$5\mathrm{.}37$ Air is contained in a piston$-$cylinder assembly at $2$ MPa and $400$ K $($state $1).$ The $0\mathrm{.}15-m-$diameter piston is locked in place by stops at the $0\mathrm{.}2-m$ position, and a $2-$kg steel block sits on top of the piston, as shown in the sketch. The mass of the piston is $0\mathrm{.}1$ kg $.$ The stops are removed and the air rapidly expands until the piston comes to rest at the upper position $)=(0\mathrm{.}4m,$ while the block continues upward as shown in the sketch on the right. The temperature is $310$ K $($state $2).$ Assume that the process is so rapid that it can be considered adiabatic and that the constant$-$pressure specific heat is constant $(c_p=1\mathrm{.}013kJ)kg*K).$ The atmospheric pressure is $100$ kPa $.$

A$.$ Considering the air, piston, cylinder, and the block to be the system, determine the work done by the system on the surroundings.

B$.$ Determine the velocity of the steel block immediately after the piston comes to rest.

C$.$ Neglecting drag, determine the maximum height achieved by the block measured from the bottom of the cylinder.