Heat and Thermodynamics

5.4 Discussions on Van der Waals’ Equation

Van der Waals’ equation is given by

 

 

or

 

(pν² + a)(ν − b) = RTν²

 

or

 

pν³ − bpν² + aν − ab = RTν²

 

or

 

 

This is a cubic equation in v for a particular isotherm; and for a particular p, we get three roots of v which are

1. All real and different;
2. All real and identical;
3. One real and two imaginary.

 

Again, from

 

 

in the limit v tending to infinity, p tends to zero and v tending to b, p tends ...