States of Matter and the van der Waals Equation

One of the simplest transformations of matter is the melting of solids or the vaporization of liquids. In thermodynamics the various states of matter—solid, liquid, gas—are often referred to as phases. At a given pressure every compound has a definite temperature, at which it melts and a definite 

Typical p-V curves at a fixed T, the p-V isotherms, for a van der Waals gas are shown in Fig. 1.5. These curves show a transition from a gas to a liquid in the region where the p-V curve is multivalued, i.e. a given pressure does not correspond with a unique volume. This region represents a state in which the liquid and the gas phases are in thermal equilibrium. As we shall see in Chapter 13, the van der Waals curve in this region represents unstable states. The actual state of the gas follows the straight line ACB shown in Fig. 1.5. 

The van der Waals equation also exhibits a critical temperature Tc. if the temperature T is greater than Tc the p-V curve is always single-valued. 

Using these equations one can obtain the following relations between the critical constants and the constants a and b (exc 1.11)  

Thus every gas has a characteristic temperature Tc, pressure pc, and volume Unic- In view of this, one can introduce dimensionless reduced variables defined by 

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