Critical exponents 611.
P
V
PcVcLiquid
regionVa por
regionIdeal gas
regionCritical
isothermC
Fig. 16.2Equation of state of a simple, one-component fluid.Cdenotes an inflection point.
critical point on the phase diagram. The isotherm that contains thepointCis called
thecritical isotherm. The phase transition that occurs at this point is an example
of asecond-orderphase transition. For a one-component system, the critical pointis
theonlypoint at which a second-order phase transition is possible. A two-component
system, for example, could have lines of second-order phase transitions, called critical
lines. As discussed in Section 4.7,Cis a point of zero curvature, meaning that∂P/∂ρ
and∂^2 P/∂ρ^2 both vanish atC.
16.2 The critical exponentsα,β,γ, andδ
The liquid–gas critical point is characterized by a number of important properties.
First, certain thermodynamic variables are observed to diverge asthe temperature
T approaches the critical temperatureTc; the divergence obeys a power-law form
in|T−Tc|−^1. Other thermodynamic variables are found to exhibit a nondivergent
power-law dependence as the critical point is approached in either|T−Tc|or|ρ−ρc|,
whereρcis the critical density—the density at which the inflection pointCoccurs in
Fig. 16.2. The exponents that govern the aforementioned power laws are calledcritical
exponents. A second important property is the fact that large classes of systems,
known asuniversality classes, possessthe same critical exponents. This phenomenon
of universality indicates that near a critical point, the details of thelocal interactions
between specific pairs or clusters of particles become less important than long-range
cooperative effects, which are largely insensitive to the particularsof an interaction
potential. Thus, it is possible to obtain information about all of the systems in a