Welcome to Thermal & Kinetic Physics (PHY-5214) Home Page

The Module Organiser is Dr. Kevin Donovan

The Deputy Module Organiser is Dr. John Dennis

Introduction

Thermal and Kinetic Physics is a course designed as an introduction to the notion of energy and its transformations. The thermodynamic methodology that is constructed, largely through the paradigm of the ideal gas, is widely applicable throughout the realm of physics. We begin by developing a language capable of dealing with the thermodynamic method and this requires that  concepts of equilibrium and temperature are disentangled before  work and heat are described in detail en route to the First Law of Thermodynamics. With the First Law many things become readily accessible to an analytic approach previously unavailable including; engines, refrigerators and heat pumps. Entropy will then make a natural appearance as a macroscopic thermodynamic variable in the build up to the Second Law of Thermodynamics with a brief look at its microscopic origins. New thermodynamic potentials including the Gibbs potential and the Helmholtz free energy, and their applications, are discussed in order to generalise further the thermodynamic method.  Phase changes for simple systems are briefly covered and the Third law of Thermodynamics described. Finally an introduction to the kinetic description of gases in equilibrium and of phenomena such as diffusion and heat conduction will complete the module.

Lectures.

There are three lectures per week taking place at the following times and venues;

Lecture 1. 10am Monday, PP 2

Lecture 2. 12pm Monday, FB 2.40

Lecture 3. 1pm Tuesday, FB 2.40

Exercise Classes.

Thermal & Kinetic Physics includes exercise classes on Fridays where the week's lectures will be reviewed and an opportunity offered for questions to be asked concerning that week's material. Solutions to the returned marked coursework may be covered where necessary. Set problems related to the week's material will then be worked through with the aid of  the lecturer. 

There are four timetabled slots for exercise classes per week and students are expected to attend the one allocated to them. These are;

Exercise Classes; Fridays at; 10am -11am , 11am - 12pm,  2pm - 3pm & 3pm - 4pm all in BR 4.01

Attendance Requirements.

The department has a strong attendance policy the details of which can be found here. Attendance and performance in all aspects of this module are monitored and a student monitoring programme will maintain a record of individual student attendance at lectures and exercise classes and of homework completion.

Mid-Term Exam.

There will be a 50 minute duration mid-term exam on Monday 11th November at 10am in PP 2

The exam will start at 10:05am so students are asked to make sure they arrive promptly at 10am.

Students should bring pen and other drawing tools along with a simple calculator. The answers will be written in the question book.

The exam will consist of;

Section A with brief questions requiring 1 line answers. This counts 50% to the overall mark.

Section B requiring the student to answer 2 from 3 questions. This counts 50% to the overall mark.

The Mid-Term exam is compulsory and will count 10% to the overall module assessment.

Plagiarism.

Put bluntly, plagiarism is theft by copying the work of someone else in order to gain marks or credit unfairly. It can occur in the TKP coursework as well as in written exams. It will be dealt with most severely in TKP. The Departmental policy on plagiarism and the punishments associated are explained in Policy on Plagiarism . The Course Organiser and the marker will be especially vigilant in looking out for plagiarism in coursework. If you have copied from someone else or if you have allowed your work to be copied you will be subject to the Departmental and College Disciplinary Rules. Any offence of plagiarism must be reported to the College and will be placed on your record.

Note, however, that it is a valuable part of learning to discuss exercise questions with your fellow students, but on no account should you copy solutions, or allow your work to be copied. Write your solutions and essay in your own words. Do not feel that you must hand in the complete set of exercises each week. If you have managed only half of the work, better to hand that in for marking rather than to hand nothing in or to try to copy from someone else.

Office Hours.

While generally available for questions concerning the module Dr Donovan's office hours are - Tuesdays 2:30-3:30 pm in Room 117.

Textbooks & Lecture Notes.

Aims

The aim of Thermal and Kinetic Physics is to explore how energy transformations are constrained by the Laws of Thermodynamics and how such macroscopic processes are related to microscopic kinetic phenomena at the molecular level.

Learning Outcomes

A student who successfully completes this course will be able to:

1.     State the four Laws of Thermodynamics.

2.     Describe and contrast the concepts of empirical temperature, ideal gas temperature, kinetic temperature and thermodynamic temperature.

3.     Analyze reversible processes represented in a P - V diagram in terms of work done and heat flows by use of the First Law of Thermodynamics.

4.     Describe heat engines, heat pumps and refrigerators and calculate their figures of merit from their cyclic representation in a P - V diagram.

5.     Understand how the Second Law of Thermodynamics limits the efficiency of all engines and to evaluate this maximum efficiency for a Carnot engine.

