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An ideal gas with pressure P, volume V a...

An ideal gas with pressure `P`, volume `V` and temperature `T` is expanded isothermally to a volume `2V` and a final pressure `P_i`. If the same gas is expanded adiabatically to a volume `2V`, the final pressure is `P_a`. The ratio of the specific heats of the gas is `1.67`. The ratio of `P_a / P_i` is ........

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