$(1)\{45$ Marks$\}$ Steam from a thermal power plant operating between $5$ MPa and $10$ kPa of pressure, as shown in the

figure. The superheated vapor enters in a steady state turbine with temperature of $600C.$ Assuming the turbine

and pump operates as an ideal process and saturated vapor enters in the Superheater and saturated liquid leaves

the condenser, calculate:

$($a$)$ The specific heat transfer in Boiler, Superheater and Condenser. $(30\%\}$

$($b$)$ The efficiency of the thermal power plant and compare with the Carnot efficiency. $\{40\%\}$

$($c$)$ Plot the states in the Temperature$-$Entropy diagram. $(30\%)$