The piston cylinder shown below is filled will air. Initially it has $q,m^3$ of air at $500$ kPa and $417$ C $.$ The valve is opened for $5\mathrm{.}2$ mins and the final volume is $0\mathrm{.}5m^3$ while keeping at the same temperature. The final pressure is $400$ kPa $.$ Using constant specific heats, determine a$)$ the mass flow rate of the air as it leaves and b$)$ The flow work knowing that we don't know the process path that occurred during this process $($can$\text{'}$t find boundary work directly$).$ Start with general mass and energy balance.