$1.)(20$ points$)$ The cogeneration plant shown below can supply process heat or electricity to its neighbors. The system is set up to allow for a certain amount of working fluid $(\backslash ($ z $\backslash )$ is the mass fraction sent to process heat exchanger$)$ to bypass the turbine. In addition, it can extract additional fluid part way through the turbine $($ y is mass fraction extracted$).$ The process heater also acts as a mixer. The process runs at steady$-$state and the working fluid can be assumed to be that of water.

a$)$ Define a closed system below, by using a solid line to outline the boundaries of your system.

b$)$ Add arrows and label the energy transfer into and out of your closed system at the appropriate devices.

c$)$ Consider just the heat exchanger $/$ mixer device.

a$.$ Identify the type of system:

b$.$ Add a dash$-$lined to show the system boundaries of the heat exchanger $/$ mixer

c$.$ Add arrows and label the energy transfer into and out of the heat exchanger $/$ mixer.

d$)$ How many distinct processes are identified in the diagram below? $\backslash (\backslash$mathrm$\{$M$\}=\backslash )$

e$)$ How many distinct states of the working fluid exist in the diagram below? $\backslash (\backslash$mathrm$\{$N$\}=\backslash )($Indicate these states below by showing numbers $1$ to N $)$

f$)$ How many state properties need to be known at each state to fully describe the state of the water?