CHAPTER 2 SYSTEMS AND THEIR PROPERTIES
2.2 PHASES ANDPHYSICALSTATES OFMATTER 33
occurs at the liquid–gascoexistence curve. This curve ends at acritical point, at which
all intensive properties of the coexisting liquid and gas phases become identical. The fluid
state of a pure substance at a temperature greater than the critical temperature and a pressure
greater than the critical pressure is called asupercritical fluid.
The termvaporis sometimes used for a gas that can be condensed to a liquid by increas-
ing the pressure at constant temperature. By this definition, the vapor state of a substance
exists only at temperatures below the critical temperature.
The designation of a supercritical fluid state of a substance is used more for convenience
than because of any unique properties compared to a liquid or gas. If we vary the tempera-
ture or pressure in such a way that the substance changes from what we call a liquid to what
we call a supercritical fluid, we observe only a continuous density change of a single phase,
and no phase transition with two coexisting phases. The same is true for a change from
a supercritical fluid to a gas. Thus, by making the changes described by the path ABCD
shown in Fig.2.2, we can transform a pure substance from a liquid at a certain pressure
to a gas at the same pressure without ever observing an interface between two coexisting
phases! This curious phenomenon is calledcontinuity of states.
Chapter 6 will take up the discussion of further aspects of the physical states of pure
substances.
If we are dealing with a fluidmixture(instead of a pure substance) at a high pressure, it
may be difficult to classify the phase as either liquid or gas. The complexity of classification
at high pressure is illustrated by thebarotropic effect, observed in some mixtures, in which
a small change of temperature or pressure causes what was initially the more dense of two
coexisting fluid phases to become the less dense phase. In a gravitational field, the two
phases switch positions.
2.2.4 The equation of state of a fluid
Suppose we prepare a uniform fluid phase containing a known amountniof each constituent
substancei, and adjust the temperatureT and pressurepto definite known values. We
expect this phase to have a definite, fixed volumeV. If we change any one of the properties
T,p, orni, there is usually a change inV. The value ofV is dependent on the other
properties and cannot be varied independently of them. Thus, for a given substance or
mixture of substances in a uniform fluid phase,V is a unique function ofT,p, andfnig,
wherefnigstands for the set of amounts of all substances in the phase. We may be able
to express this relation in an explicit equation:V D f .T; p;fnig/. This equation (or a
rearranged form) that gives a relation amongV,T,p, andfnig, is theequation of stateof
the fluid.
We may solve the equation of state, implicitly or explicitly, for any one of the quantities
V,T,p, andniin terms of the other quantities. Thus, of the 3 Csquantities (wheresis
the number of substances), only 2 Csare independent.
Theideal gas equation,pDnRT=V(Eq.1.2.5on page 23 ), is an equation of state.
It is found experimentally that the behavior of any gas in the limit of low pressure, as
temperature is held constant, approaches this equation of state. This limiting behavior is
also predicted by kinetic-molecular theory.
If the fluid has only one constituent (i.e., is a pure substance rather than a mixture), then
at a fixedT andpthe volume is proportional to the amount. In this case, the equation of