$(1)$ Consider a steam power plant operating on the ideal Rankine cycle. Steam enters the

turbine at $3$ MPa and $350C$ and is condensed in the condenser at a pressure of $10$

kPa $.$ Determine $($a$)$ the thermal efficiency of this power plant, $($b$)$ the thermal efficiency

if steam is superheated to $600C$ instead of $350C,$ and $($c$)$ the thermal efficiency if the

boiler pressure is raised to $15$ MPa while the turbine inlet temperature is maintained

at $600C.$