Practice Problems: Refrigeration Cycles

A refrigeration engineer is designing a vapor-compression refrigeration system for a cold storage facility. The system uses R-134a as the refrigerant. The evaporator operates at -20°C and the condenser operates at 40°C. The refrigerant enters the compressor as saturated vapor and leaves the condenser as saturated liquid. The refrigeration load is 50 kW. Using the following property data for R-134a:
At -20°C (saturated): h_g = 386.1 kJ/kg, s_g = 1.7395 kJ/kg·K
At 40°C (saturated): h_f = 256.5 kJ/kg
At 40°C and s = 1.7395 kJ/kg·K: h = 428.4 kJ/kg
What is the required mass flow rate of the refrigerant?
(a) 0.286 kg/s
(b) 0.386 kg/s
(c) 0.486 kg/s
(d) 0.586 kg/s

A mechanical engineer is evaluating the performance of an existing ammonia refrigeration system. The compressor inlet conditions are -10°C with h = 1433 kJ/kg and s = 5.463 kJ/kg·K. The compressor discharge is at 1200 kPa where h = 1672 kJ/kg. The condenser outlet enthalpy is 346 kJ/kg. The system delivers 100 tons of refrigeration (1 ton = 3.517 kW). What is the coefficient of performance (COP) of this system?
(a) 3.55
(b) 4.55
(c) 5.55
(d) 6.55

A consulting engineer is designing an ice-making plant using R-22 refrigerant. The evaporator temperature is -15°C and condenser temperature is 35°C. The compressor has an isentropic efficiency of 85%. Given the following property data for R-22:
At -15°C (saturated vapor): h₁ = 402.5 kJ/kg, s₁ = 1.7862 kJ/kg·K
At 35°C (saturated liquid): h₄ = 241.8 kJ/kg
At 35°C and s = 1.7862 kJ/kg·K: h_2s = 448.6 kJ/kg
What is the actual enthalpy at the compressor discharge?
(a) 444.7 kJ/kg
(b) 454.7 kJ/kg
(c) 464.7 kJ/kg
(d) 474.7 kJ/kg

A refrigeration technician is troubleshooting a commercial freezer system that uses R-404A. Measurements indicate the evaporator pressure is 150 kPa (corresponding to -35°C saturation) and the condenser pressure is 1800 kPa (corresponding to 45°C saturation). The refrigerant leaves the evaporator with 8°C of superheat. At -27°C (superheated at 150 kPa): h = 368.2 kJ/kg. At 45°C (saturated liquid): h = 256.8 kJ/kg. At 45°C and 1800 kPa (superheated): h = 437.5 kJ/kg after isentropic compression from -27°C. What is the refrigeration effect per unit mass?
(a) 91.4 kJ/kg
(b) 101.4 kJ/kg
(c) 111.4 kJ/kg
(d) 121.4 kJ/kg

A process engineer is sizing a compressor for a new R-134a refrigeration system. The system must remove 75 kW of heat from a cold storage room. The evaporator operates at 200 kPa where saturated vapor has h = 398.6 kJ/kg and s = 1.7274 kJ/kg·K. The condenser operates at 1000 kPa where saturated liquid has h = 268.4 kJ/kg. After isentropic compression to 1000 kPa, h = 432.8 kJ/kg. What is the theoretical power requirement for the compressor?
(a) 17.3 kW
(b) 19.7 kW
(c) 21.5 kW
(d) 23.8 kW

A facilities engineer is analyzing a water chiller system for a commercial building. The chiller uses R-123 and operates between 4°C evaporator temperature and 38°C condenser temperature. The actual COP measured is 5.2. The Carnot COP operating between the same temperature limits would be a benchmark for comparison. What is the Carnot COP for these operating temperatures?
(a) 7.15
(b) 8.15
(c) 9.15
(d) 10.15

A refrigeration designer is specifying a cascade refrigeration system for a low-temperature application. The low-stage cycle uses R-508B with an evaporator at -80°C (h = 195.4 kJ/kg) and condenser at -30°C (h_f = 121.3 kJ/kg, h_g = 245.8 kJ/kg after compression). The refrigeration load is 25 kW. What is the mass flow rate required in the low-stage cycle?
(a) 0.237 kg/s
(b) 0.337 kg/s
(c) 0.437 kg/s
(d) 0.537 kg/s

