$6.$ A piston$-$cylinder system contains $0\mathrm{.}6$ kg of water vapor with a volume of$0\mathrm{.}1$m $3.$ The mass of the piston is such that it maintains a pressure of $800$kPa. The cylinder is then connected to a supply pipe that provides water vapor at $5$ MPa and $500$C by a valve. The valve is opened and the water vapor slowly enters the cylinder until the volume doubles and the temperature reaches $250$C$.$ The valve is closed. To find$($A$)$ the body of water entered and$($B$)$ net heat transfer.