Modern Thermodynamics
- Chapter 1
1.2 Equilibrium and Nonequilibrium Systems
It is our experience that if a physical system is isolated, its state -- specified by macroscopic variables
such as pressure, temperature and chemical composition -- evolves irreversibly towards a time-invariant
state in which we see no further physical or chemical change. This is the state of thermodynamic
equilibrium. It is a state characterized by a uniform temperature throughout the system. The state of
equilibrium is also characterized by several other physical features that we will describe in the following
The evolution of a system towards the state of equilibrium is due to irreversible processes, such
as heat conduction and chemical reactions, which act in a specific direction but not its reverse. For
example, heat always flows from a higher to a lower temperature, never in the reverse direction; similarly,
chemical reactions causes compositional change in a specific direction not its reverse (which, as we shall
see in Chapter 4, is described in terms of "chemical potential", a quantity similar to temperature, and
"affinity", a thermodynamic force that drives chemical reactions). At equilibrium, these processes vanish.
Thus, a nonequilibrium state can be characterized as a state in which irreversible processes are taking
place driving the system towards the equilibrium state. In some situations, especially during chemical
transformations, the rates at which the state is transforming irreversibly may be extremely small, and an
isolated system might appear as if it is time-invariant and has reached its state of equilibrium.
Nevertheless, with appropriate specification of the chemical reactions, the nonequilibrium nature of the
state can be identified.
Two or more systems that interact and exchange energy and/or matter will eventually reach the
state of thermal equilibrium in which the temperature within each system is spatially uniform and the
temperature of all the systems are the same. If an system A is in thermal equilibrium with system B and if
B is in thermal equilibrium with system C, then it follows that A is in thermal equilibrium with C. This
"transitivity" of the state of equilibrium is sometimes called the Zeroth Law. Thus, equilibrium systems
have a well defined, spatially uniform temperature; for such systems the energy and entropy are functions
of state as expressed in (1.1.1).
Uniformity of temperature, however, is not a requirement for the entropy or energy of a system to
be well defined. For nonequilibrium systems in which the temperature is not uniform but is well
defined locally at every point x, we can define densities of thermodynamic quantities such as energy and
entropy. Thus, the energy density at x would be:
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