A $200-$Liter boiler tank is connected to a turbine and initially contains saturated liquid water at $150$ kPa $.$ There is a pressure valve between the tank and the turbine that opens when the pressure inside the tank reaches $1000$ kPa $.$ If this pressure is achieved, saturated vapor exits the tank $($at $1000$ kPa $)$ and goes into the turbine and exits the turbine to the atmosphere as saturated vapor at $150$ kPa $.$

Heat is added to the boiler tank until all the saturated liquid $($state $1)$ becomes a saturated vapor $($state $2),$ at which point the heat is turned off.

The turbine is an adiabatic turbine.

$($a$)$ Determine the heat transfer to the boiler during that time period $(20$ points$)$

$($b$)$ Determine the work from the turbine during that time period $(10$ points$)$

SHOW WORK PLEASE