A nitrogen line, 540 R, and 75 lbf/in.^2, is connected to a turbine that exhausts to a closed initially empty tank of 2000 ft^3, as shown in Fig. P4.137. The turbine operates to a tank pressure of 75 lbf/in.^2, at which point the temperature is 450 R. Assuming the entire process is adiabatic,

Question

A nitrogen line, 540 R, and 75 [latex]lbf / in .^{2}[/latex], is connected to a turbine that exhausts to a closed initially empty tank of 2000 [latex]ft ^{3}[/latex], as shown in Fig. P4.137. The turbine operates to a tank pressure of 75 [latex]lbf / in .^{2}[/latex], at which point the temperature is 450 R. Assuming the entire process is adiabatic, determine the turbine work.

Accepted Answer

C.V. turbine & tank ⇒ Transient problem

Conservation of mass: [latex]m _{ i }= m _{2}= m[/latex]

Energy Eq.: [latex]m _{ i } h _{ i }= m _{2} u _{2}+ W _{ CV } ; W _{ CV }= m \left( h _{ i }- u _{2} ight)[/latex]

Inlet state: [latex]P _{ i }=75 lbf / in ^{2}, T _{ i }=540 R[/latex]

Final state 2: [latex]P _{2}=75 lbf / in ^{2}, T _{2}=450 R[/latex]

[latex]v _{2}= RT _{2} / P _{2}=55.15 imes 450 /(75 imes 144)=2.298 ft ^{3} / lbm[/latex]

[latex]m _{2}= V / v _{2}=2000 / 2.298=870.32 lbm[/latex]

[latex]h _{ i }- u _{2}= u _{ i }+ RT _{ i }- u _{2}= RT _{ i }+ C _{ v }\left( T _{ i }- T _{2} ight)[/latex]

[latex]=\frac{55.15}{778.17} 540+0.178(540-450)=38.27+16.02=54.29 \frac{ Btu }{ lbm }[/latex]

[latex]W _{ CV }=870.32 imes 54.29= 4 7 2 5 0 ~ B t u[/latex]

Question 4.210E: A nitrogen line, 540 R, and 75 lbf/in.^2, is connected to a ...

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