Nitrogen, modeled as an ideal gas, flows at a rate of 3 kg/s through a well-insulated horizontal nozzle operating at steady state. The nitrogen enters the nozzle with a velocity of 20 m/s at 400 K, 400 kPa and exits the nozzle at 100 kPa. To achieve an exit velocity of 500 m/s, determine: (a) the exit temperature, in K. (b) the exit area, in m