Physics 320

Thermal Physics

Winter Term, 2012

8:30-9:40 MWF,  Youngchild Hall Room 115

Professor Matthew Stoneking


Document links:

            Excerpts from Fermi

            Joule’s paper


Problem sets



Catalog course description: Treats elementary statistical mechanics; Bose-Einstein and Fermi-Dirac statistics; kinetic theory; and classical thermodynamics.


Text: An Introduction to Thermal Physics, by Daniel V. Schroeder (Addison Wesley Longman, 2000).


Other thermal physics texts:

Thermal Physics, 2nd Edition, by Charles Kittel and Herbert Kroemer (Freeman, 1980).

Thermodynamics, by Enrico Fermi (Dover, 1936).


Office hours: Tuesdays 9:30 AM – 11:00 AM, Thursdays 1:30 PM – 3:00 PM


Grading policy:

Grades will be assigned based on the following elements, weighted as indicated:

·         Midterm Exam: 25%

·         Final Exam: 30%

·         Problem sets: 20%

·         Problem Presentations: 15%

·         Attendance / Participation: 10%



There will be one in-class midterm exam.  The final exam will be cumulative and will take place during the regularly scheduled final exam time (Tuesday, 13 March, 3:00-5:30 PM).


Problem sets:

Problem sets will be assigned almost every week.  For most problem sets, students are encouraged to collaborate on problem solutions, but each student must submit her own write-up of solutions and each student must participate in the solution of each problem.  There will be a small number of assigned problems that must be completed without collaboration from other students.  These will be clearly indicated.


Problem Presentations:

Each student will make two problem solution presentations in class.  Grades will be based on the effectiveness of the presentation style as well as the quality and completeness of the solution.  Presentations should therefore be rehearsed and solutions should be checked by the instructor prior to class.



Outline of Topics Covered:

I.                   Classical Thermodynamics (Chs. 1&4)

II.                Entropy, Temperature and the Second Law of Thermodynamics (Chs. 2&3)

III.             Classical (Boltzmann) Statistical Mechanics (Ch. 6)

IV.             Quantum Statistical Mechanics (Ch. 7)

V.                Free Energy, Chemical Potential, and Phase Transformations (Ch. 5) –if time permits


Schedule (subject to change):


UNIT I: Classical Thermodynamics


M 2 Jan: The First Law of Thermodynamics

Operational definition of temperature

Thermal equilibration

Heat and calorimetry – heat capacity and latent heat

Mechanical equivalent of heat and internal energy

Pressure and compression work – P-V diagrams


W 4 Jan: Thermodynamics of Ideal Gases

READ: Chapter 1 (sections 1.1 – 1.6)

Absolute temperature – Charles’ Law

The Ideal Gas Law

Internal energy of an ideal gas

Microscopic (kinetic) model of an ideal gas

Equipartition theorem


F 6 Jan: Heat Engines and Refrigerators

READ: Chapter 4 (sections 4.1 – 4.4)

Reversible thermodynamic cycles

Efficiency of heat engines

Carnot engine

Stirling engine

Refrigerators and the coefficient of performance


M 9 Jan: Classical Definition of Entropy and the Second Law of Thermodynamics

Heat engine (Kelvin) and refrigerator (Clausius) statements of the 2nd Law

Clausius’ theorem

Entropy and the 2nd Law

Examples of calculating entropy production


W 11 Jan: Problem Presentation Day #1




UNIT II: Entropy, Temperature and the Second Law of Thermodynamics


F 13 Jan: Microstates and Macrostates

READ: Chapter 2 (sections 2.1 – 2.4)

2-state paramagnet

Microstates, macrostates and multiplicity

Stirling’s approximation

Einstein solid


M 16 Jan:  MLK Day, no class


W 18 Jan: Understanding Entropy and Temperature

READ: Chapter 2 (sections 2.5- 2.6) & Chapter 3 (sections 3.1 – 3.2)

Interacting systems and thermal equilibration

Fundamental definitions of entropy and temperature

2-state paramagnet revisited


F 20 Jan: Mechanical and Diffusive Equilibrium

READ: Chapter 3 (sections 3.3 – 3.6)

