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# 1.nature - 1 DESCRIPTION OF THE PHYSICAL SYSTEMS...

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1 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 mass-energy, 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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2 sess inexact differentials . While the above type composite physico-mathematical 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 multi-variables . The vari- ous thermodynamic concepts were developed in the same time frame as the needed mathematics of defining and treating multi-variable functions were just becoming clear to the workers at the time. The mathematics of multi-variable functions is, however, well developed by now. Thus, it
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1.nature - 1 DESCRIPTION OF THE PHYSICAL SYSTEMS...

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