6.     Appreciate the macroscopic definition of entropy and relate it to disorder at the molecular level through Boltzmann's hypothesis.

7.     Apply the Laws of Thermodynamics to physical processes occuring in simple fluids, ideal paramagnets, elastic substances and cavity radiation.

8.     Use the mathematics of partial differentiation to derive Maxwell relations and other thermodynamic identities.

9.     Derive the ideal gas law and the Maxwell-Boltzmann velocity distribution for a gas starting from molecular kinetic assumptions.

10.   Describe how diffusion and heat conduction take place at a molecular level and to express the role of the mean free path in such transport phenomena.

Thermal & Kinetic Physics Syllabus

Classical Newtonian Mechanics takes the world view that objects can be completely described through a set of conservation principles that constrain the allowed motions of individual objects which may with the aid of those principles be completely specified. Such a clockwork view of the world has no room for dissipation the inclusion of which sees that clockwork running down. In the Newtonian world view energy was relegated to a minor role being a late arrival on the scene. It took the industrial revolution to bring the study of these dissipative mechanisms in the study of thermodynamics. Thermodynamics is a subject whose primary concern is with the description of how “systems”  interact with other systems and with their environment through energy exchange as one form of energy is transformed. The description of these interactions at the macroscopic level is given in terms of the flow of energy in the forms of heat and work as interactions and transformations take place and in terms of macroscopic variables such as temperature, volume and pressure  and how they inter-relate. Within this framework a whole new variety of macroscopic variables, entropy, enthalpy, internal energy and free energy to name but a few, have been established and used to provide such descriptions. This module will develop equilibrium thermodynamics and seek to relate it to the kinetic theory of matter where the motions of the atomic constituents of these systems form the basis of the explanation of the origin of heat, internal energy and temperature.

Part I: Thermodynamics.

1. Internal Energy, Equations of State, Temperature and Work.

The module begins by establishing a vocabulary for the study of thermodynamics. The ideal gas will be used as a paradigm of a thermodynamic system allowing concepts of  internal energy with, accompanying an equation of state including state variables and state function, to be defined. The idea of temperature is approached through the Zeroth Law of Thermodynamics and equilibrium states before using Boyles Law to define temperature through another equation of state. The concept and calculation of work through consideration of processes on a P-V diagram is studied.

2. The First Law of Thermodynamics, Heat andHeat Capacity.

Consideration of the first law allows the concept of heat flow to be introduced along with the adiabatic process, where heat flow is zero, and the rules governing such processes. Heat capacity is defined in terms of state functions at constant volume and constant pressure and enthalpy is introduced as a new state function. Diatomic molecules and equipartition are discussed and modified equations of state found.

3. Heat Engines and the Carnot Cycle.

The concept of a heat engine is introduced and efficiencies of a heat engine, refrigerator and heat pump defined in terms of heat flows. The efficiencies of several engine cycles are derived from consideration of P-V diagrams. The Carnot cycle efficiency is found in terms of the temperatures of the heat reservoirs and thermodynamic temperature defined.

4. Clausius Inequality and Entropy.

The Clausius Inequality is established using the properties of the Carnot engine and through this a new state function, Entropy, is defined, Simple entropy calculations are carried out. Boltzmann’s description of entropy and Boltzmann’s equation are deduced from consideration of intensive and extensive properties. The thermodynamic identity is established.

5. Other Thermodynamic Systems.

Thermodynamics, as understood through the ideal gas paradigm, is applied to other systems including cavity radiation and paramagnets. The paramagnetic refrigerator.

6. New Thermodynamic Potentials.

New thermodynamic potentials , the Gibbs free energy and the Helholtz free energy are defined. Natural variables for these potentials are found and from these Maxwell relations discovered relating thermodynamic properties through partial differentals.

7. Phase Changes and the Third Law of Thermodynamics.

Phase diagrams, the critical point and the triple point. The description of phase boundaries in terms of the Gibbs free energy, The Clausius Clapeyron equation is derived. The third law of thermodynamics is discussed in various forms.

Part II: Kinetic Physics.

8. Maxwell Speed Distribution

Velocity and Speed Distributions are derived. Particle flux and effusion are discussed. 

9. Mean Free Path.

The definition of the mean free path and derivation of the mean free path distributions.

10. Diffusion

The diffusion equation. Fick's law. The heat conduction equation.

Coursework.

There will be one coursework per week that will be handed out in the Tuesday lecture and posted on this website.Hand-in of the worked problems must take place by 4:00 p.m. on the following Tuesday at the box provided outside the Teaching Administrators office on the first floor. This time will be strictly adhered to and no late working will be accepted unless accompanied by an extenuating circumstances form. The solutions will appear later in the week on this website.The return of the marked problems will be by the Tuesday of the week after hand in and the scripts will be returned via the homework return boxes outside the Teaching Administrators office.

