Problem $1(25$ points$)$

The diagram at the right illustrates a Rankine cycle with $\backslash (80\backslash$mathrm$\{$~kg$\}/\backslash$mathrm$\{$s$\}\backslash )$ of water flowing through it$.$ Various properties are shown at appropriate points. The turbine is adiabatic. The turbine and pump isentropic efficiencies are also shown in the figure. Pressure losses and heat losses occur in the piping connecting the boiler and the turbine as indicated. Cold river water flows through the condenser. Do the following:

a$)$ Draw this cycle on a T$-$s diagram

b$)$ Determine the net power output in MW$.$

c$)$ Determine the cycle efficiency.

d$)$ Determine the heat loss in the pipe connecting the boiler and turbine in MW$.$

e$)$ Determine the mass flow rate of river water flowing the condenser in $\backslash (\backslash$mathrm$\{$kg$\}/\backslash$mathrm$\{$s$\}\backslash ).$ You may assume negligible pressure drop for the river water flowing through the condenser.