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dW p C C
VF     1  2 (3.1.7)
dr r 7 r 13

where C  6a , C  12a ; the first term describes forces of molecular
2
1
2
1
attraction (Van der Waals forces) and the second term describes forces of
repulsion.

3.2. Real Gases. Van der Waals’ Equation

Van der Waals gas is such a model of real gas in which molecules are

considered to be perfectly rigid balls with the diameter d. Finite balls sizes
mean that forces of attraction and repulsion are taken into account.
Van der Waals showed that the intermolecular attraction and the space

occupied by the molecules themselves can be taken into account in the
general gas law. According to Van der Waals equation for 1 mole of gas:

 a 

p   V  b  RT (3.2.1)
 2  mol
 V mol 
where a and b are constant characteristics of the given gas that do not
depend on temperature, pressure and volume. The constant b is a
correction that takes into account the fact that the molecules by themselves

occupy a finite amount of space. A detailed analysis shows that constant b

is about 4 times the actual volume of the molecules. The term a 2
V mol

takes into account the attractive forces between the molecules, which have
the effect of reducing the volume just as the pressure does.
For an arbitrary mass m of the real gas with the molecular mass

M Van der Waals equation is written in the following way

 m 2 a  m  m


p    V  b  RT (3.2.2)

 2 2  M  M
 M V  
First of all, consider one mole of gas, composed of non-interacting point
particles that satisfy the ideal gas law, for derivation of the Van der
Waals’ equation:

RT
pV mol  R T  p  (3.2.3)
V mol

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