Q$1$: In a hypothetical cyclic steam power plant incorporating a single direct$-$contact feed wa steam leaves the boiler at $6$MPa and $500$ v $C$ and the condenser pressure is $10$kPa. Expansior is reversible and adiabatic. The feed water heater takes steam bled from the turbine at pres. and heats the feed water to the corresponding saturation temperature. Temperature and er of the fluid in passing through any pumps may be neglected. Calculate:

a$.$ the mass of steam bled from the turbine per $kg$ of steam leaving the boiler.

b$.$ The cycle efficiency.

C$.$ The improvement in thermal efficiency due to the introduction of this single stage of fee heating, expressed as a percentage of the Rankine cycle efficiency.