TITLE.PM5

740 ENGINEERING THERMODYNAMICS

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\M-therm\Th14-2.pm5

or

p

p

v

v

d

s

n

=

F

HG

I

KJ

4

3

or v 4 = v 3.

p

p

d

s

F n

HG

I

KJ

1/

If the clearance ratio,

C =

v

vv

3

13 −

=Clearance volume

Swept volume

Thus ηcv =

vv

vv

vv v v

vv

14

13

14 44

13

−

−

= −′− −′

−

()( )

()

=

()( )

()

vv v v

vv

13 43

13

−−−

− (Q v^4 ′ = v^3 )

= 1 – vv

vv

43

13

−

−

= 1 –

v p

p

v

vv

v

vv

p

p

d

s

n

d

s

3 n

1

3

13

3

13

1

11

F

HG

I

KJ

−

−

=+

−

−F

HG

I

KJ

L

N

M

M

O

Q

P

P

/

/

= 1 + C – C p

p

d

s

F n

HG

I

KJ

1/

Hence clearance volumetric efficiency,

ηcv = 1 + C – C

p

p

d

s

F n

HG

I

KJ

1/

...(14.11)

Total volumetric efficiency. The total volumetric efficiency (ηtv) of a compressor is best

obtained by actual laboratory measurements of the amount of refrigerant compressed and deliv-

ered to the condenser. It is very difficult to predict the effects of wire-drawing, cylinder wall

heating, and piston leakage to allow any degree of accuracy in most cases. The total volumetric

efficiency can be approximately calculated if the pressure drop through the suction valves and the

temperature of the gases at the end of the suction stroke are known and if it is assumed that there

is no leakage past the piston during compression, it can be calculated (by modifying the eqn. 14.11)

by using the following equation :

ηtv = 1

1

+−F

HG

I

KJ

L

N

M

M

O

Q

P

P

CCp ××

p

p

p

T

T

d

s

n

c

s

s

c

/

...(14.12)

where the subscript ‘c’ refers to compressor cylinder and ‘s’ refers to the evaporator or the suction
line just adjacent to the compressor.

14.3.10.Mathematical analysis of vapour compression refrigeration

(i)Refrigerating effect. Refrigerating effect is the amount of heat absorbed by the
refrigerant in its travel through the evaporator. In Fig. 14.10 this effect is represented by the
expression.
Qevap. = (h 2 – h 1 ) kJ/kg ...(14.13)
In addition to the latent heat of vaporization it may include any heat of superheat absorbed
in the evaporator.