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A volume of gas v at temperature T1 and pressure P, is enclosed in a sphere. It is connected to another sphere of volume v/2 by tube and stopcock. This second sphere is initially evacuated and the stopcock is closed. If the stopcock is now opened and the temperature of the gas in the second sphere becomes T2, while the first sphere is maintained at the temperature of T1, show that the final pressure P' within the apparatus is P' = 2P T2/2 T2 + T1

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