [TEST Solution]

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. [Manual Solution] [TEST Solution]

Refrigerant R-134a enters the condenser of a steady-flow Carnot refrigerator as a saturated vapor at 100 psia, and it leaves with a quality of 0.05. The heat absorption from the refrigerated space takes place at a pressure of 30 psia. (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. [Manual Solution] [TEST Solution]
Answers: (a) 0.09 kg/s, (b) 3.5, (c) 3.44

Consider a two-stage cascade refrigeration system operating between 0.15 MPa and 1 MPa. Each stage operates on the ideal cycle with R-12 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 0.12 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 were changed to 0.6 MPa? [Manual Solution] [TEST Solution]

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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 were changed to 0.8 MPa? [Manual Solution] [TEST Solution]

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Answers: (a) , (b) 29.9 tons, (c) 3.49, (d) 3.18

Consider a two-stage cascade refrigeration system operating between the pressure limits of 0.8 and 0.14 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, and (c) the coefficient of performance of this cascade refrigerator. What-if-scenario: How would the COP change if the heat exchanger pressure were (d) 0.4 MPa, (e) 0.6 MPa. [Manual Solution] [TEST Solution]

A two-stage compression refrigreation 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 0.5 MPa. The refrigerant leaving the low-pressure compressor at 0.5 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 0.25 kg/s through the condenser, and (c) the coefficient of perfromance. What-if-scenario: (d) Do a parametric study of how the COP changes with the flash chamber pressure. [Manual Solution] [TEST Solution]

Consider a two-stage compression refrigeration system operating between the pressure limits of 0.8 and 0.14 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 compresser. The liquid in the flash chamber is throttled to the evaporator pressure, and it cools the refrigerated space as it vaporizes in the evaporator. A ssuming 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. What-if-scenario: (d) How would the answer change if R-134a were used instead? [Manual Solution] [TEST Solution]

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 were to increase to 85%? [Manual Solution] [TEST Solution]
Answers: (a) , (b) 0.016 kg/s, (c) 0.37, (d) 0.52

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. What-if-scenario: How would the COP change if the turbine inlet temperatue were increased to 60oC? [Manual Solution] [TEST Solution]

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. What-if-scenario: How would the COP changes if the compressor inlet temperature were 15oC? [Manual Solution] [TEST Solution]
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Answers: (a) , (b) 3.7 kW, (c) 1.72, (d) 1.71

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 30 oC by rejecting heat to the surrounings. 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. What-if-scenario: How would the COP change if the pressure ratio were 5? [Manual Solution] [TEST Solution]

Air enters the compressor of a perfect-gas refrigeration cycle at 12oC and 50 kPa and the turbine at 50 oC and 250 kPa. The mass flow rate through the cycle is 0.1 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. What-if-scenario: How would the COP change if the IG model were used for air? [Manual Solution] [TEST Solution]

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. [Manual Solution] [TEST Solution]

An ideal-gas refrigeration cycle using air as the working fluid to maintain a refrigerated space at -25oC while rejecting heat to the surrounding medium at 25oC. If the pressure ratio of the compressor is 3, 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 0.09 kg/s. What-if-scenario: How would the COP change if the PG model were used for air? [Manual Solution] [TEST Solution]

Air enters the compressor of an ideal Brayton refrigeration cycle at 100 kPa, 270 K. The compressor pressure ratio is 3, and the temperature at the turbine inlet is 315 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. What-if-scenario: (e) How would the COP change if the IG model were used for air? [Manual Solution] [TEST Solution]

In the previous problem 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. [Manual Solution] [TEST Solution]

An ideal Brayton refrigeration cycle has a compressor pressure ratio of 4. At the compressor inlet, the pressure and temperature of the entering air are 45 lbf/in2. and 500oR. The temperature at the exit of the turbine is 370oR. For a refrigerating capacity of 10 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. [Manual Solution] [TEST Solution]

In the previous problem consider that the compressor and turbine each have isentropic efficiencies of 85%. Determine for the modified cycle (a) the mass flow rate of air, in lb/min, and (b) the coefficient of performance. What-if-scenario: (c) Do a parametric study of how the COP would change if the isentropic efficiency varied from 570% to 100%. [Manual Solution] [TEST Solution]

Air enters the compressor of an ideal Brayton refrigeration cycle at 150 kPa, 270 K, with a volumetric flow rate of 1 m3/s, and is compressed to 450 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. What-if-scenario: (c) How would the COP change if a reversible cycle could be operated between the highest and lowest temperatures of the cycle? [Manual Solution] [TEST Solution]

An ideal vapor-compression heat pump cycle with Refrigerant R-134a as the working fluid provides 15 kW to maintain a building at 22oC when the outside temperature is 5oC. Saturated vapor at 2.4 bar 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. What-if-scenario: How would the answers in part (b) and (c) change if the outside temperature were 0 oC? [Manual Solution] [TEST Solution]

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 105oF at the condenser exit. Pressure drops in the flows through the evaporator and condenser are negligible. The compression process is adaibatic, and the temperature at the compressor exit is 360oF. 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. [Manual Solution] [TEST Solution]

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 9 bar, 60oC, 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. What-if-scenario: (e) How would the COP change if the refrigerant temperature at the compressor exit were 70oC? [Manual Solution] [TEST Solution]

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 punp, 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 transfered 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. [Manual Solution] [TEST Solution]

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