In a heat-powered refrigerator, a turbine is used to drive the compressor using the same working fluid. Consider the combination shown in Fig. P9.157 where the turbine produces just enough power to drive the compressor and the two exit flows are mixed together. List any assumptions made and find

Question

In a heat-powered refrigerator, a turbine is used to drive the compressor using the same working fluid. Consider the combination shown in Fig. P9.157 where the turbine produces just enough power to drive the compressor and the two exit flows are mixed together. List any assumptions made and find the ratio of mass flow rates [latex]\dot{ m }_3 / \dot{ m }_1 ext { and } T _5\left( x _5 ight.[/latex] if in two-phase region) if the turbine and the compressor are reversible and adiabatic

Accepted Answer

CV: compressor

[latex]\begin{aligned}& s _{2 S }= s _1=1.0779 \,kJ / kg K ightarrow h _{2 S }=317.43 \,kJ / kg \& w _{ SC }= h _1- h _{2 S }=271.89-317.43=-45.54 \,kJ / kg\end{aligned}[/latex]

CV: turbine

[latex]\begin{aligned}& s _{4 S }= s _3=1.0850 \,kJ / kgK ext { and } P _{4 S } \Rightarrow h _{4 S }=319.72 \,kJ / kg \& w _{ ST }= h _3- h _{4 S }=341.29-319.72=21.57 \,kJ / kg\end{aligned}[/latex]

[latex] ext { As } \dot{ w }_{ TURB }=-\dot{ w }_{ COMP }, \quad \dot{ m }_3 / \dot{ m }_1=-\frac{ w _{ SC }}{ w _{ ST }}=\frac{45.54}{21.57}= 2 . 1 1 1[/latex]

CV: mixing portion

[latex]\begin{aligned}& \dot{ m }_1 h _{2 S }+\dot{ m }_3 h _{4 S }=\left(\dot{ m }_1+\dot{ m }_3 ight) h _5 \& 1 imes 317.43+2.111 imes 319.72=3.111 h _5 \& \Rightarrow h _5=318.984 \,kJ / kg \quad \Rightarrow \quad T _5= 5 8 . 7 ^ { \circ } { C }\end{aligned}[/latex]

Question 9.CSGP.157: In a heat-powered refrigerator, a turbine is used to drive t......

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