A simplified flow diagram for a $($relatively low power$)$ pressurized water reactor $($PWR$)$ nuclear power plant is given

in Fig. $1.$ Partial information on the various states in the cycle is shown in Table $1.$

In contrast to a boiling water reactor $($BWR$),$ the water in the reactor of a PWR is pressurized to suppress boiling

as much as possible. The pressurized water is heated in the reactor, which supplies $157$ MW of heat, and is then

transferred from the reactor to a steam drum to produce the steam that drives the turbines. Saturated vapor leaves

the steam drum to power the turbines $(1),$ while liquid water is pumped from the steam drum back to the reactor $(19).$

The cycle implements $$regenerative feed heating$,$ where small amounts of steam are bled off from the high$-$pressure

and low$-$pressure turbines to feed$-$water heaters $(8,9,12,17).$ Waste heat primarily leaves the cycle in the condenser.

For your analysis, you may assume that any individual component of the system $($i$.$e$.,$ any pump, turbine, condenser,

etc.$)$ is a reversible process.

For your analysis, you may assume that any individual component of the system other than the reactor and the

condenser $($i$.$e$.,$ any pump, turbine, regenerative heat exchanger$)$ is approximately adiabatic from an energetic

perspective $($i$.$e$.,$Q $$mh$,$ so $$Q $0$ in a first$-$law analysis$).$ You may also assume that the pumps and turbines are

approximately reversible from an energetic perspective, in the sense that you do not have to consider any lost work

in the turbines or pumps. However, the system may not be taken as approximately isentropic in the sense that we

cannot say that $($Q$/$T $+$Sgen$)$ is negligible in an entropy analysis of the components.

For the power plant, complete the following:

a$)$ Find values for all missing entries for phase, $$m$,$ P $,$ T $,$ and h in Table $1($you may skip P and T for state $14)$

b$)$ Find the quality at $(4)$ assuming the moisture separator is adiabatic

c$)$ Find the power output of the high$-$pressure turbine

d$)$ Find the power output of the low$-$pressure turbine

e$)$ Find the thermal efficiency of the power plant

f$)$ Find the quality of the steam leaving the reactor at $(21)$

g$)$ Find the power that the pump that feeds water to the reactor transfers to the water

h$)$ Find the power that the pump that feeds water to the high$-$pressure heater transfers to the water

i$)$ Find the power that the pump that feeds water to the low$-$pressure heater transfers to the water

e$)$ Find the thermal efficiency of the power plant

j$)$ Find an upper limit to the temperature of the heat sink used by the condenser for the same net power output of

the plant if the temperature of the heat source is assumed to be equal to the temperature of the water leaving

the reactor

k$)$ Find the amount of leaked waste heat over the cycle $($i$.$e$.,$ heat lost in parts of the cycle other than the condenser$)$

Figure $1$: Flow diagram of the power plant

Table $1$: Partial thermodynamic information for the power plant