Modern Thermodynamics
- Chapter 1
18
1.5 States of Matter and the van der Waals Equation
The simplest transformations of matter caused by heat is the melting of solids and the vaporization of
liquids. In thermodynamics, the various states of matter -- solid, liquid, gas -- are often referred to as
phases. Every compound has a definite temperature, Tm, at which it melts and a definite temperature, Tb,
at which it boils. In fact, this property can be used to identify a compound or separate the constituents of
a mixture. With the development of the thermometer, these properties could be studied with precision.
As noted earlier, Joseph Black and James Watt discovered another interesting phenomenon associated
with the changes of phase: at the melting or the boiling temperature the heat supplied to a system does
not result in an increase in temperature; it only has the effect of converting the substance from one phase
to another. This heat that lays "latent" or hidden without increasing the temperature was called the latent
heat. When a liquid solidifies, for example, this heat is given out to the surroundings. This phenomenon
is summarized in Fig. 1.3
Clearly the ideal gas equation, good as it is in describing many properties of gases, does not help
us to understand why gases convert to liquids when compressed. An ideal gas remains a gas at all
temperatures and its volume can be compressed without limit. Gay-Lussac's friend, Cagniard de la Tour
(1777-1859), discovered in 1822 that a gas does not liquefy when compressed unless its temperature is
below a critical value, called the critical temperature. This behavior of gases was studied in detail by
Thomas Andrews (1813-1885) who published his work in 1869. During this time, atomic theory was
gaining more and more ground while Maxwell, Clausius others advanced the idea that heat was related to
the molecular motion and began to find en explanation of the properties of gases, such as pressure and
viscosity, in the random motion of molecules. It was in this context that Johannes Diderik van der Waals
(1837-1923) sought a single equation of state for the liquid and gas phases of a substance. In 1873, van
der Waals presented his doctoral thesis titled "On the Continuity of the Gas and Liquid State" in which he
brilliantly explained the conversion of a gas to a liquid and the existence of critical temperature as the
consequence of forces between molecules and molecular volume.
Van der Waals realized that two main factors modify the ideal gas equation: the effect of
molecular volume and the effect of intermolecular forces. Since molecules have a non-zero volume, the
volume of a gas cannot be reduced to arbitrarily small value by increasing p. The corresponding
modification of the ideal gas equation would be, (V-bN) = NRT/p, in which the constant b is the
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