3. Suppose that a gas expands adiabatically into a vacuum. (a) What is the work done by the gas? (5) (b) Suppose that the total energy of the gas is given by N E = NIW NKT - Na where a is a positive constant. Initially the gas occupies a volume Vi at a temperature Ti. The gas then expands adiabatically into a vacuum so that it occupies a total volume V2. What is the final temperature of the gas? (10) [15]