Question 12.CSGP.29: A two-stage air compressor has an intercooler between the tw......
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=\left( P _1 P _4\right)^{1 / 2}, for minimum total compressor work. Find the specific compressor works and the intercooler heat transfer for the optimal P_2.
Optimal intercooler pressure P_2=\sqrt{100 \times 1600}=400 \,kPa
\text { 1: } \quad h _1=290.43 \,kJ / kg , \quad s _{ T 1}^{ o }=6.83521 \,kJ / kg KC.V. C1:
C.V. Cooler: T _3= T _1 \Rightarrow h _3= h _1
q_\text { out }= h _2- h _3= h _2- h _1= w _{ C 1}= 1 4 1 . 6 ~ k J / k g
C.V. C2: T _3= T _1, \quad s _4= s _3 \quad \text { and since } s _{ T 3}^{ o }= s _{ T 1}^{\circ}, \quad P _4 / P _3= P _2 / P _1
\Rightarrow \quad \stackrel{\circ}{ s _{ T 4}}= s _{ T 3}^{ o }+ R \ln \left( P _4 / P _3\right)= s _{ T 2}^{\circ} \text {, so we have } T _4= T _2
Thus we get w _{ C 2}= w _{ C 1}= 1 4 1 . 6 { kJ } / { kg }
