In a steam power plant operating on the Rankine cycle, steam enters the turbine at $$4$$ $$MPa,$$ $${350^ \circ }C$$ and exits at a pressure of $$15$$ $$kPa.$$ Then it enters the condenser and exits as saturated water. Next, a pump feeds back the water to the boiler. The adiabatic efficiency of the turbine is $$90\% $$. The thermodynamic states of water and steam are given in the table.

$$h$$ is specific enthalpy, $$s$$ is specific entropy and $$v$$ the specific volume; subscripts $$f$$ and $$g$$ denote saturated liquid state and saturated vapour state.

Heat supplied $$(kJ/kg)$$ to the cycle is

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.

If mass flow rate of steam through the turbine is $$20kg/s,$$ the power output of the turbine (in $$MW$$) is

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