Question

Air at 100 kPa and 10°C enters a compressor and is brought to 1000 kPa and 50°C. The constant pressure heat capacity of air is 1.01 kJ/kg K. If 15 kg/min of air are to be compressed, determine the power require- ment of the compressor. State your assumptions. (12.625 kW)

Answer 1

SOLUTION:

Assumptions:(1).Air to be an ideal gas.

(2).The compressor is well-insulated and the compression process is totally reversible.

GIVEN:p1=100 kpa, T1=10C=283K

p2=1000kpa, T2 =50C=323K, Cp=1.01Kj/kg-K ,m=15kg/min=0.25kg/sec

From Steam table :At 100kpa and 10C

h1=42.12kj/kg, s1=0.15108kj/kg-K

and at 1000kpa and 50C

h2=201.19kj/kg , s2=0.70335kj/kg-K

=0.25{(210.19-42.12)-283(0.70335-0.15108-0.287ln(1000/100))}

=0.25{(168.07)-283(-0.10857)}

=0.25(168.07+30.725)

=49.69KW