This book provides an introduction to the subject at the advanced undergraduate level for students interested in careers in basic or applied physics.

1. Statistical and Thermal Physics
STATISTICAL AND THERMAL PHYSICS
The subject of statistical and thermal physics is concerned with the description of macroscopic sys-
tems made up of large numbers of particles of the order of Avogadro’s number NA = 6.02 × 1023mol−1.
The particles may be atoms or molecules in gases, liquids, and solids or systems of subatomic par-
ticles such as electrons in metals and neutrons in neutron stars. A rich variety of phenomena are
exhibited by many particle systems of this sort. The concepts and relationships that are established
in thermal physics provide the basis for discussion of the properties of these systems and the pro-
cesses in which they are involved. Applications cover a wide range of situations from basic science,
in many important felds that include condensed matter physics, astrophysics, and physical chemis-
try, to practical devices in energy technology.
The origins of modern thermal physics may be traced to the analysis of heat engines in the nine-
teenth century. Following this early work, a number of researchers contributed to the development of
the subject of thermodynamics with its famous laws. By the end of the nineteenth century, thermody-
namics, classical mechanics, and electrodynamics provided the foundation for all of classical physics.
Today, thermodynamics is a well-developed subject, with modern research focused on special topics
such as nonequilibrium thermodynamics. Application of the methods of thermodynamics to complex
systems far from equilibrium, which include living organisms, presents a major challenge.
The microscopic classical statistical description of systems of large numbers of particles began
its development in the late nineteenth century, particularly through the work of Ludwig Boltzmann.
This approach was transformed by the development of quantum mechanics in the 1920s, which
then led to quantum statistics that is of fundamental importance in a great deal of modern research
on bulk matter. Statistical techniques are used to obtain average values for properties exhibited
by macroscopic systems. The microscopic approach on the basis of classical or quantum mechan-
ics together with statistical results has given rise to the subject known as statistical mechanics or
statistical physics. Bridge relationships between statistical physics and thermodynamics have been
established and provide a unifed subject.
TEMPERATURE
The concept of temperature has evolved from man’s experience of hot and cold conditions with tem-
perature scales devised on the basis of changes in the physical properties of substances that depend on
temperature. Practical examples of thermometers for temperature measurement include the following:
• Constant volume gas thermometers, which make use of the pressure of a fxed quantity of
gas maintained at a constant volume as an indicator
• Liquid in glass thermometers, which use the volume of a liquid, such as mercury or alcohol,
contained in a reservoir attached to a capillary tube with a calibrated scale
• Electrical resistance thermometers, which use the variation of the resistance of a metal,
such as platinum, or of a doped semiconductor, such as GaAs, to obtain temperature
• Vapor pressure and paramagnet thermometers for special purposes particularly at low
temperatures

2. IDEAL GAS EQUATION OF STATE
An equation of state establishes a relationship among thermodynamic variables. For an ideal gas,
the variables chosen are the pressure P, the volume V, and the absolute temperature T. Experiments
carried out on real gases, such as helium, under conditions of low density have shown that the fol-
lowing equation describes the behavior of many gases:
PV = nRT,
where n is the number of moles of gas and R is a constant called the gas constant with a value of
8.314J mol−1 K−1. As mentioned above, the constant volume gas thermometer involves the measure-
ment of the pressure of a constant volume of gas as a function of temperature.
ENERGY SOURCES
In order to gain perspective on energy availability and future energy trends, it is instructive to
examine the energy sources available on earth. These sources are frst classifed as either renewable
or nonrenewable. Nonrenewable fossil fuels include natural gas, oil (petroleum, jet fuel), and coal.
All of these fuels are hydrocarbons produced from the remains of plants and animals that accumu-
lated millions of years ago. The heat produced by burning these fuels is thus originally derived from
solar energy and is made available by oxidation of the carbon content.
Electricity is produced using high-pressure steam to drive steam turbines, which drive electric-
ity generators. A modern multistage steam turbine is a form of heat engine generally powered by
fossil fuels or nuclear reactors. It is interesting to compare the energy produced by the various fos-
sil fuels. In the case of petroleum, the energy released as heat of combustion is 45 MJ kg−1. Natural
gas has a value around 50 MJ kg−1, while for good quality coal, the value is lower at 25 MJ kg−1.
Natural gas and coal are largely used to generate electrical energy, which is sold to users in units
of kW-h (1kW - h = 3.6MJ). A representative fgure of the daily consumption of electrical energy
in developed countries is 44 MJ day−1 per individual with some variation from country to country.
The element uranium, and in particular uranium-235 isotope, which is used as the energy source
in nuclear reactors, is another nonrenewable energy source. In a natural uranium light water reac-
tor, 500 GJ kg−1 of energy is released during fssion of uranium-235 into lighter nuclei. The release
of energy is explained using the Einstein mass-energy relation E = mc2
with m the mass loss that
occurs in the uranium-235 fssion process and c the speed of light in vacuum. Note that the energy
per kg of unenriched uranium is a factor 104
larger than that of natural gas. Enriched uranium
(3.5% uranium-235) provides a further factor 10 increase in the energy per kg. Allowing for the
large atomic mass difference between 12C and 235U by considering the energy per atom increases
the uranium energy production advantage by 20 to exceed 106. The fssion energy is released as
kinetic energy of fssion fragments together with neutrons, which produce further fssion processes,
and gamma rays. Most of the fssion energy ends up as heat, which is removed by a coolant passed
through the reactor core. Steam from a nuclear reactor is used to drive a turbine-generator system
to produce electricity.

