Refrigeration Problems:1) The temperature in a refrigerator coil is 267 K and that in condenser coil is 295 K. Assuming that the machine operates on the reversed Carnot cycle, calculate : a) C.O.P.ref b) The refrigerating effect per kW of input work. c) The heat rejected to the condenser. Ans: [a) 9.54 b) 9.54kw c) 10.54 kW] 2) An ammonia vapour compression refrigerator operates between an evaporator pressure of 2.077bar and a condenser pressure of 12.37bar. The following cycles are to be compared; in each case there is no undercooling in the condenser, and isentropic compression may be assumed: a) The vapour has a dryness fraction of 0.9 at entry to the compressor. b) The vapour is dry saturated at entry to the compressor. c) The vapour has 5 K of superheat at entry to the compressor. In each case calculate the C.O.P.ref and the refrigerating effect per kg. What would be the C.O.P.ref of reversed Carnot cycle operating between the same saturation temperature? Ans:[4.5;957.5kJ/kg;4.13;1089.9kJ/kg;4.1;1101.4kJ/kg] 3) A refrigerator using Freon-12 operates between saturation temperatures of 263 K and 333 K, at which temperatures the latent heat are 156.32kJ/kg and 113.52kJ/kg respectively. The refrigerant is dry saturated at entry to the compressor and liquid is not under-cooled in the condenser. The specific heat of liquid Freon is 0.970kJ/kg K and that of superheated Freon vapour is 0.865kJ/kg K. The vapour is compressed isentropically in the compressor. Using no other information than that given, calculate the temperature at the compressor delivery, and the refrigerating effect per kg of Freon. Ans:[342.9K;88.42kJ/kg] 4) A heat pump using ammonia as the refrigerant operates between saturation temperatures of 279K and 311K. The refrigerant is compressed isentropically from dry saturation and there is 6 K under-cooling in the condenser. Calculate: a) C.O.P. heat pump b) The mass flow of refrigerant c) The heat available per KW input Ans:[8.8;25.06kg/h;8.8KW] 5) An ammonia refrigerator operates between evaporating and condensing temperature of 257K and 323K respectively. The vapour is dry saturated at the compressor inlet, the compression process is isentropic and there is no undercooling of the condensate. Calculate a) The refrigerating effect per kg, b) The mass flow and power input per KW of refrigeration,
c) The C.O.P.ref Ans:[1003.4kJ/kg;3.59kg/h;0.338KW;2.96] 6) 30 tonnes of ice from and at 273K is produced in a day of 24 hrs by an ammonia refrigerator. The temperature range in the compressor is from 298K to 258K. The vapour is dry saturated at the end of compression and expansion valve is used. Assume a coefficient of performance of 60% of the theoretical and calculate the power in KW required to drive the compressor. Latent heat of ice is 334.72 kJ/kg. Ans: [21.59KW] Temp. Enthalpy(kJ/kg) Entropy of Entropy of (K) Liquid vapour liquid(kJ/kgK) vapour(kJ/kg) 298 100.04 1319.22 0.3473 4.4852 258 -54.56 1304.99 -2.1338 5.0585 7) A refrigerant plant works between temperature limits of 268K (in the evaporator) and 298K (in the condenser). The working fluid ammonia has a dryness friction of 0.6 at entry to the compressor. If the machine has relative efficiency of 50%, calculate the amount of ice form during a period of 24 hrs. the ice is to be formed at 273K from water at 298K and 6kg of ammonia is circulated per min. specific heat of water is 4.187kJ/kg and latent heat of ice is 335kJ/kg. properties of ammonia (datum 233K). Ans: [1640.5kg] Temp. Liquid heat(kJ/kg) Latent heat Entropy of (K) (kJ/kg) liquid(kJ/Kg 0c) 298 298.9 1167.1 1.124 268 158.2 1280.8 0.630 8) A vapour compression refrigerator uses methyl chloride and work in the pressure range of 11.9bar and 5.67bar. At the beginning of the compression, the refrigerant is 0.96 dry and at the end of isentropic compression, it has a temperature of 328K. The refrigerant liquid leaving the condenser is saturated. If the mass flow of refrigerant is 1.8kg/min. Determine a) Coefficient of performance b) The rise in temp of condenser cooling water if the water flow rate is 16 kg/min. c) The ice produced in the evaporator in kg/hr from water at 288K and ice at 273K. Properties of methyl chloride. Saturation Pressure Enthalpy Entropy 0 temp. ( c) (bar) (kJ/kg) (kJ/kgK) hf hg sf sg -20 11.9 30.1 455.2 0.124 1.803
