Chapter 1
Basic Background Material
This chapter introduces a number of basic terms and concepts that are fundamental
to a statistical mechanical description of the properties of bulk matter. It begins with
some basic definitions, followed by brief considerations of the equation of state
for ideal gases whose constituents are either classical (typified by hard spheres)
or quantum mechanical (typified by photons) in nature. A number of statistical
concepts, such as fluctuation, ensemble, ensemble average, variance, and standard
deviation, are defined and illustrated.
1.1 Introduction
There are two general approaches to the description of physical systems. The
macroscopic approach in many ways represents the world as we see it, with matter
considered in ‘large’ units, while the microscopic approach looks at a physical
system in terms of the individual constituent atoms and molecules, i.e., in units
of matter that are considered ‘small’. We shall come to appreciate what is meant by
‘large’ and ‘small’ as we proceed. More specifically, our employment of these terms
is outlined below.
Macroscopic A physical system is described macroscopically in terms of a set of
appropriate variables, many of which will already be familiar. We tend to separate
these variables into two distinct classes, referred to as ‘mechanical variables’,
exemplified by volume, V ; number, N; pressure, P ; internal energy, U ; enthalpy,
H ; rate constant, k; surface tension, γ ; and ‘non-mechanical variables’, exemplified
by temperature, T ; entropy, S; Helmholtz energy, A; and Gibbs energy, G.
Microscopic As we have earlier indicated, a physical system may be described in
terms of its component atoms and/or molecules, so that its behaviour is examined on
a fine scale, for which we have developed two means of description. These are:
© Springer Nature Switzerland AG 2021
F. R. W. McCourt, Statistical Thermodynamics for Pure and Applied Sciences,
https://doi.org/10.1007/978-3-030-52006-9_1
1
Basic Background Material
This chapter introduces a number of basic terms and concepts that are fundamental
to a statistical mechanical description of the properties of bulk matter. It begins with
some basic definitions, followed by brief considerations of the equation of state
for ideal gases whose constituents are either classical (typified by hard spheres)
or quantum mechanical (typified by photons) in nature. A number of statistical
concepts, such as fluctuation, ensemble, ensemble average, variance, and standard
deviation, are defined and illustrated.
1.1 Introduction
There are two general approaches to the description of physical systems. The
macroscopic approach in many ways represents the world as we see it, with matter
considered in ‘large’ units, while the microscopic approach looks at a physical
system in terms of the individual constituent atoms and molecules, i.e., in units
of matter that are considered ‘small’. We shall come to appreciate what is meant by
‘large’ and ‘small’ as we proceed. More specifically, our employment of these terms
is outlined below.
Macroscopic A physical system is described macroscopically in terms of a set of
appropriate variables, many of which will already be familiar. We tend to separate
these variables into two distinct classes, referred to as ‘mechanical variables’,
exemplified by volume, V ; number, N; pressure, P ; internal energy, U ; enthalpy,
H ; rate constant, k; surface tension, γ ; and ‘non-mechanical variables’, exemplified
by temperature, T ; entropy, S; Helmholtz energy, A; and Gibbs energy, G.
Microscopic As we have earlier indicated, a physical system may be described in
terms of its component atoms and/or molecules, so that its behaviour is examined on
a fine scale, for which we have developed two means of description. These are:
© Springer Nature Switzerland AG 2021
F. R. W. McCourt, Statistical Thermodynamics for Pure and Applied Sciences,
https://doi.org/10.1007/978-3-030-52006-9_1
1