Air at 100 kPa and 20degree C enters an industrial compresso

Air at 100 kPa and 20degree C enters an industrial compressor with negligible velocity and is discharged at three times the atmospheric pressure and 30degree C through a pipe with 1 m^2 area. The mass flow rate is 10 kg/8. The power input to the compressor is 300 kW. Take C_p of air to be about 1 kJ/kgK. At steady state, determine the rate of heat transfer, in kW, if gravity and other sources of work are neglected..

Solution

sol :

Rate of heat transfer Q = mCp (T2-T1)

given T1 = 20 ^oC

T2 = 3* atmospheric pressure

T2 = 3*30

T2 = 90 ^oC

Q = m * Cp * (T2-T1)

Q = 10*1*(90-20)

Q = 700 kJ/sec

Q = 700 kW <-------------answer