The three$-$stage turbine system has the properties shown. Determine the total power produced by the system $($kW$)$ and the power produced by the first, second and third stage turbines. Always start with the general energy balance.

The piston cylinder shown below is filled will air. Initially it has $m^3$ 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.