The Real gases are those which does not obeys the Boyle's Charle's and gas law. To explain the behavior of real gases following two corrections are applied in the gas equation PV = RT

Volume correction: According to kinetic theory of ideal gases the volumes of molecule is presumed to be negligible where as the molecule occupy some volume due to their finite size (10^-10m) consequently the whole volume of the container is not available for free kinetic motion of gas molecule as some fraction of it is occupied by the molecules themselves. Hence the effective volume of gas is = (V - b)

Pressure correction: According to ideal gas theory, inter molecular forces among the molecules is zero, But at high pressure and low temperature inter molecular distances decreases and consequently the intermolecular attractive forces converts into effective. As a result of this the molecules do not exert as much force as they could exert in the absence of attractive force. Hence the effective pressure would be greater than the observed pressure (P).

Hence the perfect pressure of gas is = (P+a/V²)

Equation for real gas: (Vander waal's equation)

(P+a/V²)(V-b = RT) for 1 mol. of Gas; (P+an²/V²)(V-nb = nRT) for n numbers of particle of Gas

Unit:     α→ Newton × m⁴ ; b → m³ ;

Dimension: [a] = [ML⁵T^-2] ; [b] = [L³]

The value of constants 'a' and 'b' relays upon the nature of gas

or   , Here P_o = critical pressure, T_c = critical temperature, V_c = critical volume.

Various information in Table

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