Question $3(55$ points$)$: This question has FOUR parts. Answer all parts. Show calculations and provide logical explanations wherever required.

Consider the following power cycle $($shown by the dotted green boundary$)$ using water as a working substance and operating between a hot and a cold reservoir with temperatures $T_H=800C$ and $T_C=25C$ respectively.

The four processes involved are:

Process A: From state $1$ to state $2$: Adiabatic compression through a pump that requires work as input. During the process pressure increases from $5$ bar to $80$ bar.

Process B: From state $2$ to state $3$: Isothermal internally reversible volume expansion in a boiler with heat addition $(($:$Q_H$