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1.
DESCRIPTION OF THE PHYSICAL SYSTEMS
Thermodynamics derives from dynamics. Dynamics is a branch of mechanics dealing with
matter in motion. In thermodynamics, dynamics of thermal phenomena are studied. The essence
of thermodynamics as well as any other branch of physicochemical science consists of experi
ments and theories. Experiments are planned observations of the physical world. Theories are
ideals correlated to experimental observables. The ideals are simplified models whose final out
puts are (preferably) expressed as mathematical relations among the experimental observables.
Other than being faithfully correlated to experimental results, the theories shall also be in a form
that is concise and precise, or else communicating the knowledge will not be probable, if not im
possible. Thus, universal constants, such as
π
and
e
are associated with mathematics, or else it
will be extremely difficult to describe circles, balls, and logarithmic functions, etc. Correspond
ingly, in physical science, the concept of conserved quantities, such as energy, momentum, and
massenergy, etc., play pivotal roles.
In this chapter we first introduce a few topics describing the physical world, which underline
the formulation of the thermodynamic laws.
1.1.
Introductory Remarks
1.1.1
Notes on Mathematics
To study thermodynamics, mathematics is needed. Generally, such needed mathematics fall
into two branches: geometry and algebra. The needed geometry in thermodynamics is minimal.
Algebra is nothing more than adding. The use of addition dates to antiquity and perhaps is also
used by some animals (note the reaction of the mother duck if one of her young is missing!). The
various ways of manipulating equations are but symbolic representations of the adding process
made efficient. In handling mathematics, computers do nothing but addition.
A problem associated with studying thermodynamics, at least at the beginning, is the confu
sion due to the conventional terminologies used. Invariably, discussions of the physical and
mathematical properties of the thermodynamic quantities were carried out in an intermingled
manner. Examples are the statements that (i)
internal energy
is a
state function
, its values are
in
dependent of the thermodynamic paths
, it possesses an
exact differential
; whereas (ii)
heat
and
work
are
not
state functions, their values are
dependent upon the thermodynamic paths
, they pos
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sess
inexact differentials
. While the above type composite physicomathematical statements con
tain nothing wrong either physically or mathematically, they can certainly give rise to serious
confusions. Such a way of presenting the subject seems to be historically based. The mathemati
cal representation of thermodynamics consists of several
functions
of
multivariables
. The vari
ous thermodynamic concepts were developed in the same time frame as the needed mathematics
of defining and treating multivariable functions were just becoming clear to the workers at the
time. The mathematics of multivariable functions is, however, well developed by now. Thus, it
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 Fall '11
 DR.TAN
 Thermodynamics, Energy, Potential Energy, Entropy

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