Law of Corresponding State or Reduced Equation of State

Law of Corresponding State or Reduced Equation of State

Law of Corresponding State or Reduced Equation of State

Law of Corresponding State or Reduced Equation of State

According to this law,
two different gases behave similarly, if their reduced properties (i.e. P, V and T) are same.
The ratio of P to Pc, V to Vc and T to Tc are called reduced pressure(Pr), reduced volume(Vr) and reduced temperature(Tr) respectively.
so, Pr = P/Pc
or, P = PrPc     --------(equation 1)
Vr = V/Vc
or, V = VrVc    --------(equation 2)
similarly,
Tr = T/Tc
or, T = TrTc    --------(equation 3)
Now replacing the value P, V and T in Vander Waal equation, we get-
(PrPc + a/Vr2Vc2)(VrVc − b) = RTrTc    --------(equation 4)
Now putting the values of critical constants in the equation (4) we get-
(Pr a/27b2 + a/Vr29b2)(Vr3b − b) = 8a.RTr/27Rb
or, (Pr a/27b + a/Vr29b)(3Vr − 1) = 8a.Tr/27b
multiply the above equation by 27b/a we get-
  (Pr + 3/Vr2) (3Vr − 1) = 8Tr  
This equation is completely free from constants such as R, a, b hence this is applicable to all substances n fluid state.This is law of corresponding states.

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