An insulated, rigid tank whose volume is $0\mathrm{.}5m^3$ is connected by a valve to a large vessel holding steam at $40$ bar, $440C.$ The tank is initially evacuated. The valve is opened only as long as required to fill the tank with steam to a pressure of $20$ bar.

Determine:

$($a$)$ the final temperature of the steam in the tank, in $C,$ the final mass of the steam in the tank, in $kg.$ and

Ib$)$ the amount of entropy produced, in $k\frac{J}{K}$