PHY2023 Thermal Physics 2013-14
Dr M.E. Portnoi

Delivery Weeks: T2:01-11
Level: 5 (NQF)
Credits: 15 NICATS / 7.5 ECTS
Enrolment: 71 students (approx)

### Description

This module builds on the discussion of thermal properties in the Stage 1 PHY1024 Properties of Matter module, introduces classical thermodynamics and shows how its laws arise naturally from the statistical properties of an ensemble. Real-world examples of the key ideas are presented and their application in later modules such as PHY2024 Condensed Matter I and PHY30703 Stars from Birth to Death is stressed. The concepts developed in this module are further extended in the PHYM001 Statistical Physics module.

### Module Aims

The aim of Classical thermodynamics is to describe the states and processes of of systems in terms of macroscopic directly measurable properties. It was largely developed during the industrial revolution for practical purposes, such as improving the efficiency the steam-engines, and its famous Three Laws are empirically based.

The aim of statistical mechanics, which had major contributions from Maxwell, Boltzmann and Gibbs, is to demonstrate that statistical methods can predict the bulk thermal properties of a system from an atomistic description of matter. The theory provides the only tractable means of analysing the almost unimaginable complexity of an N-body system containing 1023 particles. The classical Second Law of Thermodynamics finds a natural explanation in terms of the evolution of a system from the less probable to the more probable configurations.

### Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
1. explain the nature of classical entropy, and its relationship to the second law of thermodynamics;
2. determine the maximum efficiency of simple heat-engines and heat pumps;
3. calculate the equilibrium energy distribution of a system using the Boltzmann distribution;
4. explain the origin of the second law from a statistical viewpoint;
5. describe the significance of various thermodynamic potentials and deduce relations between them;
6. demonstrate, by calculating certain properties of real gases, an understanding of the limitations of the ideal gas law;
7. calculate bulk thermodynamic properties such as heat capacity, entropy and free energy from the partition function;
8. predict whether a gas constitutes a classical or a quantal gas, and explain key differences in the behaviour of these;
• Discipline Specific Skills and Knowledge:
1. use calculus to calculate maximum and minimun values of constrained multivariable systems;
2. use graphs and diagrams to illustrate arguments and explanations;
• Personal and Key Transferable / Employment Skills and Knowledge:
1. use a range of resources to develop an understanding of topics through independent study;
2. solve problems;
3. apply general concepts to a wide range of specfic systems and situations;
4. meet deadlines for completion of work for problems classes and develop appropriate time-management strategies.

### Syllabus Plan

1. Introduction
Brief historical survey.
2. Classical Thermodynamics
1. Zeroth, first and second laws of thermodynamics
2. Temperature scales, work, internal energy and heat capacity
3. Entropy, free energies and the Carnot Cycle
4. Changes of state
5. Heat engines and heat pumps
6. The Fundamental Thermodynamic Relationship
7. Thermodynamic potentials and Maxwell relations
8. Real gases
3. Statistical Physics
1. Maxwell-Boltzmann distribution
2. Boltzmann energy sharing
3. Microscopic / statistical interpretation of entropy
4. Statistical Thermodynamics
1. Density of states
2. The partition function Z
3. Macroscopic functions of state in terms of Z.
4. Equation of state for an ideal monatomic gas
5. The equipartition theorem
6. Quantum statistical mechanics; the Bose-Einstein and Fermi-Dirac distributions

### Learning and Teaching

#### Learning Activities and Teaching Methods

Description Study time KIS type
22×1-hour lectures 22 hours SLT
5×6-hour self-study packages 30 hours GIS
8×2-hour problems sets 16 hours GIS
Problems class support 8 hours SLT
Tutorial support 3 hours SLT
Reading, private study and revision 71 hours GIS

#### Assessment

Weight Form Size When ILOS assessed Feedback
0% Exercises set by tutor 3×1-hour sets (typical) Scheduled by tutor 1-14 Discussion in tutorials
0% Guided self-study 5×6-hour packages Fortnightly 1-14 Discussion in tutorials
10% 8 × Problems sets 2 hours per set Weekly 1-14 Marked in problems class, then discussed in tutorials
15% Mid-term Test 30 minutes Weeks T2:06 1-13 Marked, then discussed in tutorials
75% Examination 120 minutes May/June assessment period 1-13 Mark via MyExeter, collective feedback via ELE and solutions.

### Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

Supplementary texts:

ELE:

### Further Information

#### Prior Knowledge Requirements

Pre-requisite Modules Properties of Matter (PHY1024) and Mathematics for Physicists (PHY1026) Mathematics with Physical Applications (PHY2025)

#### Re-assessment

Re-assessment is not available except when required by referral or deferral.

Original form of assessment Form of re-assessment ILOs re-assessed Time scale for re-assessment
Whole module Written examination (100%) 1-13 August/September assessment period

Notes: See Physics Assessment Conventions.

#### KIS Data Summary

Learning activities and teaching methods
SLT - scheduled learning & teaching activities 33 hrs
GIS - guided independent study 117 hrs
PLS - placement/study abroad 0 hrs
Total 150 hrs
Summative assessment
Coursework 10%
Written exams 90%
Practical exams 0%
Total 100%

#### Miscellaneous

 IoP Accreditation Checklist TD-01 Zeroth, first and second laws of thermodynamics TD-02 Temperature scales, work, internal energy and heat capacity TD-03 Entropy, free energies and the Carnot Cycle TD-04 Changes of state SM-02 Statistical basis of entropy SM-03 Maxwell-Boltzmann distribution SM-04 Bose-Einstein and Fermi-Dirac distributions SM-05 Density of states and partition function Availability unrestricted Distance learning NO Keywords Physics; Thermodynamic; Properties; Heat; Energy; System; State; Distribution; Boltzmann; Entropy; Functions. Created 01-Oct-10 Revised 01-Oct-11