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A gas in a rigid vessel is at ambient temperature and at a pressure, P1, slightly higher than ambient pressure, P0. A valve on the vessel is opened, so gas escapes and the pressure drops quickly to ambient pressure. The valve is closed, and after a long time the remaining gas returns to ambient temperature, at which point the pressure is P2. Develop an ex- pression that allows a determination of the ratio of specific heats, k, in terms of the pressures.

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