REFRIGERATION CYCLES 727

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\M-therm\Th14-2.pm5

(i)Mass of air circulated per minute, m :

For the expansion process 1-2, we have

T

T

p

p

1

2

1

2

(^1) 14 1
1000 14
100

F
HG
I
KJ
=F
HG
I
KJ
γ− −
γ
.
.
= 1.9306
or T 2 =
T 1
9306
303

1. 
   
   
   
   1. 9306
   
   
   
   

= = 156.9 K

Refrigerating effect per kg = 1 × cp (T 3 – T 2 ) = 1.005 (268 – 156.9) = 111.66 kJ/kg

∴ Mass of air circulated per minute =

Refrigerating effect

Refrigerating effect per kg

=

2000

111 66.

= 17.91 kg/min. (Ans.)

(ii)Compressor work (Wcomp.), expander work (Wexp.) and cycle work (Wcycle) :

For compression process 3-4, we have

T

T

p

p

4

3

4

3

(^1) 14 1
1000 14
10

F
HG
I
KJ
=FHG IKJ
γ− −
γ
.
.
= 1.9306
or T 4 = 268 × 1.9306 = 517.4 K. (Ans.)
Compressor work, Wcomp. : γ
γ− 1
mR (T 4 – T 3 )

1.4
1.4 1− × 17.91 × 0.287 (517.4 – 268)
= 4486.85 kJ/min. (Ans.)
Expander work, Wexp. : γ
γ− 1
mR (T 1 – T 2 )

1.4
1.4 1− × 17.91 × 0.287 (303 – 156.9)
= 2628.42 kJ/min. (Ans.)
Cycle work, Wcycle : Wcomp. – Wexp.
= 4486.85 – 2628.42 = 1858.43 kJ/min. (Ans.)
(iii)C.O.P. and power required (P) :
COP =
Refrigerating effect
Work required
2000
1858.43
= = 1.076 (Ans.)
Power required, P = Work per second =
1858 43
60
.
kJ/s or kW = 30.97 kW. (Ans.)
+Example 14.11. A refrigerating machine of 6 tonnes capacity working on Bell-Coleman
cycle has an upper limit of pressure of 5.2 bar. The pressure and temperature at the start of the
compression are 1.0 bar and 16°C respectively. The compressed air cooled at constant pressure to
a temperature of 41°C enters the expansion cylinder. Assuming both expansion and compression
processes to be adiabatic with γ = 1.4, calculate :
(i)Co-efficient of performance.
(ii)Quantity of air in circulation per minute.