CHAP. 4: APPLICATION OF THERMODYNAMICS [CONTENTS] 119
4.3.2 Cooling engine
A cooling engine is a device that cyclically absorbs heatQ 1 from the cooler reservoir of tem-
peratureT 1 and transfers it to the warmer reservoir of temperatureT 2. The workW is needed
for this transfer.
Thecooling engine efficiency(economy) is defined by the relation
β=heat taken from the cooler reservoir
work needed for this heat transfer=
Q 1
W
. (4.32)
The efficiency of a reversible cooling engine operating between the temperaturesT 1 andT 2 is
always higher than that of an irreversible engine [compare with (4.31)], and it is
β=T 1
T 2 −T 1
. (4.33)
Example
A refrigerator is a device consisting of a cooling engine and a cooler reservoir (i.e. the space in
which foods are kept) of temperatureT 1. The room in which the fridge is placed represents the
warmer reservoir of temperatureT 2. If we neglect the losses, the workWneeded for the transfer
of heat from the space of the fridge to the room equals the amount of electric energy consumed
from the electric network. IfT 1 = 275 K, andT 2 = 300 K, assess the amount of electric energy
needed for the transfer of 1100 J of heat from the cooled space to the room.Solution
According to (4.33), the cooling engine efficiency is:β=275
300 − 275
= 11.
We calculate the work needed for the heat transfer from (4.32)W=
Q 1
β=
1100
11
= 100J.
A total of 100 J of electric energy is needed to transfer 1100 J of heat.