Transport Processes
1. If there is any tendency for a process to occur in a system, that system is not
at equilibrium.
2. The macroscopic description of nonequilibrium states of fluid systems
requires two classes of variables that do not occur in equilibrium
thermodynamics: variables to specify the extent to which the system deviates
from equilibrium and variables to express the rates of processes.
3. The three principal transport processes are heat conduction, diffusion, and
viscous flow.
4. Each transport process is described macroscopically by an empirical linear
law.
5. Molecular theories of transport processes in dilute gases are based on gas
kinetic theory.
6. The electrical conductivity of solutions of ions can be understood on the
basis of ionic motion in an electric field.
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Transport Processes
The Macroscopic Description of Nonequilibrium
States
In a onephase simple system at equilibrium, the intensive macroscopic state is
specified by s + 1 variables, where s is the number of independent chemical substances.
These variables could be T, P, and s
1 concentrations or mole fractions. (We use the
letter s now rather than the letter c for the number of substances because we will use c
for concentrations.) Nonequilibrium states are more complicated than equilibrium states
and require more variables to specify them. The discussion of this chapter is limited to a
onephase simple system containing several substances in which no chemical reactions
can occur and in which the deviation from equilibrium is not very large. Processes that
take place far from equilibrium, including such things as explosions and turbulent flow,
are difficult to describe mathematically, and we do not attempt to describe them.
The thermodynamic variables of a nonequilibrium system can depend on position,
although the definitions of these variables require measurements at equilibrium. In order
to define these variables in a nonequilibrium system, we visualize the following
process: A small portion of the system (a subsystem) is suddenly removed from the
system and allowed to relax adiabatically to equilibrium at fixed volume. Once
equilibrium is reached, variables such as the temperature, pressure, density, and
concentrations in this subsystem are measured. These measured values are assigned
to a point inside the volume originally occupied by the subsystem and to the time at
which the subsystem was removed. This procedure is performed repeatedly at different
times and different locations in the system, and interpolation procedures are carried out
to obtain smooth functions of position and time to represent the temperature,
concentrations, etc.
T = T(x,
y, z, t) = T(r, t)
(11.11 a)
P :
P(x,
y, z, t) = P(r, t)
(11.11 b)
c i  ci(x, y, z, t) =
ci(r, t)
(i  1,2 .
.... s)
(11.11 c)
where
r
is the concentration of substance i, measured in mol m 3 or mol L 1. The
symbol r stands for the position vector with components x, y, and z.
The intensive variables are measured after each subsystem comes to equilibrium, so
they obey the same relations among themselves as they would in an equilibrium system.
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 Spring '11
 chan
 Fluid Dynamics, Equilibrium, Adolf Fick

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