CHAPTER 7
7 Pure Substances in Single Phases
This chapter applies concepts introduced in earlier chapters to the simplest kind of system,
one consisting of a pure substance or a single component in a single phase. The system has
three independent variables if it is open, and two if it is closed. Relations among various
properties of a single phase are derived, including temperature, pressure, and volume. The
important concepts of standard states and chemical potential are introduced.
7.1 Volume Properties
Two volume properties of a closed system are defined as follows:
cubic expansion coefficient defD1
V
@V
@T
p(7.1.1)
isothermal compressibility T defD 1
V
@V
@pT(7.1.2)
The cubic expansion coefficient is also called the coefficient of thermal expansion and
the expansivity coefficient. Other symbols for the isothermal compressibility are and(^) T.
These definitions show that is the fractional volume increase per unit temperature
increase at constant pressure, andT is the fractional volume decrease per unit pressure
increase at constant temperature. Both quantities areintensiveproperties. Most substances
have positive values of ,^1 and all substances have positive values ofT, because a pressure
increase at constant temperature requires a volume decrease.
If an amountnof a substance is in a single phase, we can divide the numerator and
denominator of the right sides of Eqs.7.1.1and7.1.2bynto obtain the alternative expres-
sions
(^1) The cubic expansion coefficient is not always positive. is negative for liquid water below its temperature
of maximum density,3:98C. The crystalline ceramics zirconium tungstate (ZrW 2 O 8 ) and hafnium tungstate
(HfW 2 O 8 ) have the remarkable behavior of contracting uniformly and continuously in all three dimensions
when they are heated from0:3K to about 1050 K; is negative throughout this very wide temperature range
(Ref. [ 110 ]). The intermetallic compound YbGaGe has been found to have a value of that is practically zero
in the range 100 – 300 K (Ref. [ 148 ]).
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