In a Rankine cycle, superheated steam at $6$MPa pressure and $500\backslash$deg C temperature enters the turbine. The fluid at $100$ kPa pressure coming out of the turbine enters the condenser. In the case where the flow rate of steam is $40$ kg$/$s and the turbine efficiency is $70\%$;

a$)$ Show the cycle on the T$-$S diagram.

b$)$ Determine the heat supplied to the boiler, the heat withdrawn from the condenser, the turbine power and the thermal efficiency of the cycle.

c$)$ If the work done in the pump is $10$ kJ$/$kg$,$ find the thermal efficiency of the cycle.