In an adiabatic piston-cylinder setup, you have 3.12 g of nitrogen gas initially at a temperature of 23 °C and confined within a volume of 400 cm³. If the piston undergoes a release allowing the nitrogen to expand adiabatically and reversibly until the volume increases to 2.00 dm³, determine the final temperature of the gas, the change in internal energy (∆U), the amount of heat transferred (q), and the work performed by the system. Assume that the nitrogen behaves as an ideal gas.