Problem $2(3$ points total$)$

In industrial and engineering applications, such as power generation and refrigeration systems,

optimizing the use of energy is crucial. Understanding the thermodynamic principles and

evaluating different system components, such as throttling valves and turbines, is essential for

designing more efficient and sustainable industrial processes. In this problem, you will conduct a

simple engineering analysis to determine the benefit of replacing a simple valve with a turbine.

Consider a case where saturated liquid water passes through an adiabatic throttling valve. The fluid

enters the valve at a pressure of $1\mathrm{.}0135$ bar $,$ and exits at $0\mathrm{.}5$ bar $.$ You are considering replacing the

valve with a turbine. In this scenario, the same desired pressure drop would still occur, but the

turbine would also produce some work.

A$.$ Determine the mass quality of the fluid leaving the valve

B$.$ Calculate the rate of entropy generation in the valve per kilogram of entering water

C$.$ Determine the maximum work that could be produced by a turbine per kilogram of eittering

water, assuming the conditions of the stream entering the turbine are identical to those entering the

valve, and the pressure leaving the turbine is $0\mathrm{.}5$ bar

D$.$ Compare the physical state of the fluid leaving the idealized turbine $($as described in part C$)$ to

the physical state of the fluid leaving the valve $($as described in part A$).$ Are they identical? Can

you rationalize why they are, or are not, identical?