Thermodynamics and Chemistry

CHAPTER 2 SYSTEMS AND THEIR PROPERTIES

2.2 PHASES ANDPHYSICALSTATES OFMATTER 30

a subscript or a formula in parentheses. Examples are

Molar volumeD

V

n

DVm (2.1.2)

Molar volume of substanceiD

V

ni

DVm;i (2.1.3)

Molar volume of H 2 O DVm(H 2 O) (2.1.4)
In the past, especially in the United States, molar quantities were commonly denoted
with an overbar (e.g.,Vi).

2.2 Phases and Physical States of Matter

Aphaseis a region of the system in which each intensive property (such as temperature and
pressure) has at each instant either the same value throughout (auniformorhomogeneous
phase), or else a value that varies continuously from one point to another. Whenever this
book mentions a phase, it is auniformphase unless otherwise stated. Two different phases
meet at aninterface surface, where intensive properties have a discontinuity or change
over a small distance.
Some intensive properties (e.g., refractive index and polarizability) can have directional
characteristics. A uniform phase may be eitherisotropic, exhibiting the same values of these
properties in all directions, oranisotropic, as in the case of some solids and liquid crystals.
A vacuum is a uniform phase of zero density.
Suppose we have to deal with anonuniformregion in which intensive properties vary
continuously in space along one or more directions—for example, a tall column of gas in
a gravitational field whose density decreases with increasing altitude. There are two ways
we may treat such a nonuniform, continuous region: either as a single nonuniform phase,
or else as an infinite number of uniform phases, each of infinitesimal size in one or more
dimensions.

2.2.1 Physical states of matter

We are used to labeling phases by physical state, or state of aggregation. It is common
to say that a phase is asolidif it is relatively rigid, aliquidif it is easily deformed and
relatively incompressible, and agasif it is easily deformed and easily compressed. Since
these descriptions of responses to external forces differ only in degree, they are inadequate
to classify intermediate cases.
A more rigorous approach is to make a primary distinction between asolidand afluid,
based on the phase’s response to an applied shear stress, and then use additional criteria
to classify a fluid as aliquid,gas, orsupercritical fluid.Shear stressis a tangential force
per unit area that is exerted on matter on one side of an interior plane by the matter on the
other side. We can produce shear stress in a phase by applying tangential forces to parallel
surfaces of the phase as shown in Fig.2.1on the next page.

Asolidresponds to shear stress by undergoing momentary relative motion of its parts,
resulting indeformation—a change of shape. If the applied shear stress is constant and
small (not large enough to cause creep or fracture), the solid quickly reaches a certain