Question

Consider a two stage reciprocating air compressor

with a perfect intercooler operating at the best

intermediate pressure. Air enters the low pressure

cylinder at 1 bar, 27qC and leaves the high pressure

cylinder at 9 bar. Assume the index of compression

and expansion in each stage is 1.4, and that for air R= 286.7 J/kgK. The work done per kg air in the high

pressure cylinder is​

Answer 1

Answer:

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Answer 2

Two stage reciprocating air compressor

              A two stage reciprocating air compressor is a type of compressor, in which the air is compressed in two stages; in between the stages, the air is cooled.

Given

    low pressure, $p_{1}$ = 1 bar

    high pressure, $p_{3}$ = 9 bar

    index , n = 1.4 , R = 286.7 J/Kg

Solution

  intermediate pressure, $p_{2}$ = $\sqrt{(p_{1}* p_{3} )}$

                                                       = $\sqrt{1*9}$

                                                       = 3bar

work done in either cylinder is calculated by

                                               = $\frac{n}{n-1} RT_{1} (p_{2} ^{\frac{n-1}{n} }-1 )$

                                                       = $\frac{1.4}{0.4}$ × 286.7 × 300 × $(3^{\frac{0.4}{1.4} }-1 )$

                                                       = 3.5 × 286.7 × 300 × (1.37  ₋ 1)

                                                       = 111 kJ

Work done per kg air in the high pressure cylinder = 111 kJ