A line with a steady supply of octane, C8H18, is at 750 F, 440 lbf/in.^2 . What is your best estimate for the availability in an steady flow setup where changes in potential and kinetic energies may be neglected?

Question

A line with a steady supply of octane, [latex]C _{8} H _{18}[/latex], is at 750 F, 440 [latex]lbf / in .^{2}[/latex] . What is your best estimate for the availability in an steady flow setup where changes in potential and kinetic energies may be neglected?

Accepted Answer

Availability of Octane at [latex]T _{ i }=750 F , P _{ i }=440 lbf / in. ^{2}[/latex]

R = 13.53 ft lbf/lbm-R = 0.017 39 Btu/lbm-R

[latex]P _{ ri }=\frac{440}{361}=1.219, T _{ ri }=\frac{1209.7}{1023.8}=1.182[/latex]

From D.2 and D.3:

[latex]\begin{aligned}&\left( h _{1}^{*}- h _{1} ight)=0.01739 imes 1023.8 imes 1.15=20.5 Btu / lbm \&\left( s _{1}^{*}- s _{1} ight)=0.01739 imes 0.71=0.0123 Btu / lbm R\end{aligned}[/latex]

Exit state in equilibrium with the surroundings

Assume [latex]T _{0}=77 F , P _{0}=14.7 lbf / in .^{2}[/latex]

[latex]T _{ r 0}=\frac{536.7}{1023.8}=0.524, P _{ r 0}=\frac{14.7}{361}=0.041[/latex]

From D.2 and D.3:

[latex]\left( h _{0}^{*}- h _{0} ight)= RT _{ C } imes 5.41=96.3 ext { and } \quad\left( s _{0}^{*}- s _{0} ight)= R imes 10.38=0.1805[/latex]

[latex]\begin{aligned}&\left( h _{ i }^{*}- h _{0}^{*} ight)=0.409(1209.7-536.7)=275.3 Btu / lbm \&\left( s _{ i }^{*}- s _{0}^{*} ight)=0.409 \ln \frac{1209.7}{536.7}-0.01739 \ln \frac{440}{14.7}=0.2733 Btu / lbm R \&\left( h _{ i }- h _{0} ight)=-20.5+275.3+96.3=351.1 Btu / lbm \&\left( s _{ i }- s _{0} ight)=-0.0123+0.2733+0.1805=0.4415 Btu / lbm R \&\psi_{ i }= w ^{ rev }=\left( h _{ i }- h _{0} ight)- T _{0}\left( s _{ i }- s _{0} ight)=351.1-536.7(0.4415)= 1 1 4 . 1 Btu / lbm\end{aligned}[/latex]

Question 12.177E: A line with a steady supply of octane, C8H18, is at 750 F, 4...

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