CHAPTER 2 SYSTEMS AND THEIR PROPERTIES
2.4 THESTATE OF THESYSTEM 48
poor choice because the molar volume of water passes through a minimum asTis
varied at constantp. Thus, the valuespD1:000bar andV D18:016cm^3 would
describe one mole of water at both 2 C and 6 C, so these values would not uniquely
define the state. Better choices of independent variables in this case would be eitherT
andp, or elseTandV.How may we describe the state of a system that has nonuniform regions? In this case
we may imagine the regions to be divided into many small volume elements or parcels,
each small enough to be essentially uniform but large enough to contain many molecules.
We then describe the state by specifying values of independent variables for each volume
element. If there is internal macroscopic motion (e.g., flow), then velocity components
can be included among the independent variables. Obviously, the quantity of information
needed to describe a complicated state may be enormous.
We can imagine situations in which classical thermodynamics would be completely
incapable of describing the state. For instance, turbulent flow in a fluid or a shock wave in
a gas may involve inhomogeneities all the way down to the molecular scale. Macroscopic
variables would not suffice to define the states in these cases.
Whatever our choice of independent variables, all we need to know to be sure a system
is in the same state at two different times is thatthe value of each independent variable is
the same at both times.
2.4.4 Equilibrium states
Anequilibrium stateis a state that, when present in an isolated system, remains unchanged
indefinitely as long as the system remains isolated. (Recall that an isolated system is one
that exchanges no matter or energy with the surroundings.) An equilibrium state of an
isolated system has no natural tendency to change over time. If changesdooccur in an
isolated system, they continue until an equilibrium state is reached.
A system in an equilibrium state may have some or all of the following kinds of internal
equilibria:
Thermal equilibrium: each phase has the same temperature.
Mechanical equilibrium: each phase has the same pressure.
Transfer equilibrium: there is equilibrium with respect to the transfer of each species
from one phase to another.
Reaction equilibrium: every possible chemical reaction is at equilibrium.
Ahomogeneoussystem has a single phase of uniform temperature and pressure, and so
has thermal and mechanical equilibrium. It is in an equilibrium state if it also has reaction
equilibrium.
Aheterogeneoussystem is in an equilibrium state if each of the four kinds of internal
equilibrium is present.
The meaning of internal equilibrium in the context of an equilibrium state is that no
perceptible change of state occurs during the period we keep the isolated system under
observation. For instance, a system containing a homogeneous mixture of gaseous H 2 and
O 2 at 25 C and 1 bar is in a state of reaction equilibrium on a time scale of hours or days; but
if a measurable amount of H 2 O forms over a longer period, the state is not an equilibrium