Proble

Problem $2.(12$ points$)$ Steam enters the turbine shown in Fig. $1,$ at $\frac{80}{b}ar,440C$ with a mass flow rate of $100k\frac{g}{s},$ and exits the turbine as a two$-$phase mixture at $0\mathrm{.}3$ bar as shown in Fig. $1.$ The quality of the two$-$phase mixture at the turbine exit is $0\mathrm{.}93.$ The mixture then enters the condenser operating at $0\mathrm{.}3$ bar and leaves the condenser at $50C.$ Assuming the system operates at steady state, and ignoring stray heat transfer and kinetic and potential energy effects,

$($a$)$ Determine the power produced by the turbine in $MW,$

$($b$)$ Determine the rate of heat removal from the water in the condenser in $MW.$

$($c$)$ Sketch the processes in $p-v$ and $T-v$ diagrams.

Figure $1.$ System diagram for Problem $2.$m $1.(8$ points$)$ A rigid $($i$.$e$.,$ constant volume$)$ tank contains $1$ kg of water $($two$-$phase mixture$)$ initially at $100C$ with the quality of $0\mathrm{.}75.$ The water in the tank is then heated until the temperature of the water reaches $200C.$

$($a$)$ Determine the initial specific volume of the water inside the tank.

$($b$)$ Calculate the initial internal energy of the water inside the tank.

$($c$)$ Find the total amount of heat added to the water during the heating process.