$[$Q$1]$ Consider a steam power plant operating on the ideal Rankine cycle. Steam enters the turbine at $3$ MPa and $300C$ and is considered in the condenser at a pressure of $15$ kPa $.$ Determine $($a$)$ the thermal efficiency of this power plant, $($b$)$ the thermal efficiency if steam is superheated to $600C$ instead of $300C,$ and $($c$)$ the thermal efficiency if the boiler pressure is raised to $15$ MPa while the turbine inlet temperature is maintained at $600C.$

$15$ points