$6.$ A $\backslash (2\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ rigid insulated tank initially containing saturated water vapor at $1$ MPa is connected through a valve to a supply line that carries steam at $\backslash (400^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Now the valve is opened, and steam is allowed to flow slowly into the tank until the pressure in the tank rises to $2$ MPa $.$ At this instant the tank temperature is measured to be $\backslash (300^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine the mass of the steam that has entered and the enthalpy of the steam in the supply line.