Problem #$2(10$ points$)$

$10k\frac{g}{s}$ of water enters a turbine at $4$ MPa and $500C($state $1)$ and leaves the turbine at $10$ kPa

$($state $2).$ After leaving the turbine, the water is condensed isobarically in a condenser $($heat

exchanger$)$ to $40C($state $3).$ The energy from the condensing steam is absorbed by liquid cooling

water that enters the condenser at $20C($state $5).$

a$)$ If the power output of the turbine is $30$ MW $,$ what is the

state of the water at the outlet of the turbine? If it is a

saturated mixture, calculate its quality.

b$)$ What is the rate of heat transfer from the process water

$($the water used to generate power$)$ to the cooling

water?

c$)$ What is the mass flow rate of the cooling water? You

may treat the cooling water as having a constant specific

heat at an appropriate average temperature. There is

negligible pressure drop on the cooling water side of the

heat exchanger. Show that you can make this calculation

$3$ different ways:

i$.$ by considering just the cooling water side of the

condenser as your CV$,$

ii$.$ by considering the entire condenser as your CV$,$ and

iii. by considering a CV that includes both the turbine and the condenser.