25 5.67 100.5 476.8 0.379 1.642 Take, specific enthalpy of fusion of ice =336kJ/kg Specific heat of water=4.187kJ/kg. 0 Ans: [4.97; 10.9 c; 91.3kg] 9) A vapour compression refrigerator circulated 4.5 kg of Nh 3 per hr. condensation take place at 303K and evaporation at 258K. There is no under-cooling of the refrigerant. The temp. after isentropic compression is 348K and specific heat of superheated vapour is 2.82kJ/kgK. Determine a) Coefficient of performance 0 0 b) Ice produced in kg per hr in the evaporator from water at 20 c and ice at 0 c. Take: enthalpy of fusion of ice approximately 336kJ/kg, specific heat of water approximately. 4.187kJ/kg. 3 c) The effective swept volume of the compressor in m /min. Properties of ammonia: Sat. temp. Enthalpy Entropy Volume (K) (kJ/kg) (kJ/kgK) (m3/kg) hf hg sf sg vf vg 303 323.1 1469 1.204 4.984 0.00168 0.111 258 112.3 1426 0.457 5.549 0.00152 0.509 Ans:[4.95;682kg/hr;2.2 m3/min] 10) A refrigerating machine using Nh 3 operates between the temp. limits of 258K and 303K. Find the cop of the system. Also find the corresponding values for a reversed Carnot cycle operating between the same temperature. The properties of Nh 3 are given below; Pressure Temp. liquid Vapour 0 (bar) ( c) hf(kJ/kg) sf(kJ/kgK) hg(kJ/Kg) sg(kJ/kgK) 2.41 -5 351 3.95 1667.5 9.05 11.895 30 562 4.69 1711 8.48 11) A refrigerator using co 2 as refrigerant works between the temperature 290.5K and 255.5K. The co 2 leaves the compressor at 303K. The gas is completely condensed but there is no other cooling. Find theoretical cop. Properties of refrigerant are given below: Temp. hf hfg Hg sf Sg 0 ( c) (kJ/kg) (kJ/kg) (kJ/kg) (kJ/kg) (kJ/kg)
17.5 470 169.6 639.6 4.37 4.95 -17.5 378.5 279.5 658 4.05 5.12 0 0 12) A CO2 refrigerator works between a temperature range of 18.5 C to -18 C. 0 The co2 leaves the compressor at a temperature of 30 C and with a total heat of 243.2kJ/kg. The gas is completely condensed in condenser but there is no undercooling. Find theoretical C.O.P. of the system. Properties of co2 are given below: Temp. hf hg sf sg 0 ( c) (kJ/kg) (kJ/kg) (kJ/kgK) (kJ/kgK) 18.5 52.95 215 0.168 0.727 -18.0 -37.8 235.6 0.151 0.92 13) A simple vapour compression plant produces 5 tonnes of refrigeration. The enthalpy values at inlet to compressor, at exit from the compressor, and at the exit from the condenser are 183.9, 209.41 and 74.59 kJ/kg resp. estimate a) The refrigerant flow rate b) The C.O.P. c) The power required to drive the compressor, and d) The rate of heat rejection to the condenser. Ans: [0.179kg/s; 4.142; 4.69KW; 24.13KW] 14) A heat pump is used for heating the interior of a house in cold climate. The 0 0 ambient temperature is -5 c and the desired interior temperature is 25 c. The 0 compressor heat pump is to be driven by a heat engine working between 1000 c 0 and 25 c. Treating both cycles as reversible, calculate the ratio in which the heat pump and heat engine share the heating load. Ans:[ratio=7.608] 0 15) 28 tonnes of ice from and at 0 c is produced per day in an ammonia 0 0 refrigerator. The temperature range in the compressor is from 25 c to -15 c. The vapour is dry and saturated at the end of compression and an expansion valve is used. Assuming a coefficient of performance of 62% of the theoretical, calculate the power required to drive the compressor. Temp. Enthalpy Entropy of Entropy of 0 ( c) (kJ/kg) (kJ/kgK) (kJ/kgK) Liquid Vapour liquid vapour 25 100.04 1319.22 0.3473 4.1852 -15 -54.56 1304.99 -2.1338 5.0585 Ans:[19.67KW] 0 0 16) A refrigerating plant works between temperature limits of -5 c and 25 c, the working fluid ammonia has a dryness fraction of 0.62 at entry to compressor. If the
