The inlet and the outlet conditions of steam for an adiabatic steam turbine are as indicated in the figure. The notations are as usually followed.

Assume the above turbine to be part of a simple Rankine cycle. The density of water at the inlet to the pump is $$1000$$ $$kg/{m^3}.$$ Ignoring kinetic and potential energy effects, the specific work (in $$kJ/kg$$) supplied to the pump is

A thermal power plant operates on a regenerative cycle with a single open feed water heater, as shown in the figure. For the state points shown, the specific enthalpies are: $${h_1} = 2800\,\,kJ/kg$$ and $${h_2} = 200\,\,kJ/kg$$. The bleed to the feed-water heater is $$20\% $$ of the boiler steam generation rate. The specific enthalpy at state $$3$$ is

Which combination of the following statements is correct?

The incorporation of re-heater in a steam power plant.

$$P:$$ always increases the thermal efficiency of the plant.
$$Q:$$ always increases the dryness function of steam at condenser inlet.
$$R:$$ always increases the mean temperature of heat addition
$$S:$$ always increases the specific work output.

Determine the correctness or otherwise of the following Assertion $$(a)$$ and the Reason$$(r).$$

Assertion(A): In a power plant working on a Rankine cycle, the regenerative feed water heating improves the efficiency of the steam turbine.

Reason(R): The regenerative feed water heating raises the average temperature of heat addition in the Rankine cycle.