1.3 Thermodynamic Systems and the General Concept
of Equilibrium
A common practice in physics starts with the separation of a finite portion of matter
or a restricted region of space from its surroundings. The portion/region that is set
aside and on which the investigation is focused is called the system, and the totality
of everything outside the system that has a direct bearing on its behavior is known
as the surroundings.
Equilibrium in simple systems In microscopic physics—take the Newtonian
mechanics, for example, the state of a system composed of N mass points requires
the knowledge of 6N time-dependent variables (3 variables for the position and 3
for the momentum for each of the N mass points). Thermodynamics deals with the
macroscopic set of the N particles of the corresponding system and, in this case, it is
unnecessary to know the motion of each particle individually in order to represent
the thermodynamic state, i.e., the macroscopic properties, of the system. When a
simple system is in a state of thermodynamic equilibrium, the average properties of
the system can be described in terms of time-independent thermodynamic coordinates. Thermodynamic coordinates are also known as state variables or properties
(or property functions). Examples of thermodynamic coordinates are volume and
mass, pressure and temperature.
Imagine that an experiment is performed on a constant mass of gas in a vessel
equipped so that the pressure p, volume V, and temperature t can be measured.
(Note that t is temperature in one of the empirical scales; later we shall use T to
denote temperature defined by a gas thermometer or at the absolute scale [Sect. 4.3
].) The empirical finding of such an experiment is that two of the three variables of a
simple system in equilibrium can be set arbitrarily; once the two variables are set,
the value of the third variable at equilibrium will be determined. For example, once
V and t are chosen, the value of p is determined. That is, the three variables satisfy a
functional relationship, f p; V; t
ð
Þ¼0. We shall call the concrete expression of a
functional relationship of state variables the EQUATION OF STATE.
When a system is not in a state of equilibrium, no single-valued thermodynamic
coordinates are defined for the system as a whole. The description of the
nonequilibrium system is still possible based on the concept of LOCAL THERMODYNAMIC EQUILIBRIUM,
The assumption that the same equilibrium thermodynamic relations, f p; V; t
ð
Þ¼0, which is
originally determined for a whole equilibrium system, for instance, remain valid for the
state variables assigned to every elemental volume of the nonequilibrium system.
(Local thermodynamic equilibrium is a central concept in the modern formalism
of thermodynamics, as it will be presented in Chap. 6, Sect. 6.4.) Nonequilibrium
systems are in general time-dependent as a result of the flows of various kinds
driven by their corresponding “thermodynamic forces” in the interior of the
nonequilibrium systems, e.g., a temperature gradient drives heat flow; a pressure
gradient drives fluid motion; a chemical affinity drives chemical reaction (see
discussion in Chaps. 7 and 9).
1.3 Thermodynamic Systems and the General Concept of Equilibrium
7
of Equilibrium
A common practice in physics starts with the separation of a finite portion of matter
or a restricted region of space from its surroundings. The portion/region that is set
aside and on which the investigation is focused is called the system, and the totality
of everything outside the system that has a direct bearing on its behavior is known
as the surroundings.
Equilibrium in simple systems In microscopic physics—take the Newtonian
mechanics, for example, the state of a system composed of N mass points requires
the knowledge of 6N time-dependent variables (3 variables for the position and 3
for the momentum for each of the N mass points). Thermodynamics deals with the
macroscopic set of the N particles of the corresponding system and, in this case, it is
unnecessary to know the motion of each particle individually in order to represent
the thermodynamic state, i.e., the macroscopic properties, of the system. When a
simple system is in a state of thermodynamic equilibrium, the average properties of
the system can be described in terms of time-independent thermodynamic coordinates. Thermodynamic coordinates are also known as state variables or properties
(or property functions). Examples of thermodynamic coordinates are volume and
mass, pressure and temperature.
Imagine that an experiment is performed on a constant mass of gas in a vessel
equipped so that the pressure p, volume V, and temperature t can be measured.
(Note that t is temperature in one of the empirical scales; later we shall use T to
denote temperature defined by a gas thermometer or at the absolute scale [Sect. 4.3
].) The empirical finding of such an experiment is that two of the three variables of a
simple system in equilibrium can be set arbitrarily; once the two variables are set,
the value of the third variable at equilibrium will be determined. For example, once
V and t are chosen, the value of p is determined. That is, the three variables satisfy a
functional relationship, f p; V; t
ð
Þ¼0. We shall call the concrete expression of a
functional relationship of state variables the EQUATION OF STATE.
When a system is not in a state of equilibrium, no single-valued thermodynamic
coordinates are defined for the system as a whole. The description of the
nonequilibrium system is still possible based on the concept of LOCAL THERMODYNAMIC EQUILIBRIUM,
The assumption that the same equilibrium thermodynamic relations, f p; V; t
ð
Þ¼0, which is
originally determined for a whole equilibrium system, for instance, remain valid for the
state variables assigned to every elemental volume of the nonequilibrium system.
(Local thermodynamic equilibrium is a central concept in the modern formalism
of thermodynamics, as it will be presented in Chap. 6, Sect. 6.4.) Nonequilibrium
systems are in general time-dependent as a result of the flows of various kinds
driven by their corresponding “thermodynamic forces” in the interior of the
nonequilibrium systems, e.g., a temperature gradient drives heat flow; a pressure
gradient drives fluid motion; a chemical affinity drives chemical reaction (see
discussion in Chaps. 7 and 9).
1.3 Thermodynamic Systems and the General Concept of Equilibrium
7