Please answer Problem $2$ A$-$F$.$ Problem $1$ is provided because problem $2$ references it$.$

Problem #$1(10$ pts$)$

Consider water in a Rankine Cycle used for a nuclear powerplant with a turbine, a condenser, a pump, and a boiler. A nuclear reactor supplies heat to the boiler. Water enters

the turbine as a superheated vapor at $520$ C and $8$ MPa $.$ It exits the turbine at $100$ kPa $.$ The turbine has an isentropic efficiency of $80\%.$ The pump has an isentropic efficiency

of $70\%.$ Water enters the pump as a saturated liquid at $100$ kPa $,$ and exits at the same pressure as it enters the turbine $(8$ MPa $).$ The cycle is required to have a net power

output of $50$ MW $.$

A$.$ Determine the work$/$mass from the turbine.

B$.$ Determine the work$/$mass into the pump $($report as a positive value; you may assume the isentropic case is isothermal and incompressible$)$

C$.$ Determine the mass flow rate of the cycle

D$.$ Determine overall efficiency of the cycle $(\{$: eta$=$W$^()\_($net$)//$Q$^()\_($H$))$

E$.$ If the boundary temperature on the hot side is $520$ C and the boundary temperature on the cold side is $50$ C $,$ what is the rate of entropy production $($ sigma$^())$ for the entire

cycle?

F$.$ Draw the process on a T$-$s diagram; label all $4$ states $(1$ into turbine, $2$ into condenser, $3$ into pump, $4$ into boiler$)$

G$.$ Problem #$2(10$ pts$)$

The Rankine Cycle from problem $2$ is modified to add reheat $($this adds two state points$).$ The initial temperature and pressure into the first turbine $($state $1)$ remain the same as

problem $1.$ The first turbine drops to a pressure of $1$ MPa $.$ From State $2$ to State $3,$ it is heated isobarically until it has a temperature of $360$ C $.$ In the second turbine, it drops to

$100$ kPa $,$ so the pressure into the condenser $($and into the pump$),$ and the pressure out of the pump $($and into the boiler and first turbine$)$ are the same as Problem $2.$ The

turbine and pump efficiencies are the same as Problem $2.$

Note: this means that the pump has the same enthalpy in and out $($and work$/$mass$)$ as problem $2,$ so you do not need to repeat that work; h$\_(6)-$h$\_(5)$ for this problem is the

same as h$\_(4)-$h$\_(3)$ in problem $2.$

The net power output $($W$^())$ remains at $50$ MW $.$

A$.$ Determine the work$/$mass from state $1$ to state $2.$

B$.$ Determine the work$/$mass from state $3$ to state $4.$

C$.$ Determine the mass flow rate of the cycle

D$.$ Determine overall efficiency of the cycle

E$.$ Determine how much less heat is required from the nuclear reactor; report as a positive value in kW $.$

F$.$ Suppose that the If the cost to add the extra turbine is $$100$ million, the energy is worth $$0\mathrm{.}15//$kW$-$hr$,$ and that the power plant will last longer if there is less heat required

due to the extra turbine. How much longer $($in years$)$ will the power plant need to last to pay off the cost? Will it last this this long if the formula for how much longer it will

last is ExtraYears $=40$ years $**($Q$^()\_($saved$))/($Q$^()\_($H$,1))$ where Q$^()\_("$saved $")$ is your answer to part e and Q$^()\_($H$,1)$ is the heat required in problem $1?$

G$.$ Draw the process on a T$-$s diagram; label all $6$ states $(1$ into first turbine, $2$ into reheater, $3$ into second turbine, $4$ into condenser, $5$ into pump, $6$ into boiler