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## Introduction

This course is given to all second year physicists and is examined on paper A1 at the end of the second year. I gave this lecture course up until the end of Hilary Term 2011.

Thermal physics arises from thinking about the behaviour of large numbers of atoms and molecules. The basic ideas in this subject are at the root of fields as diverse as statistical physics, random and stochastic processes, vacuum technology, financial markets, condensed matter physics and atmospheric physics. The lectures are aimed at introducing techniques for thinking about and manipulating probability distributions, providing the fundamentals of the kinetic theory of gases and thermodynamics, illustrating this material with a number of applications of the subject to real physical situations. The course includes statistical methods and probability distributions, the Boltzmann distribution, the Maxwell-Boltzmann velocity distribution function, molecular effusion, collision times and transport processes (viscosity, thermal conductivity and self-diffusion), the laws of thermodynamics, energy, entropy, equations of state, thermodynamic potentials, chemical potential and phase changes.

## Synopsis

Kinetic Theory:
Maxwell distribution of velocities: derivation assuming the Boltzmann factor, calculation of averages, experimental verification. Derivation of pressure and effusion formulae, distribution of velocities in an effusing beam, simple kinetic theory expressions for mean free path, thermal conductivity and viscosity; dependence on temperature and pressure, limits of validity. Practical applications of kinetic theory.

Heat transport:
Conduction, radiation and convection as heat-transport mechanisms. The approximation that heat flux is proportional to the temperature gradient. Derivation of the heat diffusion equation. Generalization to systems in which heat is generated at a steady rate per unit volume. Solution by separation of variables for problems with spherical and planar symmetry. Steady-state problems, initial-value problems, and problems involving sinusoidally varying surface temperatures.

Thermodynamics:
Zeroth & First laws. Heat, work and internal energy: the concept of a function of state. Slow changes and the connection with statistical mechanics: entropy and pressure as functions of state. Heat engines: Kelvin's statement of the second law of thermodynamics and the equivalence and superiority of reversible engines. The significance of integral round a closed loop of dQ/T=0 and the fact that entropy is a function of state. Practical realization of the thermodynamic temperature scale. Entropy as dQ_{reversible}/T. Enthalpy, Helmholtz energy and Gibbs energy as functions of state. Maxwell relations. Concept of the equation of state; thermodynamic implications. Ideal gas, van der Waals gas. Reversible and free expansion of gas; changes in internal energy and entropy in ideal and non-ideal cases. Joule-Kelvin expansion; inversion temperature and microscopic reason for cooling. Impossibility of global entropy decreasing: connection to latent heat in phase changes. Constancy of global entropy during fluctuations around equilibrium (non-examinable). Chemical potential and its relation to Gibbs energy. Equality of chemical potential between phases in equilibrium. Latent heat and the concepts of first-order and continuous phase changes. Clausius-Clapeyron equation and simple applications. Simple practical examples of the use of thermodynamics.