Solved Examples For Vapor Compression Refrigeration Cycles

Note: For example 1, values are obtained from the following book:

G. van Wylen, R. Sonntag, C. Borgnakke, Fundamentals of Classical Thermodynamics, 4th Ed., Wiley, 1994

Example 1

A conventional refrigerator uses HFC-134a as its working fluid. Saturated vapor at − 20°C leaves the evaporator and enters the insulated compressor whose compression ratio is 9:1, i.e., the outlet pressure is 9 times the inlet pressure. The compressor is 85% efficient based on an adiabatic reversible compression over the same pressure range. The gas leaving the compressor is cooled and condensed isobaricly to a saturated liquid. The saturated liquid is passed through an insulated throttle valve whose downstream pressure corresponds to a saturation temperature of − 20°C. The mixture from the throttle valve goes to the evaporator, where it absorbs just enough heat from the ice trays and the interior of the refrigerator box to become saturated vapor, which enters the compressor and repeats the cycle. Under summertime conditions (greatest load) it is expected that 120 kJ/min will have to be absorbed in the evaporator.

a) What is the rate of circulation of the refrigerant in kg/min?

b) Determine the power of the compressor.

Solution

The cycle can be schematically represented as follows:

a) Since the rate of heat that must be removed from the low temperature region, Q_c is given, then:

State: 1

At the exit of the evaporator, we have saturated vapor at − 20°C. From HFC-134a table we obtain:

State: 3

At the exit of the condenser, we have saturated liquid. The pressure is

P₃ = P₂ = (9)(0.1337) = 1.2 MPa

Hence,

State: 4

The energy balance around the throttling valve gives:

                                                 

Thus, the circulation rate can be determined from Eq. (1) as follows:

b) The pressure at state 2 is 1.2 MPa. If the compression takes place reversibly and adiabatically:

Example 2

A heat pump is being used to maintain a room at 21°C by removing heat from groundwater and discharging heat to the room. For the cycle shown in the figure below:

a) What is the quality of the fluid leaving the evaporator?

b) What is the maximum quantity of heat that can be delivered to the room per J removed from the groundwater?

c) If the room is to receive 1.7 kW, what is the minimum horsepower rating of the motor driving the compressor?

d) What is the minimum energy that would have to be supplied to provide 1.7 kW into the room using the groundwater as a source?

The fluid properties are as follows:

Solution

a) Since compressor operates reversibly and adiabatically, then:

b) The entropy at state 4 is:

c) The circulation rate of the refrigerant can be calculated from:

d) Power required will be minimum when a Carnot refrigeration cycle is to be operated between evaporator and condenser temperatures. The coefficient of performance of such a heat pump is: