Van Der Waas Equation of State (EOS)

 

 The Van Der Waals Equation of State (EOS)

  What is Equation of State (EOS) ?

• Any equation that relates the thermodynamic variables like Pressure (P), Temperature (T), Moles of Substance (n) and Volume (V) of any thermodynamic system is known as equation of state.
• Ideal gas law is only applicable to system if the pressure is very low and temperature is very high. At this condition gas behaves like an ideal gas. If the pressure is very high then ideal gas law cannot able to predict the thermodynamic behaviour of the system. It cannot able to explain the forces that is acting between the molecules of gases when the gas is not in ideal condition.

Van Der Waals equation takes these into account by introducing certain factors in the ideal equation of state in terms of pressure and volume.

In 1873, J. D. Van Der Waals proposed first equation of state which explains the thermodynamic behaviour of real gases.

 

 

Where, P is absolute pressure of the system in kPa, V is molar volume, R is gas constant, and T is absolute temperature in kelvin and a and b are constant which can be evaluated from following two equations,

 

 

 

Where, Tc is critical temperature and Pc is critical pressure respectively.

Van Der Waals equation of state is cubic in volume and it gives three real roots below the critical temperature.

·               Largest root indicates vapor molar volume

·               Smallest root indicates liquid molar 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.

The result obtained by the ideal gas law and the Van Der Waals are calculated and computed in following thermodynamic 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.

Values of Van Der Waals constant are

                          a = 0.365 Nm⁴/mol²

                          b = 4.28 * 10-5 m³/mol

Solution:

Date given:

Molar Volume (V) = 0.381 m³/kmol

                                = 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 Equation of State (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.