Question 7.234E: Repeat Problem 7.199E for a pump/compressor isentropic effic...

C.V.: Pump/Compressor, \dot{ m }=1   lbm / s,  R-410A

a) State 1: Table F.9.1,  x _{1}=1.0        Saturated vapor,    P _{1}= P _{ g }=76.926 \text { psia },

Ideal Compressor is isentropic,  s _{2}= s _{1}=0.2535   Btu / lbm  R

Energy Eq.4.13:      q _{ c }+ h _{1}= h _{2}+ w _{ c } ; \quad q _{ c }=0

w _{ cs }= h _{1}- h _{2}=118.21-134.54=-16.33   Btu / lbm;

Now the actual compressor

b) State 1:  T _{1}=10 F , x _{1}=0        Saturated liquid. This is a pump.

Energy Eq.4.13:        q _{ p }+ h _{1}= h _{2}+ w _{ p } ; \quad q _{ p }=0

Ideal pump is isentropic and the liquid is incompressible, Eq.7.18:

Now the actual pump

Assume State 2 is approximately a saturated liquid  \Rightarrow T _{2} \cong 1 2 . 2   F

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Eq.4.13 : q+h_{i}+\frac{ V _{i}^{2}}{2}+g Z_{i}=h_{e}+\frac{ V _{e}^{2}}{2}+g Z_{e}+w

Eq.7.18 :
\begin{aligned}w &=-\int_{i}^{e} v d P \quad \text { and } \quad P v^{n}=\text { constant }=C^{n} \\w &=-\int_{i}^{e} v d P=-C \int_{i}^{e} \frac{d P}{P^{1 / n}} \\&=-\frac{n}{n-1}\left(P_{e} v_{e}-P_{i} v_{i}\right)=-\frac{n R}{n-1}\left(T_{e}-T_{i}\right)\end{aligned}