Page 28 - Low Temperature Energy Systems with Applications of Renewable Energy

Principles and operation of refrigeration and heat pump systems 17

1.5.3 Thermodynamic efficiency of vapor compression
refrigerators
Since the configuration shown in Fig. 1.11 can be viewed as a refrigerator as well as a
heat pump, there is no need to devise a new flow diagram for a refrigerator. The state-
point diagrams in Fig. 1.12 are also applicable here. The difference lies in the objective
of the cycle, namely, to remove heat from the low-temperature reservoir, while dis-
charging heat to the surroundings. Thus, with reference to the definition of terms given
above, the coefficient of performance, COP R , may be written as

Q 1;2 h 2 h 1
COP R ¼ ¼ (1.7)
W 2;3 h 3 h 2

where Q 1,2 is the cooling effect, i.e., the heat removed from the space that is being
cooled. The refrigeration cycle may be seen as thermodynamically the same as the heat
pump cycle but with a shift to lower temperatures. For the refrigerator, the
heat discharge from the cycle is at or above ambient temperature, whereas for the heat
pump, the heat input to the cycle is close to ambient temperature. Otherwise, the
working equations to determine the state-point properties are the same.

Example 2 e Basic vapor-compression refrigerator

Let us suppose that Example 1 is now viewed as a refrigerator. This will not be a prac-
tical case, but it will illustrate an interesting relationship between the COP of heat
pumps and refrigerators.
The heat removed from the “cold space” is the objective and the work supplied is
the input. Thus the COP R can be found from

Q 1;2 h 2 h 1 520.09 403.59
COP R ¼ ¼ ¼ ¼ 1:50
W 2;3 h 3 h 2 597.78 520.09

Notice that the heat pump has a COP HP that is greater than the COP R for the refrig-
erator by exactly one. Thus,

COP HP ¼ COP R þ 1

We leave it to the reader to prove that this is a general equation that applies to any
cycle operating as either a heat pump or a refrigerator; see Problem 1 at the end of the
chapter.