A $3-m^3$ rigid tank $($Tank A$)$ has air at $200$kPa and $500K.$ The tank is connected by a valve to an empty piston$-$cylinder device $($Cylinder B$).$ The piston has a mass of $20kg$ and a cross$-$sectional area of $0\mathrm{.}2m^2.$

The valve is opened and the piston moves slowly upward $0\mathrm{.}5m$ and then the valve is closed. During the process, the air temperature remains at $500K.$ If the atmospheric pressure is $101\mathrm{.}3$kPa, determine the pressure in the cylinder needed to float the piston and the final pressure in the tank A$.$ The gas constant R for air is $0\mathrm{.}2870$kPa$*\frac{m^3}{k}g*K.$

Hint: to solve this problem you will have to consider multiple systems separately.

Ans: $102\mathrm{.}3$kPa,$196\mathrm{.}6$kPa