3.
EQUATIONS OF STATE FOR REAL GASES
An important empirical equation of state that provides a fairly good description of the properties of
real gases at high densities is the van der Waals equation:
(
ˇ
˘
ˆ
˝
˙
Equation 1.2 is similar to the ideal gas equation in Equation 1.1 but with a pressure correction term
a/V2, which increases in importance with a decrease in volume, and a volume correction term b.
The van der Waals constants a and b are determined experimentally for a given gas. The pressure
correction term allows for interparticle interactions, and the volume correction term allows for the
fnite volume occupied by the particles themselves.
Another widely used empirical equation of state is the virial equation:
˙ N ˘ ˙ N ˘
2
PV = nRT 1+ ˇ B T
( )+ ˇ C T
( )+,
ˆ V ˆ V
B(T) and C(T) are called the second and third virial coeffcients, respectively, and are generally
temperature-dependent. The correction terms become important as the volume decreases and the
particle density N/V increases. Virial coeffcients have been measured for a large number of gases
and are available in tables. Further discussion of these two empirical real gas equations of state is
given in later chapters.
a
=
)
−
V b
P + nRT.
V2
EQUATION OF STATE FOR A PARAMAGNET
An ideal paramagnet consists of N particles, each of which possesses a spin and an associated magnetic
momentμproportional to the spin, with negligible interactions between spins. Real paramagnetic systems
approximate ideal systems only under certain conditions, such as high temperature, and in magnetic
felds that are not too large. A more detailed discussion of these conditions is given later in this book.
For an ideal paramagnet, experiment and theory show that the magnetic moment per unit vol-
ume, or magnetization M, is given by
CH
M = ,
T
with H an external applied magnetic feld and C a constant called the Curie constant. In the SI system
of units applied to ideal paramagnetic systems, we shall often, to a good approximation, take the feld
that the spins see as H = B/μ0, with μ0 = 4π × 10−7 Hm−1 the permeability of free space and B the
magnetic induction in tesla. M, H, and T are state variables analogous to P, V, and T. Any two fx the
value of the third variable. Like the ideal gas equation of state, the ideal paramagnet equation, called
Curie’s law, is very useful in calculations related to processes that involve changes in the state vari-
ables. Note that for T → 0 K, Equation 1.4 predicts that M will diverge. This unphysical prediction
shows that the equation breaks down at low temperatures, where the magnetization saturates after it
reaches a maximum value with all spins aligned parallel to H. In many magnetic systems, the spins
interact to some extent and order below a temperature called the Curie point. Examples are metals
such as iron and nickel. The Curie–Weiss equation takes interactions into account and has the form

4. CH
M = .
− c
T T
Tc is called the Weiss constant and has the dimensions of temperature. Equation 1.5 provides a sat-
isfactory description of the magnetic properties of magnetic materials for T Tc. For a given system
at a particular temperature T ≃ Tc, spontaneous order among spins sets in and the system undergoes
a phase transition. Values of Tc