# Thermodynamics: Air compressor

## Homework Statement

Air enters a compressor at 100 kPa and 290 K, where it is compressed adiabatically, where the flow rate is 0.1 kg/s. If the volume compression ratio is (V1/V2=8). Determine the following (Assuming the air is ideal with constant specific heat):

1- The temperature and the pressure at the exit

2- The compressor’s power in kW

3- The transferred heat amount and the change in entropy

## Homework Equations

W - Q = m(h + KE + PE)
∆h = m CP (T2 – T1)
P1 V1k= P2 V2k=C

## The Attempt at a Solution

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P1 V1k= P2 V2k=C --> (k=1.4 for air)

P2= P1(V1/V2)1.4= 100(8)1.4

P2=1837.9 kPa --> Pressure at exit

Q1-2 = 0 (The process is adiabatic) --> The transferred heat amount

∆s1-2≈ 0 (The process is adiabatic) --> The change in entropy

And we may compute ∆s1-2 using of the these two equations:

∆s1-2= CV ln(T2/T1) + R ln(V2/V1)

∆s1-2= CP ln(T2/T1) - R ln(P2/P1)

W1-2 = - m ∆h = m CP (T1 – T2) = (0.1) (1.0035) (290 – 666.23)

W1-2 = -37.75 kW à The compressor’s power in kw

(k, R, CP and Cv are constants we get it from the tables)