A compressor is used to bring saturated water vapor at 103 lbf / in ^{2} up to 2000 lbf / in ^{2}, where the actual exit temperature is 1200 F. Find the irreversibility and the second law efficiency.
A compressor is used to bring saturated water vapor at 103 lbf / in ^{2} up to 2000 lbf / in ^{2}, where the actual exit temperature is 1200 F. Find the irreversibility and the second law efficiency.
Inlet state: Table F.7.1 h _{ i }=1188.4 Btu / lbm , s _{ i }=1.601 Btu / lbm R
Actual compressor F.7.2: h _{ e }=1598.6 Btu / lbm , s _{ e }=1.6398 Btu / lbm R
Energy Eq. actual compressor: – w _{ c , ac }= h _{ e }- h _{ i }=410.2 Btu / lbm
Eq.8.13: i = T _{0}\left( s _{ e }- s _{ i }\right)=536.67 \times(1.6398-1.601)= 2 0 . 8 2 Btu / lbm
Eq.8.15: w _{ rev }= i + w _{ c , ac }=20.82+(-410.2)=-389.4 Btu / lbm
\eta_{I I}=- w _{ rev } /\left(- w _{ c , ac }\right)=389.4 / 410.2= 0 . 9 4 9
………………………………………..
Eq.8.13 : \dot{I}=\dot{W}^{ rev }-\dot{W}_{ c.v.ac }=\dot{Q}_{0}^{ rev }=T_{0} \dot{S}_{\text {gen ac }}
Eq.8.15 :
\begin{aligned}i &=\dot{I} / \dot{m}=w^{ rev }-w_{ c.v. ac }=q_{0}^{ rev }=T_{0} S_{ gen ac } \\&=T_{0}\left[s_{e}-s_{i}-\sum \frac{q_{j}}{T_{j}}\right]\end{aligned}