Modern Thermodynamics

- Chapter 1

17

In this equation the constant "a" is a measure of the attractive forces between molecules and "b" is

proportional to the size of the molecules. For example, the values of, a and b for helium are smaller than

the corresponding values for a gas such as CO2. The values of the constants a and b for some of the

common gases are given in Table 1.1. Unlike the ideal gas equation, this equation explicitly contains

molecular parameters and it tells us how the ideal gas pressure and volume are to be "corrected" because

of the molecular size and intermolecular forces. We shall see how van der Waals arrived at this equation

in the next section. At this point we encourage the students to pause and try deriving this equation on

their own before proceeding to the next section.

As one might expect, the energy of the gas is also altered due to forces between molecules. In

chapter 6 we will see that the energy Uvw of a van der Waals gas can be written as:

Uvw = Uideal − a

N2

V

V

(1.4.11)

The van der Waals equation was a great improvement over the ideal gas law, in that it described

the observed liquefaction of gases and the fact that, above a certain temperature, called the critical

temperature, gases could not be liquefied regardless of the pressure, as we will see in the following

section. But still, it was found that van der Waals equation failed at very high pressures (exc 1.13).

Various improvements were suggested by Clausius, Berthelot and others are discussed in chapter 6.