A fundamental definition of pressure

Chemical potential

The thermodynamic identity

Entropy of mixing


UNIT III: Classical (Boltzmann) Statistical Mechanics


M 23 Jan: The Boltzmann Factor and the Partition Function

READ: Chapter 6 (sections 6.1, 6.2, and 6.4)

The Boltzmann Factor

The Partition Function

Average Values

The Maxwell-Boltzmann Distribution


W 25 Jan: The Equipartition Theorem and the Sackur-Tetrode Equation

READ: Chapter 6 (sections 6.3, 6.5 – 6.7)


F 27 Jan: The Saha Equation


UNIT IV: Quantum Statistical Mechanics


M 30 Jan: The Gibbs Distribution and the Saha Equation

READ: Chapter 7 (section 7.1)


W 1 Feb: The Fermi-Dirac and Bose-Einstein Occupancy Functions

READ: Chapter 7 (section 7.2)



F 3 Feb: Degenerate Fermi Gas

READ: Chapter 7 (section 7.3)


M 6 Feb: Degenerate Fermi Gas continued and White Dwarf Stars


W 8 Feb: Midterm Exam


F 10 Feb:  Mid-term Reading Period, no class


M 13 Feb: Planck’s Blackbody Radiation Spectrum

READ: Chapter 7 (section 7.4)


W 15 Feb: The Blackbody Spectrum continued and Johnson Noise


F 17 Feb: Problem Presentation Day #2


M 20 Feb: Debye Theory

READ: Chapter 7 (section 7.5)


W 22 Feb: Bose-Einstein Condensation

READ: Chapter 7 (section 7.6)


F 24 Feb: Problem Presentation Day #3

M 27 Feb: Bose-Einstein Condensation continued


UNIT V: Free Energy and Chemical Thermodynamics


W 29 Feb: Thermodynamic Potentials

READ: Chapter 5(sections 5.1 – 5.2)


Helmholtz Free Energy

Gibbs Free Energy


            Thermodynamic identity revisited


F 2 Mar: Problem Presentation Day #4


M 5 Mar: Phase Transformations

READ: Chapter 5 (sections 5.3 – 5.4)

Phase transformations for pure substances

Clausius-Clapeyron equation

Phase transformations of mixtures


W 7 Mar: Dilute Solutions and Chemical Reactions

READ: Chapter 5 (sections 5.5 – 5.6)

F 9 Mar: Review of the Course

Physics 320: Thermal Physics


Excerpts from Thermodynamics, by Enrico Fermi (1936):




Thermodynamics is mainly concerned with the transformations of heat into mechanical work and the opposite transformations of mechanical work into heat.  Only in comparatively recent times have physicists recognized that heat is a form of energy.  Formerly, scientists had thought that heat was some sort of fluid whose total amount was invariable, and had simply interpreted the heating of a body and analogous processes as consisting of the transfer of this fluid from one body to another …


We know today that the actual basis for the equivalence of heat and dynamical energy is to be sought in the kinetic interpretation, which reduces all thermal phenomena to the disordered motions of atoms and molecules.  From this point of view, the study of heat must be considered as a special branch of mechanics: the mechanics of an ensemble of such enormous numbers of particles … that the detailed description of the state and the motion loses importance and only the average properties of large numbers of particles are to be considered.  This branch of mechanics, called statistical mechanics, which has been developed mainly through the work of Maxwell, Boltzmann, and Gibbs, has led to a very satisfactory understanding of the fundamental thermodynamical laws.”


Chapter II: The First Law of Thermodynamics


“The first law of thermodynamics is essentially the statement of the principle of the conservation of energy for thermodynamical systems. As such, it may be expressed by stating that the variation in [internal] energy of a system during any transformation is equal to the [net] amount of energy that the system receives from the environment [via heat and/or work].”


Chapter III: The Second Law of Thermodynamics


“A transformation whose only final result is to transform into work heat extracted from a source which is at the same temperature throughout in impossible. (Postulate of Lord Kelvin.)


A transformation whose only final result is to transfer heat from a body at a given temperature to a body at a higher temperature is impossible. (Postulate of Clausius.)”










Joule’s apparatus (1850)