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Course Outline

I. Probability

1. Random Variables: Discrete, Continuous, and Mixed
2. Multiple Variables: Joint and Conditional Densities
3. Functions of a Random Variable
4. Sums of Random Variables

Examples: Drawn from Kinetic Theory, Poisson Processes, and Quantum Mechanical Wave Functions

II. Thermodynamic Systems

1. Definitions
2. The Concept of Temperature
3. The First Law

III. Micro-canonical Ensemble

1. The Postulate of Equal a Priori Probabilities
2. Temperature, Entropy, and the Second Law
3. Probabilities for Microscopic Variables

Examples: Ideal Gas, 2 Level Problem, Shottkey Defects, 1 Dimensional Ising Model, Harmonic Oscillators

IV. Canonical Ensemble

1. Earlier Examples Revisited
2. Connection with Thermodynamic Potentials
3. Fluctuations

Examples: Polyatomic Gases, Paramagnetism, Thermal Radiation and Phonons in Solids, Noise in Electronic Circuits

V. Ideal Quantum Gases

1. Zero Temperature Behavior
2. Counting of States, Failure of Canonical Ensemble
3. Low Temperature Behavior

Examples: Bose-Einstein Condensation; Metals, Semiconductors, and Insulators; Neutron Stars and White Dwarfs

Description

This course offers an introduction to probability, statistical mechanics, and thermodynamics. Specific topics in probability include random variables, joint and conditional probability densities, and functions of a random variable. Topics in statistical mechanics include macroscopic variables, thermodynamic equilibrium, fundamental assumptions of statistical mechanics, and microcanonical and canonical ensembles. Topics in thermodynamics include the first, second, and third laws of thermodynamics.

Prerequisites

Physics III: Vibrations and Waves (8.03), Differential Equations (18.03) and Concurrent Enrollment in Quantum Physics I (8.04) is recommended.

Books

Required

Reif, F. Fundamentals of Statistical and Thermal Physics. New York, NY: McGraw-Hill, June 1, 1965. ISBN: 9780070518001.

Optional

Zemansky, M., and R. Dittman. Heat and thermodynamics: an intermediate textbook. 7th ed. New York, NY: McGraw-Hill Companies, 1996. ISBN: 9780070170599.

Exams

There will be four one-hour exams. Each exam contributes 21% toward the final grade.

Homework

Problem sets are due in the lecture on the days indicated on the calendar. Since the solutions will be handed out at the end of the same lecture, no late homework will be accepted. The graded homework will be returned in the recitation sections. The homework contributes 16% toward the final grade.

Grading