$(50$ points$)$ Steam at $250C$ and $5$ bar passes through a not very effective turbine to generate electricity at a rate of $10k\frac{g}{m}in.$ The effluent from the turbine is saturated steam at $\frac{3}{b}ar\mathrm{.}90\%$ of the energy extracted from the steam is used to power a paddle that is mixing soup $($can be treated as water$)$ as the soup flows through an insulated mixer. The soup flows into the mixer as saturated water at $10k\frac{g}{m}in$ at a temperature of $100C.$ Some of the work of the paddle is transferred to the soup, and liquid soup and $0\mathrm{.}5k\frac{g}{m}in$ of steam flow out of the mixer in equilibrium at $100C.$

a$)15$ points: Draw and properly label a flowchart for this process.

b$)35$ points: What fraction of the turbine work is lost $($what is $\frac{W_{\text{f}\text{r}\text{o}\text{m}\text{t}\text{u}\text{r}\text{b}\text{i}\text{n}\text{e}}^{}-W_{\text{i}\text{n}\text{t}\text{o}\text{s}\text{o}\text{u}\text{p}}^{}}{W_{\text{f}\text{r}\text{o}\text{m}\text{t}\text{u}\text{r}\text{b}\text{i}\text{n}\text{e}}^{}})?$

a$)$

$(v_{1}sh)m_{1,i}$longrightarrow

$T_{1}i=250C$

$P_1{?}_1=\frac{5}{b}ar$