**Physics 320**

*Thermal
Physics*

**Winter
Term, 2012**

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

**Professor
Matthew Stoneking**

**Document
links:**

Excerpts
from Fermi

**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,**
2^{nd} 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%

*Exams:*

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 2^{nd}
Law

Clausius’
theorem

Entropy and the 2^{nd}
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)*

Enthalpy

Helmholtz Free Energy

Gibbs Free
Energy

Electrochemistry

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):

Introduction:

“*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)