$2.$A piston$-$cylinder device initially contains water in saturated liquid form at $3$ Mpa. At this state, the piston rests on a pair of stops and the corresponding volume occupied by the water is $2$ L$.$ The mass of the piston is such that a pressure of $90$ bar is required to move the piston. The water is now heated using a $1500$ W electric heater for $30$ minutes. During this time $0\mathrm{.}5$ kg of water vaporizes. Due to insulation issues, there is some heat exchange between the water and the surroundings. Determine the magnitude $($in kJ$)$ and direction of heat transfer. Also sketch the process on a P$-$v diagram with respect to the saturation lines.