I've been grappling with this problem for days, but can't produce the answer. The problem can be summarised as follows: We have a bottle containing a certain quantity of a perfect gas whose ratio of specific heat capacities is gamma. The pressure in the bottle is doubled by the admission of more gas from a high pressure reservoir in which the temperature and pressure remain constant. Initially the temperatures in the bottle and in the reservoir are the same, and heat transfer during the process is negligible. Using only the 1st law, determine the fraction by which the mass of gas in the bottle increases. I know the answer, and did come up with a method of producing the answer, but I was unconvinced by it. Any help/hints/prodding in the right direction is appreciated.