TITLE.PM5

716 ENGINEERING THERMODYNAMICS

dharm

\M-therm\Th14-1.pm5

14.2.2. Reversed Carnot cycle

If a machine working on reversed Carnot cycle is driven from an external source, it will
work or function as a refrigerator. The production of such a machine has not been possible prac-
tically because the adiabatic portion of the stroke would need a high speed while during isothermal
portion of stroke a very low speed will be necessary. This variation of speed during the stroke,
however is not practicable.
p-V and T-s diagrams of reversed Carnot cycle are shown in Figs. 14.1 (a) and (b). Starting
from point l, the clearance space of the cylinder is full of air, the air is then expanded adiabatically
to point p during which its temperature falls from T 1 to T 2 , the cylinder is put in contact with a
cold body at temperature T 2. The air is then expanded isothermally to the point n, as a result of
which heat is extracted from the cold body at temperature T 2. Now the cold body is removed ; from
n to m air undergoes adiabatic compression with the assistance of some external power and tem-
perature rises to T 1. A hot body at temperature T 1 is put in contact with the cylinder. Finally the
air is compressed isothermally during which process heat is rejected to the hot body.

p (Pressure)

v (Volume)

T 1

l Isotherms

m Adiabatics

n

p Exp.

Exp.

T 2

Comp.

Comp.

(a)

T 1

T 2

T (Temp.)

lm

n

p

qss (Entropy)

(b)

Fig. 14.1 (a) p-V diagram for reversed Fig. 14.1 (b) T-s diagram for a reversed

Carnot cycle. Carnot cycle.

Refer Fig. 14.1 (b)

Heat abstracted from the cold body = Area ‘npqs’ = T 2 × pn

Work done per cycle = Area ‘lpnm’

= (T 1 – T 2 ) × pn

Co-efficient of performance,

C.O.P. =

Heat extracted from the cold body

Work done per cycle

=

Area

Area

‘’

‘’( )

npqs

lpnm

Tpn

TT pn

T

TT

= ×

−×

=

−

2

12

2

12

...(14.1)
Since the co-efficient of performance (C.O.P.) means the ratio of the desired effect in kJ/kg to
the energy supplied in kJ/kg, therefore C.O.P. in case of Carnot cycle run either as a refrigerating
machine or a heat pump or as a heat engine will be as given below :
(i)For a reversed Carnot cycle ‘refrigerating machine’ :

C.O.P.(ref.) =

Heat extracted from the cold body /cycle

Work done per cycle

=

Tpn

TT pn

2

12

×

()−×

=

T

TT

2

12 −

...(14.2)