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732 ENGINEERING THERMODYNAMICS

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\M-therm\Th14-2.pm5

14.3.4. Vapour compression cycle on temperature-entropy (T-s) diagram...

We shall consider the following three cases :

1. When the vapour is dry and saturated at the end of compression. Fig. 14.10
   represents the vapour compression cycle, on T-s diagram the points 1, 2, 3 and 4 correspond to the
   state points 1, 2, 3 and 4 in Fig. 14.9.

Liquid

line

kcdg f

s (Entropy)

Saturation

line

Net

refrigerating

effect

(R )n

T 2 a

b

1 Evaporation (^2) e
Compression
Compressor
work
(W)
Expansion
T (Temp.)
T 1 4 3
Condensation
Fig. 14.10. T-s diagram.
At point ‘2’ the vapour which is at low temperature (T 2 ) and low pressure enters the com-
pressor’s cylinder and is compressed adiabatically to ‘3’ when its temperature increases to the
temperature T 1. It is then condensed in the condenser (line 3-4) where it gives up its latent heat to
the condensing medium. It then undergoes throttling expansion while passing through the expan-
sion valve and its again reduces to T 2 , it is represented by the line 4-1. From the T-s diagram it
may be noted that due to this expansion the liquid partially evaporates, as its dryness fraction is
represented by the ratio
b
b
1
2

. At ‘1’ it enters the evaporator where it is further evaporated at

constant pressure and constant temperature to the point ‘2’ and the cycle is completed.
Work done by the compressor = W = Area ‘2-3-4-b-2’

Heat absorbed = Area ‘2-1-g-f-2’

∴ C.O.P. = Heat extracted or refrigerating effect

Work done

=

Area ‘2-1- - -

Area ----

gf

b

2

234 2

’

‘’

or C.O.P =

hh

hh

21

32

−

− ...[14.10 (a)]

= hh

hh

24

32

−

−

...[14.10 (b)]

(Q h 1 = h 4 , since during the throttling expansion 4-1 the total heat content remains unchanged)