A geothermal power plant on the Raft river uses isobutane as the working fluid. The fluid enters the reversible adiabatic turbine at 320 F, 805 lbf/in.^2 and the condenser exit condition is saturated liquid at 91 F. Isobutane has the properties Tc = 734.65 R, Pc = 537 lbf/in.^2 , Cpo = 0.3974

Question

A geothermal power plant on the Raft river uses isobutane as the working fluid. The fluid enters the reversible adiabatic turbine at 320 F, 805 [latex]lbf / in. ^{2}[/latex] and the condenser exit condition is saturated liquid at 91 F. Isobutane has the properties Tc = 734.65 R, Pc = 537 [latex]lbf / in. ^{2}[/latex] , Cpo = 0.3974 Btu/lbm R and ratio of specific heats k = 1.094 with a molecular weight as 58.124. Find the specific turbine work and the specific pump work.

Accepted Answer

R = 26.58 ft lbf/lbm R = 0.034 166 Btu/lbm R

Turbine inlet: [latex]T _{ r1 }=779.7 / 734.7=1.061, \quad P _{ r1 }=805 / 537=1.499[/latex]

Condenser exit: [latex]T _{3}=91 F , x _{3}=0.0 ; \quad T _{ r 3}=550.7 / 734.7=0.75[/latex]

From D.1 : [latex]P _{ r 3}=0.165, Z _{3}=0.0275[/latex]

[latex]P _{2}= P _{3}=0.165 imes 537=88.6 lbf / in .^{2}[/latex]

From D.2 and D.3,

[latex]\begin{aligned}&\left( h _{1}^{*}- h _{1} ight)=0.034166 imes 734.7 imes 2.85=71.5 Btu / lbm \&\left( s _{1}^{*}- s _{1} ight)=0.034166 imes 2.15=0.0735 Btu / lbm R \&\left( s _{2}^{*}- s _{1}^{*} ight)=0.3974 \ln \frac{550.7}{779.7}-0.034166 \ln \frac{88.6}{805}=-0.0628 Btu / lbm R\end{aligned}[/latex]

[latex]\begin{gathered}\left( s _{2}^{*}- s _{2} ight)=\left( s _{2}^{*}- s _{ F 2} ight)- x _{2} s _{ FG 2}=0.034166 imes 6.12- x _{2} imes 0.034166(6.12-0.29) \=0.2090- x _{2} imes 0.1992\end{gathered}[/latex]

[latex]\begin{aligned}&\left( s _{2}- s _{1} ight)=0=-0.2090+ x _{2} imes 0.1992-0.0628+0.0735 \Rightarrow x _{2}=0.9955 \&\left( h _{2}^{*}- h _{1}^{*} ight)= C _{ P 0}\left( T _{2}- T _{1} ight)=0.3974(550.7-779.7)=-91.0 Btu / lbm\end{aligned}[/latex]

From D.2,

[latex]\begin{gathered}\left( h _{2}^{*}- h _{2} ight)=\left( h _{2}^{*}- h _{ F 2} ight)- x _{2} h _{ FG 2}=0.034166 imes 734.7[4.69-0.9955(4.69-0.32)] \=117.7-0.9955 imes 109.7=8.5 Btu / lbm\end{gathered}[/latex]

Turbine: [latex]w _{ T }=\left( h _{1}- h _{2} ight)=-71.5+91.0+8.5= 2 8 . 0 Btu / lbm[/latex]

Pump [latex]v _{ F 3}=\frac{ Z _{ F 3} RT _{3}}{ P _{3}}=\frac{0.0275 imes 26.58 imes 550.7}{88.6 imes 144}=0.03155 ft ^{3} / lbm[/latex]

[latex]w _{ P }=-\int_{3}^{4} vdP \approx v _{ F 3}\left( P _{4}- P _{3} ight)=-0.03155(805-88.6) imes \frac{144}{778}=- 4 . 2 Btu / lbm[/latex]

Question 12.176E: A geothermal power plant on the Raft river uses isobutane as...

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