728 ENGINEERING THERMODYNAMICS

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\M-therm\Th14-2.pm5

(iii)Piston displacement of compressor and expander.
(iv)Bore of compressor and expansion cylinders. The unit runs at 240 r.p.m. and is double-
acting. Stroke length = 200 mm.
(v)Power required to drive the unit
For air take γ = 1.4 and cp = 1.003 kJ/kg K.
Solution. Refer Fig. 14.8.
T 3 = 16 + 273 = 289 K ; T 1 = 41 + 273 = 314 K
p 1 = 5.2 bar ; p 2 = 1.0 bar.
Considering the adiabatic compression 3-4, we have

T

T

p

p

4

3

1

2

(^1) 14 1
2 14
1

F
HG
I
KJ
=F
HG
I
KJ
γ− −
γ 5.
.
.
= (5.2)0.286 = 1.6
∴ T 4 = 1.6 ; T 3 = 1.6 × 289 = 462.4 K
Considering the adiabatic expansion 1-2, we have
T
T
p
p
1
2
1
2
1

F
HG
I
KJ
−γ
γ
314 5 2
2 1
04
14
T
=F
HG
I
KJ
.
.
.
= 1.6 or T 2 =
314
1.6 = 196.25 K.
p (bar)
V(m )^3
p = 5.2 1
p = 1.0 2
23
1 4
(pV = C)g
Fig. 14.8
(i)C.O.P. :
Since both the compression and expansion processes are isentropic/adiabatic reversible,
∴ C.O.P. of the machine =
T
TT
2
12
196 25
− 314 196 25

−
.

. = 1.67. (Ans.)