Van Der Waas Equation of State (EOS)

         What is Equation of State (EOS) ?

• Equation of state is thermodynamic expression which relates the pressure (P), temperature (T) and the volume (V).

The perfect gas equation fails to explain the PVT behavior of real gases as the volume occupied by the molecules of a real gas and the forces of interaction between them are not negligible as in ideal gas.

Van Der Waals equation takes into account these two features of a real gas by incorporate certain correction factors in the pressure and volume terms of the ideal gas equation.

Van Der Waals proposed following equation to explain the PVT Behavior of the Real Gases :

Where a and b are van der waals constants.

This equation is cubic in volume and it gives three real roots below the critical temperature.

•         Largest root indicates vapor volume
•        Smallest root indicates liquid volume
•        Intermediate root has no significance

 

At saturation pressure, smallest and the largest roots represents the molar volumes of saturated liquid and saturated vapour respectively.
 
Constants are evaluated by following equations : 

Where Tc and Pc are critical temperature and pressure respectively.

We can the difference in results obtained by the ideal gas law and van der waals equation of state from following problem

Problem Statement :

1 kmol of CO₂ occupies a volume 0.381 m³ at 313 K. Compare the pressures given by the ideal gas law and van der waals equation of state.

Take Van Der Waals constant

                          a = 0.365  Nm⁴/mol²

                               b = 4.28 * 10^-5  m³/mol

Solution :

Date Given :

Molar Volume (V) = 0.381 * 10^-3 m³/mol

Temperature (T) = 313 K

Gas Constant (R) = 8.314 Nm/mol.K

By Ideal Gas Law :

 

By Van Der Waals EOS :

From the above results we can see that result obtained from the ideal gas law is different than that is obtained from the van der waals equation of state and ideal gas equation cannot be applicable on the real gases.