Solution

12.29
Borgnakke and Sonntag
A two-stage air compressor has an intercooler between the two stages as shown in
Fig. P12.29. The inlet state is 100 kPa, 290 K, and the final exit pressure is 1.6
MPa. Assume that the constant pressure intercooler cools the air to the inlet
temperature, T 3 = T 1. It can be shown that the optimal pressure, P 2 = (P 1P 4) 1/2 ,
for minimum total compressor work. Find the specific compressor works and the
intercooler heat transfer for the optimal P 2.
Solution:
Optimal intercooler pressure P 2 = 100 × 1600 = 400 kPa
1: h1 = 290.43 kJ/kg, s o
T1 = 6.83521 kJ/kg K
C.V. C1: w C1 = h 2 - h 1, s 2 = s 1 leading to Eq.8.28
⇒ s o
T2 = so
T1 + R ln(P2/P1) = 6.83521 + 0.287 ln 4 = 7.2331 kJ/kg K
⇒ T 2 = 430.3 K, h 2 = 432.05 kJ/kg
w C1 = 432.05 - 290.43 = 141.6 kJ/kg
C.V. Cooler: T 3 = T 1 ⇒ h 3 = h 1
q OUT = h 2 - h 3 = h 2 - h 1 = w C1 = 141.6 kJ/kg
C.V. C2: T3 = T1, s4 = s3 and since s o
T3 = so
T1 , P4/P3 = P2/P1 ⇒ s o
T4 = so
T3 + R ln(P4/P3) = s o
T2 , so we have T4 = T2 Thus we get w C2 = w C1 = 141.6 kJ/kg
P
4
3
2
1
v
T
4
3
1600 kPa
2
1
400 kPa
100 kPa
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