machine has a relative efficiency of 55%, calculate the amount of ice formed 0 0 during the period of 24hrs. The ice is to be formed at 0 c from water at 15 c and 6.4 kg of ammonia is circulated per minute. Specific heat of water is 4.187kJ/kg and latent heat of ice is 335kJ/kg. 0 Properties of Nh3 (Datum: -40 c) Temp Liquid heat Latent heat Entropy of 0 ( c) (kJ/kg) (kJ/kg) liquid(kJ/kgK) 25 298.9 1167.1 1.124 -5 158.2 1280.8 0.630 Ans: [1896.1kg] 17) Refrigeration requirement 2400 kJ/min at 263K, condenser temperature 303K 0 0 refrigerant is sub-cooled by 6 c and super heated by 7 c after evaporation. The compression is reversibly adiabatic. Calculate refrigeration effect/kg and C.O.P. of the system. Mass of the refrigerant calculated/min, heat removed to the condenser/min. Take properties of refrigerant as follows: Sat. temp. hf hfg sf sfg Pressure. Sp.vol. 3 (K) (kJ/kg) (kJ/kg) (kJ/kgK) (kJ/kgK) (bar) (m /kg) 263 26.9 183.2 0.1080 0.7220 2.19 0.0767 303 64.6 199.6 0.2399 0.6854 7.45 0.0235 Take specific heat of liquid refrigerant as 1.235kJ/kgK and vapour refrigerant as 0.733kJ/kgK. 18) A cold storage plant is required to store 20 tonnes of fish. The fish is supplied at 0 a temperature of 30 c. The specific heat of fish above freezing point is 2.93kJ/kgK. The specific heat of fish below freezing point is 1.26kJ/kgK. The fish 0 is stored in cold storage which is maintained at -8 c. The freezing point of fish is 0 4 c. The latent heat of fish is 235kJ/kgK. If the plant requires 75 KW to drive heat, find capacity of the plant and time taken to achieve cooling. Assume actual C.O.P. of the plant is 0.3 times of the Carnot C.O.P. Ans: [44.8TR; 12.03hrs] 19) A vapour compression refrigerator works between the pressure limits of 60bar and 25bar. The working fluid is just dry at the end of compression and there is no under-cooling of the liquid before the expansion valve. Determine C.O.P. of the cycle and capacity of the refrigerator if the fluid flow rate is 5kg/min. Pressure Saturation Enthalpy Entropy (bar) Temp. (K) (kJ/kg) (kJ/kgK) Liquid Vapour Liquid Vapour 60 295 61.9 208.1 0.197 0.703
25
261 -18.4 234.5 -0.075 0.896 Ans: [5.04; 2.9TR] 20) A vapour compression refrigerant works between the temperature limit of -20 0 0 C and 25 C. The refrigerant leaves the compressor in dry saturated condition. If 0 the liquid refrigerant is under-cooled to 20 C before entering the throttle valve. Determine a) Work required to drive compressor. b) Refrigeration effect produced per kg of refrigerant. c) Theoretical C.O.P. Temp. Enthalpy Entropy 0 ( C) (kJ/kg) (kJ/kgK) Liquid Vapour Liquid Vapour -20 327.4 1655.9 3.8416 9.09 25 536.3 1703.3 4.5956 8.50 Ans: [189.7kJ/kg; 990.2kJ/kg; 5.01] 21) A food storage chamber required a refrigeration system of 12TR capacity with 0 0 evaporator temperature of -8 C and condenser temperature of 30 C. The refrigerant 0 R-12 is sub-cooled by 5 C before entering a throttle valve, and the vapour is 0 super-heated by 6 C before entering the compressor. If the liquid and vapour specific heats are 1.235 and 0.733 kJ/kgK respectively, find a) Refrigerating effect per kg b) Mass of the refrigerant circulated per minute. c) C.O.P. Saturation Enthalpy Entropy 0 Temp. ( c) (kJ/kg) (kJ/kgK) Liquid vapour Liquid Vapour -8 28.72 184.07 0.1149 0.7007 30 64.59 199.62 0.2400 0.6853 Ans: [130.05 kJ/kg; 19.4kg; 6.2] 22) A food storage locker requires a refrigeration capacity of 12TR and works 0 0 between evaporating temperature of -8 C and condensing temperature of 30 C. 0 The refrigerant R-12 is sub-cooled by 5 C before expansion valve and the vapour 0 is super-heated to -2 C before leaving the evaporator coils. Determine, a) C.O.P. b) Theoretical power per ton of refrigeration Use the following data for R-12
Saturation 0 Temp. ( C)
Pressure (bar)
-8 2.354 30 7.451 Ans:[ 6.2;0.565KW/TR]
Enthalpy (kJ/kg) liquid vapour 28.72 184.07 64.59 199.62
Entropy (kJ/kgK) liquid vapour 0.1149 0.7007 0.2400 0.6853
