$10$ E$2)$ A beverage producing facility utilizes a natural gas boiler $($fire tube$)$ of $2\mathrm{.}0$ MW capacity for its

various process and heating needs. The boiler output is a saturated vapour at a pressure of $800$ kPa $.$ A

portion of the total steam is throttled to $200$ kPa and goes to a hot water heater $($mixing chamber$),$

where it mixes with a feedwater stream. The hot water heater produces $60C$ water at a rate of

$2\mathrm{.}5k\frac{g}{s},$ but it is uninsulated and has a heat loss of $20$ kW $($the energy equation might be useful to

analyze the mixing chamber$).$ The feed water that is supplied to the boiler and hot water heater has a

line pressure of $200$ kPa and a temperature of $10C.$

a$)$ Draw a simple system schematic and a T$-$h diagram to represent all relevant states$/$processes$.$

Determine:

b$)$ the temperatures of the steam leaving the boiler and entering the water heater $C$;

c$)$ the portion of steam used by the water heater $k\frac{g}{s}$;

d$)$ the percentage of boiler steam$/$energy diverted to the water heater $[\%].$