Use the bag-of-gas trick to solve the following problem: A gas cylinder of 0.5 m3 volume containing nitrogen initially at a pressure of 20 bar and a temperature of 200 K is connected to another cylinder of 0.25 m3 volume that is evacuated. A valve between the two cylinders is opened until the pressures in the cylinders equalize. Find the final temperature and pressure in each cylinder if there is no heat flow into or out of the cylinders or between the gas and the cylinder. You may assume that the gas is ideal with a constant-pressure heat capacity of (7/2)R.