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The compressibility factor (Z) of a gas ...

The compressibility factor (Z) of a gas at critical state is
`(T_(e)=(8a)/(27Rb),p_(e)=(a)/(27b^(2)),V_(e)=3b)`

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The compressibility factor Z = ((PV)/(nRT)) of a gas above T = (a)/(Rb) will be :

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The essential conditions for liquefaction of gases were discovered by Andrews in 1869 as a result of his study of pressure-volume-temperature relationship for CO_(2) . If was found that above a certain temperature, it was impossible to liquefy a gas whatever the pressure was applied. The temperature below which the gas can be liquefied by the application of pressure alone is called critical temperature (T_(c)) . The pressure required to liquefy a gas at this temperature is called the critical pressure (P_(c)) . The volume occupied by one mole of the substance at the critical temperature and pressure is called critcal volume. Critical constants are related with van der Waals' constant as follows: V_(c) = 3b, P_(c) = (a)/(27b^(2)), T_(c) = (8a)/(27 Rb) Gas A and can be liquefied at room temperature by applying pressure but gas B cannot. This reflects: