Power required by air compressor with intercooling feature

[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

Since the velocity, elevation and work done is not mentioned, I assume that W(out), KE and PE=0.
Thus the equation:
m(h1+KE1+PE1)+W(in)=m(h2+KE2+PE2)+W(out) is reduced to:
mh1+W(in)=mh2
Then, W(in)=mh2-mh1

I have tried looking for the values for h1 and h2 at the ideal gas table(since the air has high temperature and low pressure with respect to its critical properties), but then I realized that both of them are the same, which led to W(in) been 0 (which is impossible). My friend mentioned the "state postulate", others use the PVln(P1/P2) to determine the work done.
I want to know if my attempt is the right one, if not, then what's the right way of doing this question. Your help will be greatly appreciated. God bless you all.

 

[LightHero]

Your attempt is not the right way of doing this question. The correct way to solve this problem is to use the ideal gas law. You can use the following equation: PV = mRT where P is the pressure, V is the volume, m is the mass, R is the gas constant, and T is the temperature. You can then rearrange the equation to solve for the work done (W): W = mRTln(V2/V1) You can then calculate the power required by multiplying the work done by the mass flow rate: Power = mRTln(V2/V1)*m