724 ENGINEERING THERMODYNAMICS

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\M-therm\Th14-1.pm5

But R = cp γ

γ

F −

HG

I

KJ

(^1) J
(J = 1 in S.I. units)
∴ WWcomp.− exp.=
n
n−
F
HG
I
KJ
F −
HG
I
1 KJ
γ 1
γ
mcp(T 4 – T 3 + T 2 – T 1 ) ...(14.8)
For isentropic compression and expansion,
Wnet = mcp(T 4 – T 3 + T 2 – T 1 )
Now according to law of conservation of energy the net work on the gas must be equivalent
to the net heat rejected.
Now, C.O.P. =
W
QQ
Q
W
added
rejected added
added
− net

For the air cycle assuming polytropic compression and expansion, co-efficient of perform-
ance is :
C.O.P. =
mc T T
n
n
mc TTTT
p
p
×× −
−
F
HG
I
KJ
F −
HG
I
KJ
×× −+−
()
()
32
1 4321
γ 1
γ
= ()
()
TT
n
n
TTTT
32
1 4321
1
−
−
F
HG
I
KJ
F −
HG
I
KJ
γ −+−
γ
...(14.9)
Note. The reversed Brayton cycle is same as the Bell-Coleman cycle. Conventionally Bell-Coleman cycle
refers to a closed cycle with expansion and compression taking place in reciprocating expander and compressor
respectively, and heat rejection and heat absorption taking place in condenser and evaporator respectively.
With the development of efficient centrifugal compressors and gas turbines, the processes of compression
and expansion can be carried out in centrifugal compressors and gas turbines respectively. Thus the shortcoming
encountered with conventional reciprocating expander and compressor is overcome. Reversed Brayton cycle finds
its application for air-conditioning of aeroplanes where air is used as refrigerant.

14.2.4. Merits and demerits of air refrigeration system

Merits

1. Since air is non-flammable, therefore there is no risk of fire as in the machine using
   NH 3 as the refrigerant.


2. It is cheaper as air is easily available as compared to the other refrigerants.


3. As compared to the other refrigeration systems the weight of air refrigeration system
   per tonne of refrigeration is quite low, because of this reason this system is employed in air-
   crafts.
   Demerits


4. The C.O.P. of this system is very low in comparison to other systems.


5. The weight of air required to be circulated is more compared with refrigerants used in
   other systems. This is due to the fact that heat is carried by air in the form of sensible heat.
   Example 14.9. A Bell-Coleman refrigerator operates between pressure limits of 1 bar and
   8 bar. Air is drawn from the cold chamber at 9°C, compressed and then it is cooled to 29°C
   before entering the expansion cylinder. Expansion and compression follow the law pv1.35 = con-
   stant. Calculate the theoretical C.O.P. of the system.
   For air take γ = 1.4, cp = 1.003 kJ/kg K.