The courseworks and their solutions represent a valuable revision tool.

Coursework Marks

A weekly update of coursework marks will be available here starting in week 3. Due to matters of privacy the marks can only be attributed using student ID.

Weekly Coursework pdfs

Coursework 1 will be found here. The solutions will be available here.

Useful Information

The values of useful constants for the TKP module are listed here.

A glossary of the terms frequently encountered in the module may be found here.

This is an indicative lecture schedule and may be subject to alteration.

Deadlines

1. There will be one coursework per week that will be available for download from this website after the Tuesday lecture. 

2. Hand-in of the worked problems must take place by 4:00 p.m. on the following Tuesday at the box provided outside the Teaching Administrators office on the first floor. This time will be strictly adhered to and no late working will be accepted unless accompanied by an extenuating circumstances form. The solutions will appear later in the week on this website.

3. The return of the marked problems will be by the Tuesday of the week after hand in and the scripts will be returned via the homework return boxes outside the Teaching Administrators office. 

Marking

The final assessment of this module will be comprised of three components as follows;

1. There will be Weekly Coursework set and the total mark from the coursework will comprise 10% of the overall module assessment.

2. There will be a MidTerm exam on the first lecture slot following reading week and the mark from the midterm will comprise 10% of the overall module assessment.

3. There will be a Final Exam in May/June and the mark from the final exam will comprise 80% of the overall module assessment.

Past Exams & Solutions

The 2010 TKP exam can be found here.

The 2011 TKP exam can be found here.

The 2012 TKP exam can be found here.

The 2013 TKP exam can be found here.

The 2012 TKP exam solutions can be found here.

The 2013 TKP exam solutions can be found here.

Exercise Class.

Thermal & Kinetic Physics includes exercise classes on Thursdays and Fridays where the week's lectures will be reviewed and an opportunity offered for questions to be asked concerning that week's material. The solutions to that week's returned coursework may be covered where necessary. Set problems related to the week's material will then be worked through with the aid of the lecturer. Of the four exercise classes run each week attendance at one will be expected and the groups will be organised in week one of semester A.

Exercise Class Fridays 10am -11am & 11am - 12pm, BR 4.01.

Exercise Class Fridays 2pm - 3pm & 3pm - 4pm, BR 4.01

The exercise class allocations will appear here.

Exercise 1, week 2 will appear here.

Lecture Notes.

Lecture Notes 1. Introduction: including; Internal Energy, Equations of State, Thermometers, Kinetic and Ideal Gas Temperatures available here (pdf, 26 pages, 625KB).

Lecture Notes 2. Partial Differentials: including; the reciprocal relation, the cyclical relations, thermal expansion coefficient and bulk modulus will appear here (pdf, 8 pages, 172KB).

Lecture Notes 3. The first law of thermodynamics: including;  Work, heat and the first law, specific heats, enthalpy, adiabatic equation, diatomic gases, van der Waals gases, free expansion, Joule Kelvin effect will appear here (pdf, 46 pages, 606KB).

Lecture Notes 4. Heat Engines: including; engines, refrigerators and heat pumps. Efficiencies. Carnot cycle. Thermodynamic temperature scale. Otto, Diesel and Stirling cycles will appear here (pdf, 25 pages, 403KB).

Lecture Notes 5. Entropy: including; Clausius inequality, entropy, Boltzmann's microscopic interpretation and the bridge equation. Entropy forms of Second Law. Calculations of entropy will appear here  (pdf, 38 pages, 152KB).

Lecture Notes 6. Some other examples of thermodynamic systems: including; Cavity radiation. Blackbody Radiation. Entropy of cavity radiation. Kirchoffs Law, Stefans Law. Thermodynamics of Paramagnets including a review of paramagnetism, paramagnetic work, Curies Law, Schottkies law, magnetic Gibbs free energy, entropy of paramagnets and paramagnetic cooling will appear here (pdf, 31 pages, 129KB).

Lecture Notes 7. Thermodynamic Potentials: including; The Gibbs and Helmoltz free energies, G & F, as new thermodynamic potentials,  Maxwell Relations, Phase change and the Gibbs free energy, Clausius-Clapeyron Equation, 3rd Law will appear here (pdf, 38 pages, 198KB).

Lecture Notes 8. Kinetic Theory: including; Velocity & Speed distributions, flux onto bounding wall, Mean Free Path and distribution, random walk and diffusion, Fick’s law, the diffusion equation, heat conduction, Fouriers law, the heat equation will appear here. (pdf, 52 pages, 203KB).

Revision Aids.

Mid-Term Revision Aids

Revision Lecture

News

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