General aims:

• 1. To revise basic concepts of heat, temperature, work and energy in thermal systems.

• 2. To relate microscopic and macroscopic descriptions of thermal systems and to demonstrate the statistical nature of the microscopic approach.

• 3. To relate the arguments underlying the derivation of the Maxwell-Boltzmann energy distribution and to demonstrate the widespread applicability of the concepts involved in many diverse areas of physics.

• 4. To investigate further properties of ideal gases.

• 5. To examine diffusion and thermal conductivity from a statistical viewpoint.

Section 1. Introduction to macroscopic thermal variables - 1 lecture

Objectives: On completion of this section you should be able to:

• 1. Express the meanings of “heat”, “temperature”, “work” and “internal energy”.

• 2. To select appropriate conjugate variables to describe a given thermal system.

• 3. State the First Law of Thermodynamics.

• 4. Derive expressions for the work done in thermodynamic processes.

• 5. Explain what is meant by an “equation of state” and give suitable examples.

Objectives: On completion of this section you should be able to:

• 1. Distinguish between microscopic and macroscopic variables.

• 2. Explain the relative probability of different microscopic configurations.

• 3. Explain why microscopic states can only be treated statistically.

• 4. Discuss the relationship between microscopic states and macroscopic variables.

• 5. Illustrates this relationship with a suitable example.

• 6. Describe the meaning of thermodynamic equilibrium from both the microscopic and macroscopic viewpoints.

• 7. Discuss the reversibility of thermodynamic processes from a microscopic viewpoint.

• 8. Discuss the idea of entropy from a statistical viewpoint.

Section 3. Boltzmann’s Law for the distribution of energies and related quantities in thermal systems - 3 lectures

Objectives: On completion of this section you should be able to:

• 1. State the ideal gas law.

• 2. Derive equations describing the mean kinetic energy of molecules in an ideal gas.

• 3. Relate the temperature of a thermal system to the microscopic description of the system.

• 4. Explain why molecules of an ideal gas have a distribution of energies and velocities.

• 5. Describe the general form of the energy distribution and identify the Boltzmann factor.

• 6. Discuss the distribution of velocities of an ideal gas, and the temperature dependence of this distribution.

• 7. Express the meaning of thermodynamic degrees of freedom.

• 8. State the “equipartition of energy” theorem.

• 9. Apply the Maxwell-Boltzmann energy distribution to examples in several diverse areas of physics.

Objectives: On completion of this section you should be able to:

• 1. State Dalton’s Law of partial pressures and apply it in appropriate situations.

• 2. Derive molar specific heats c_P and c_V of an ideal gas and show that c_P - c_V = R.

• 3. Demonstrate that pV^g is a constant in a adiabatic expansion of an ideal gas.

• 4. Discuss the Second Law of Thermodynamics with examples.

Objectives: On completion of this section you should be able to:

• 1. Define “mean free path” and “drift speed”.

• 2. Derive an expression for mean free path.

• 3. Explain what “Brownian motion” is and how it provides evidence of the distribution of molecular energies.

• 4. Explain the process of diffusion.

• 5. Employ statistical arguments to derive an expression for the mean rate of spread of molecules due to diffusion.

• 6. Discuss the process of thermal conductivity.