Air compressor

[jasoncurious]

An air compressor is used to compress air from 100kPa and 30°C to 800kPa at a rate of 120kg/min. By having the inter-cooling feature the compression is done at constant temperature of 30°C. Calculate the power required for the compression.

Known data:

P(initial)=100kPa

P(final)=800kPa

Temperature(constant)=30°C

Mass flow rate=120kg/min=2kg/s

My friends applied the formula of work done for isothermal process(since the compression is done at constant temperature of 30°C):

W=RTln(P1/P2)

*R used is 0.2870

 

Their assumption is that Work(in)=Work(out).

May I know what happened to the mh1 in the usual energy balance for open system?

Under what condition can we make the assumption Work(in)=Work(out)?