$(20\%)$ In a water$-$dominated geothermal power plant, hot water at $T_1=230C$ and $P1=8$MPa is

throttled to $40$ kPa and enters the flash tank separator.

a$.(10\%)$ Assuming that the tank is fully insulated, find the fraction of the total mass entering the

tank that turns into vapor.

b$.(10\%)$ If the tank is not insulated, and the rate of heat loss from the tank is $50k\frac{J}{k}g$ of water

entering the tank, what fraction of the mass entering the tank turns to saturated vapor?