A mechanical engineer is evaluating an air conditioning system using R-410A. The system operates with an evaporator temperature of 5°C and condenser temperature of 50°C. The compressor has a volumetric efficiency of 82% and operates at 1750 RPM. The compressor displacement volume is 0.0012 m³/rev. At 5°C saturated vapor, the specific volume is 0.0582 m³/kg and enthalpy is 412.3 kJ/kg. At 50°C saturated liquid, enthalpy is 270.8 kJ/kg. What is the actual refrigeration capacity of the system?
(a) 42.4 kW
(b) 52.4 kW
(c) 62.4 kW
(d) 72.4 kW

A plant engineer is optimizing a heat pump system that uses R-134a for space heating. The evaporator operates at 0°C with saturated vapor enthalpy of 398.6 kJ/kg. The condenser operates at 45°C with saturated liquid enthalpy of 261.4 kJ/kg. After isentropic compression, the enthalpy at the condenser inlet is 435.2 kJ/kg. The heating load requirement is 100 kW. What is the heating COP of this heat pump?
(a) 4.55
(b) 5.55
(c) 6.55
(d) 7.55

A refrigeration engineer is designing a system for a fish processing plant using ammonia (R-717). The evaporator operates at -25°C with h_g = 1416.7 kJ/kg and s_g = 5.5489 kJ/kg·K. The condenser operates at 30°C with h_f = 341.8 kJ/kg. After isentropic compression to 30°C, h = 1660.5 kJ/kg. The required refrigeration capacity is 200 kW. What is the heat rejection rate at the condenser?
(a) 245.4 kW
(b) 255.4 kW
(c) 265.4 kW
(d) 275.4 kW

A consulting engineer is analyzing a two-stage compression refrigeration system with intercooling. The first stage compresses R-134a from 100 kPa (h = 392.7 kJ/kg, s = 1.7395 kJ/kg·K) to an intermediate pressure of 300 kPa where h = 418.5 kJ/kg after isentropic compression. The refrigerant is then cooled to saturated vapor at 300 kPa (h = 407.3 kJ/kg) before entering the second stage. What is the work saved per kilogram due to intercooling compared to single-stage isentropic compression from 100 kPa to 900 kPa (h = 445.2 kJ/kg)?
(a) 9.8 kJ/kg
(b) 11.2 kJ/kg
(c) 13.5 kJ/kg
(d) 15.8 kJ/kg

A mechanical engineer is sizing an expansion valve for a refrigeration system using R-22. The refrigerant enters the expansion valve as subcooled liquid at 35°C and 1400 kPa with enthalpy of 237.2 kJ/kg. The evaporator operates at 250 kPa. At 250 kPa: h_f = 199.6 kJ/kg, h_g = 407.5 kJ/kg, h_fg = 207.9 kJ/kg. What is the quality of the refrigerant immediately after the expansion valve?
(a) 0.141
(b) 0.181
(c) 0.221
(d) 0.261

A refrigeration system designer is evaluating a supermarket refrigeration rack using R-507A. The system has multiple evaporators, and the main suction line carries 0.65 kg/s of refrigerant at -10°C saturated vapor conditions (h = 393.8 kJ/kg, s = 1.7156 kJ/kg·K). The condenser operates at 40°C (h_f = 249.5 kJ/kg). After isentropic compression to 40°C, h = 433.7 kJ/kg. What is the total compressor power required?
(a) 20.9 kW
(b) 23.9 kW
(c) 25.9 kW
(d) 28.9 kW

A HVAC engineer is troubleshooting a commercial chiller that uses R-134a. The evaporator operates at 3°C and the condenser at 42°C. Due to poor maintenance, the compressor isentropic efficiency has degraded to 72%. At 3°C saturated vapor: h₁ = 400.4 kJ/kg, s₁ = 1.7272 kJ/kg·K. At 42°C saturated liquid: h₄ = 259.2 kJ/kg. At 42°C and s = 1.7272 kJ/kg·K: h_2s = 435.8 kJ/kg. What is the actual COP of this degraded system?
(a) 2.46
(b) 2.87
(c) 3.28
(d) 3.69

