In the figure shown, the system is a pure substance kept in a piston- cylinder arrangement. The system is initially a two- phase mixture containing $$1$$ $$kg$$ of liquid and $$0.03$$ $$kg$$ of vapour at a pressure of $$100kPa.$$ Initially, the piston rests on a set of stops, as shown in the figure. A pressure of $$200kPa$$ is required to exactly balance the weight of the piston and the outside atmospheric pressure. Heat transfer takes place into the system until its volume increases by $$50\% $$. Heat transfer to the system occurs in such a manner that the piston, when allowed to move, does so in a very slow (quasi-static / quasi-equilibrium) process. The thermal reservoir from which heat is transferred to the system as a temperature of $${400^ \circ }C$$. Average temperature of the system boundary can be taken as $${175^ \circ }C.$$ Heat transfer to the system is $$1kJ$$, during which its entropy increases by $$10$$ $$J/K.$$

Specific volume of liquid $$\left( {{v_f}} \right)$$ and vapour $$\left( {{v_g}} \right)$$ phases, as well as values of saturation temperatures, are given in the table below.

At the end of the process, which one of the following situations will be true?

Water having a density of $$1000\,\,kg/{m^3},$$ issues from a Nozzle with a velocity of $$10$$ $$m/s$$ and the jet strikes a bucket mounted on a Pelton wheel. The wheel rotates at $$10$$ $$rad/s$$. The mean diameter of the wheel is $$1$$ $$m.$$ The jet is split into two equal streams by the bucket; such each stream is deflected by $${120^ \circ }$$, as shown in the figure. Friction in the bucket may be neglected. Magnitude of the torque exerted by the water on the wheel, per unit mass flow rate of the incoming jet, is