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Causes of Deviations

The ideal gas laws can be derived from the kinetic theory of gases which is based on the following two important assumptions:
  1. The volume occupied by the molecules is negligible in comparison to the total volume of the gas.
  1. The molecules do not exert forces of attraction upon one another.
It is because neither of these assumptions can be regarded as applicable to real gases that the latter show deviation from the ideal behaviour.

The molecules of a gas, however, do occupy a certain volume as can be seen from the fact that gases can be liquefied and solidified at low temperatures and high pressures. On decreasing the temperature of a gas, the thermal energy of molecules is decreased and the effect of applying high pressure is to bring the molecules closer to one another, thereby increasing the forces of attraction amongst them. Both these factors favour liquefaction and solidification. In the solid state, however, there is considerable resistance to any further attempt at compression. It is apparent, therefore, that the molecules of a gas must have an appreciable volume, which is probably of the same order as that occupied by the same number of molecules in the solid state.

The molecules in gases also have weak forces of attraction (called van der Waals attraction) amongst themselves; as otherwise, the gases could never be liquefied and solidified. This is also supported by the fact that when a compressed gas is passed through a porous plug of silk or cotton in adiabatic condition (thermally isolated), the emerging gas is found to be cooler than the entering gas, provided the temperature of the gas is less than its inversion temperature (Joule-Thomson effect). This is because on expansion, some work has to be done against the internal forces of attraction, which requires energy. This energy comes from the system itself.

Ideal gas equation PV = nRT changes to (P + an2/V2) (V-nb) = nRT for real gases. 

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