process, and a quantity called thermodynamic force, which is related to the gradient
[nonuniformity] in the system (Mazur and De Groot 1962). We discussed this topic
earlier in Chap. 2 in detail in Onsager relations, as well. The complete entropy
generation rate equation can thus serve as a basis for the systematic description of the
irreversible processes occurring in a system. We refer to this equation as the
thermodynamic fundamental equation.
“As yet the set of conservation laws, together with the entropy balance equation
and the equations of state are to a certain extent empty, since this set of equations
contain the irreversible fluxes as unknown parameters and can therefore not be
solved with the given initial and boundary conditions for the state of the system”
(Mazur and De Groot 1962). At this point we must therefore supplement the
equations by an additional set of phenomenological relationships, which relate the
irreversible fluxes and the thermodynamic forces appearing in the entropy source
strength. Irreversible thermodynamics, in its present form, is mainly restricted to the
study of the linear relationship between the fluxes and the thermodynamic forces as
well as possible cross-effects between various phenomena. This is not a very serious
restriction however, since even rather extreme physical situations are still described
by linear laws.”
Together with the phenomenological equations, the original set of conservation laws may be
said to be complete in the sense that one now has a consistent set of partial differential
equations for the state parameters of a material system, which may be solved with the proper
initial and boundary conditions (Mazur and De Groot 1962).
5.4.1 Conservation Laws
Thermodynamics is based on two fundamental laws: the first law of thermodynamics
or the law of conservation of energy, and the second law of thermodynamics or the
entropy law. A systematic macroscopic scheme for the description of irreversible
processes must also be built upon these two laws. However, it is necessary to
formulate these laws in a suitable way. Since we wish to develop a theory applicable
to systems of which the properties are continuous functions of space coordinates and
time, we shall give a local formulation of the law of conservation of energy. As the
local momentum and mass densities may change in time, we will also need local
formulations of the laws of conservation of momentum and conservation of mass. In
solid mechanics, the thermodynamic system is usually chosen as a collection of
continuous matter, i.e., the system is a closed system not interchanging matter with
its surroundings; the bounding surface of the system in general moves with the flow
of matter.
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5 Unified Mechanics of Thermo-mechanical Analysis
[nonuniformity] in the system (Mazur and De Groot 1962). We discussed this topic
earlier in Chap. 2 in detail in Onsager relations, as well. The complete entropy
generation rate equation can thus serve as a basis for the systematic description of the
irreversible processes occurring in a system. We refer to this equation as the
thermodynamic fundamental equation.
“As yet the set of conservation laws, together with the entropy balance equation
and the equations of state are to a certain extent empty, since this set of equations
contain the irreversible fluxes as unknown parameters and can therefore not be
solved with the given initial and boundary conditions for the state of the system”
(Mazur and De Groot 1962). At this point we must therefore supplement the
equations by an additional set of phenomenological relationships, which relate the
irreversible fluxes and the thermodynamic forces appearing in the entropy source
strength. Irreversible thermodynamics, in its present form, is mainly restricted to the
study of the linear relationship between the fluxes and the thermodynamic forces as
well as possible cross-effects between various phenomena. This is not a very serious
restriction however, since even rather extreme physical situations are still described
by linear laws.”
Together with the phenomenological equations, the original set of conservation laws may be
said to be complete in the sense that one now has a consistent set of partial differential
equations for the state parameters of a material system, which may be solved with the proper
initial and boundary conditions (Mazur and De Groot 1962).
5.4.1 Conservation Laws
Thermodynamics is based on two fundamental laws: the first law of thermodynamics
or the law of conservation of energy, and the second law of thermodynamics or the
entropy law. A systematic macroscopic scheme for the description of irreversible
processes must also be built upon these two laws. However, it is necessary to
formulate these laws in a suitable way. Since we wish to develop a theory applicable
to systems of which the properties are continuous functions of space coordinates and
time, we shall give a local formulation of the law of conservation of energy. As the
local momentum and mass densities may change in time, we will also need local
formulations of the laws of conservation of momentum and conservation of mass. In
solid mechanics, the thermodynamic system is usually chosen as a collection of
continuous matter, i.e., the system is a closed system not interchanging matter with
its surroundings; the bounding surface of the system in general moves with the flow
of matter.
216
5 Unified Mechanics of Thermo-mechanical Analysis