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The ideal compression requiring the minimum amount of work is the perfect
reversible isothermal compression process which obeys Boyle's law PV = c. This is
represented by 1-4. The work saved per cycle is [ 1-4-2-1 ]. If the compression was
isothermal the work done per cycle would be [ a-1-4-b-a ] which is

p 2 P2 dP k
W  vdp  Pv  vP ln 
1   P k 1 1 1
1 p P1

The compressor isothermal efficiency is a measure of the departure from the ideal
compression process and is defined as

W Colculated  izotermal  power
  1 
ISO
W Power  imparted  to  air

5.3 Clearance Volume effect
A practical single stage compressor cylinder will have a small clearance at the end
of the stroke. This clearance will have a significant effect on the work done per cycle.
In operation the air in the clearance volume expands to 5 before any fresh air is
drawn into the cylinder. The stroke is from 1 to 2 with a swept volume of (V2 - V1 )
but the suction is only from 5 to 2 giving a volume of (V2 - V5) taken into the cylinder
on each stroke.
The volumetric efficiency obtained from the hypothetical indicator diagram is :

V  V volume of  air  pamped / cycle
  2 5 
V
V  V Stroke volume of  cylinder
2 1

The actual compressor diagrams differ from

hypothetical diagrams because of valve
opening and closing delays and component
inertia. A typical actual indicator diagram is
shown below.
A good approximation of the volumetric
efficiency is indicated by the ratio of x to y
measured at the atmospheric pressure line.
Fig. 5.4 - Effect of Clearance Volume

The actual performance of a reciprocating
compressor used as pump is measured by the
ratio.

5.4 Multi-stage compressor
A multi-stage compressor is one in which
Fig. 5.5 - The actual compressor diagrams there are several cylinders of different
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