A process engineer is designing an industrial freezer using R-404A operating between -40°C evaporator and 35°C condenser. At -40°C saturated vapor: h = 360.8 kJ/kg, s = 1.7485 kJ/kg·K, v = 0.2156 m³/kg. At 35°C saturated liquid: h = 241.9 kJ/kg. After isentropic compression to 35°C: h = 420.3 kJ/kg. The compressor is a reciprocating type with 85% volumetric efficiency, displacement of 0.025 m³/s, operating to deliver 80 kW refrigeration. What is the actual mass flow rate?
(a) 0.573 kg/s
(b) 0.673 kg/s
(c) 0.773 kg/s
(d) 0.873 kg/s

A refrigeration consultant is analyzing a vapor-compression system with liquid-suction heat exchanger for improved efficiency. R-134a enters the heat exchanger on the low-pressure side at -5°C saturated vapor (h = 394.9 kJ/kg) and leaves at 10°C superheated (h = 412.5 kJ/kg). The high-pressure side enters at 38°C saturated liquid (h = 255.5 kJ/kg) and is subcooled. Assuming equal heat transfer, what is the enthalpy of the subcooled liquid leaving the heat exchanger?
(a) 227.9 kJ/kg
(b) 237.9 kJ/kg
(c) 247.9 kJ/kg
(d) 257.9 kJ/kg

A facilities manager is evaluating the annual energy cost of operating a refrigeration system. The system uses R-22 and operates 6000 hours per year. The evaporator is at -8°C (h = 404.2 kJ/kg, s = 1.7701 kJ/kg·K) and condenser at 40°C (h_f = 249.1 kJ/kg). After isentropic compression: h = 450.8 kJ/kg. The refrigeration load is constant at 50 kW. The actual compressor efficiency is 78%, and the motor efficiency is 92%. Electricity costs $0.12 per kWh. What is the approximate annual energy cost?
(a) $8,950
(b) $9,950
(c) $10,950
(d) $11,950

A mechanical engineer is designing an absorption refrigeration system for a facility with waste heat available. The system operates with an evaporator at 5°C and condenser at 35°C. The generator requires 2.5 kW of heat input for every 1 kW of refrigeration produced. The evaporator load is 100 kW. If a vapor-compression system operating between the same temperatures would have a COP of 4.8, what is the ratio of the heat input required for the absorption system to the work input that would be required for the vapor-compression system?
(a) 10.2
(b) 11.2
(c) 12.0
(d) 13.0

A refrigeration engineer is evaluating a multi-evaporator R-134a system with two temperature levels. The low-temperature evaporator operates at -25°C (h = 383.0 kJ/kg) with 20 kW load. The medium-temperature evaporator operates at -5°C (h = 394.9 kJ/kg) with 30 kW load. Both streams are compressed together to 40°C condenser conditions (h_f = 256.5 kJ/kg). After isentropic compression from -25°C: h = 432.8 kJ/kg. After isentropic compression from -5°C: h = 426.1 kJ/kg. What is the total compressor power required if the system uses separate compressors for each evaporator?
(a) 16.3 kW
(b) 19.3 kW
(c) 22.3 kW
(d) 25.3 kW

A plant engineer is retrofitting an old R-12 refrigeration system to use R-134a. The original system operated with an evaporator at -10°C and condenser at 35°C. For R-12 at these conditions: evaporator h_g = 345.5 kJ/kg, condenser h_f = 226.5 kJ/kg, isentropic discharge h = 375.8 kJ/kg. For R-134a at the same temperatures: evaporator h_g = 392.3 kJ/kg, condenser h_f = 249.1 kJ/kg, isentropic discharge h = 424.2 kJ/kg. If the refrigeration load remains constant at 60 kW, what is the percentage change in compressor power requirement after the retrofit?
(a) -8.5% (decrease)
(b) +8.5% (increase)
(c) -12.3% (decrease)
(d) +12.3% (increase)