Page 42 - Basics of Fluid Mechanics and Introduction to Computational Fluid Dynamics

Introduction to Mechanics of Continua 27

The main aim of thermodynamics is to establish a certain functional

dependence among the state (thermodynamic) variables known as con-
stitutive (behaviour) laws (equations). These constitutive equations will
contribute to the mathematical “closure” of the equations system de-
scribing the deformable continuum motion.
Obviously the deformation of the material systems depends essentially
on the temperature when this deformation takes place. That is why, for

a complete study, a deformable continuum should be considered as a
thermodynamic system, 1.e., a closed material system (no matter enters
or leaves the system) which changes energy with its surrounding through
work done or heat (added or taken).
By the thermodynamic state of a system, at a certain instant, we un-
derstand the set of all the values of the state (thermodynamic) variables

(parameters) which characterize the system at that moment.
By a thermodynamic process we understand a change of the thermody-
namic state (i.e., of the values of the state variables) as a consequence of
certain operations or actions or, shorter, when a thermodynamic system
changes from one state to another one.
A system is called in thermodynamic equilibrium tf its thermodynamic
state is time invariant.

Suppose now that a thermodynamic system has changed from an ini-
tial state (1) to a new state (2). By producing changes in either the
system or its surrounding, it would be possible to reverse the state from
(2) to (1). If this is possible to be done without any modification in
both system and surrounding, the process is called reversible. On the
contrary it is irreversible.

The reversible processes characterize the ideal media and they imply
infinitesimal changes which have been carried out so slowly that both
the system and the surrounding pass successively through a sequence of
equilibrium states.
The internal energy E;, associated to a material system, is the com-
plementary value of the kinetic energy Ec, vs. the total energy BE, i.e.,

B= BE; + Ec.
Depending only on the state of the system at the considered moment
(and not on the way this state has been reached), the internal energy
is an objective quantity (while the kinetic energy, due to the presence
of v, is not objective). If we postulate that the internal energy is an
absolutely continuous function of mass, there will be afunction e, called

the specific internal energy, such that

Fi; (P) = [eam = | pede.

P D