Problem $1[55$ points$]$:

A steady$-$state turbine shown below is used with a heat exchanger

unit to increase the efficiency of a power plant. Steam is injected at

the inlet of the turbine at $420C,100$ bar $($state $1)$ and exits at

$75C$ with the specific volume of $3\mathrm{.}2\frac{m^3}{k}g($state $2).$ The flow then

enters a heat exchanger where it is condensed to $75C$ at $20$ bar

$($state $3)$ through heat transfer to cooling water passing through the

condenser in a separate branch. The cooling water enters the heat

exchanger at $20C$ and $1$ bar $($state $4)$ and exits at $36C$ with no

pressure change $($state $5).$ The change of kinetic and potential

energy through the turbine and the heat exchanger are neglected.

The turbine output power develops $8\mathrm{.}5$ MW adiabatically. Apply all

the steps of problem solving methodology and draw $T_{?}-$

$v$ diagram and then answer the following parts:

A$.$ Determine the mass flow rate through the turbine in processes

$1-2-3[k\frac{g}{s}].$

B$.$ By neglecting the heat transfer from the boundaries of heat

exchanger, determine the mass flow rate of cooling water

required $k\frac{g}{s}.$