A reciprocating air compressor takes in 2m3/min at 0.11MPa, $20^oc$, which it delivers at 1.5MPa, $111^oc$ to an after cooler where the air is cooled at constant pressure to $25^oc$. The power absorbed by the compressor is 4.15kW. -

Given:

P1 = 1.1 bar; T1 = 293K

P2 = 15bar; T2 = 384K

$V = 2 m^3/min = 0.033 m^3/s$ ; W = 4.15kW

T3= 298K

Solution:

Part of the power absorbed by the compressor is used to compress the air, some heat is lost in aftercooler and the rest through compressor Power = Work on air + Heat through aftercooler + Heat through compressor

P1V1 = mRT1

1.1 x 10^5 x 0.033 = m x 280 x 293 ( R= 280 J/kg for air)

m = 0.044 kg/s

P = W + Qa

P-W = Qa

Qa = 4150 – mCp(T2-T1)

= 4150 – 0.044 x 1000 ( 384-293 ) = 0.15 kW

Similarly, heat lost in cooler

Q = mCp(T2-T3) = 0.044 x 1000 x (384 – 298) = 3.78 kW