Air flows in a frictionless, adiabatic duct at M = 0.6 and P₀ = 500 kPa. The cross-sectional area of the duct is 6 cm² and the mass flow rate is 0.5 kg/s. If the area of the duct near the exit is reduced so as to form a convergent nozzle, what is the minimum area possible without altering the flow properties in the duct? If the area is reduced to 3/4th of this value, determine the change (if any) in the mass flow rate and the static and stagnation pressure in the duct.