Study-Unit Description

Study-Unit Description


CODE PHY1187

 
TITLE Thermodynamics and Kinetic Theory

 
UM LEVEL 01 - Year 1 in Modular Undergraduate Course

 
MQF LEVEL 5

 
ECTS CREDITS 6

 
DEPARTMENT Physics

 
DESCRIPTION In all of nature, each system can be associated with some measure of degree of hotness and is crucial to understand their respective behaviour. Essentially, any system can be assigned a temperature as well as other important quantities which characterise the system such as pressure and volume. The intricate relationship between these quantities is what constitutes the basis of thermodynamics.

Throughout this study-unit, an introduction to classical thermodynamics followed by kinetic theory is presented. This will establish the main fundamental foundations of thermodynamics which are essential in describing a large number of phenomena (at least macroscopically) and later in developing the modern (microscopic) viewpoint.

Study-unit Aims:

The study-unit aims to provide an introduction to the phenomenological aspects of thermodynamics and kinetic theory while also providing the necessary tools to be able to investigate different thermodynamical systems. In particular, the following topics will be presented:

Thermodynamics:
- A review of the microscopic and macroscopic views of nature with reference to thermodynamics and kinetic theory;
- Definition of thermodynamic equilibrium (including thermal, chemical and mechanical);
- The relation between thermodynamic equilibrium and the zeroth law of thermodynamics;
- Description of empirical temperature in relation to thermometers;
- A short overview of simple thermodynamic systems beyond ideal gases;
- A review of the equation of state of hydrostatic systems including those of ideal and van der Waals gases;
- Description of thermodynamic processes including quasi-static, reversible and irreversible processes;
- Definition and distinction between intensive and extensive quantities;
- Mathematical description and use of exact and inexact differentials as well as partial derivatives;
- Statement of the first law of thermodynamics and its application particularly in the context of ideal gases;
- Definition of enthalpy in relation to specific heat capacity;
- A discussion on cyclic thermodynamic processes including the Carnot cycle;
- Statement of the second law of thermodynamics and its equivalent statements of the law;
- Definition of the absolute (thermodynamic) temperature scale and relationship with empirical temperature;
- An introduction to the concept of entropy and its application with the first law of thermodynamics leading to the TdS equations;
- Definition of Joule coefficient and Joule-Thomson coefficient including their respective forms for ideal and var der Waals gases;
- Description of the Gay-Lussac and Joule-Thompson experiments;
- An introduction to thermodynamic potentials particularly Helmholtz and Gibbs free energies leading to the Gibbs-Helmholtz equations, Maxwell’s relations and multivariable systems;
- Definition of stable, unstable and metastable states in relation to spontaneous processes, irreversible processes, supercooling and superheating;
- Overview of phase transitions including their nature (first and higher order) and the Clausius-Clapeyron equation;
- Statement of the third law of thermodynamics following Nerst’s results and Planck’s hypothesis.

Kinetic Theory
- Identification of the key basic assumptions considered in kinetic theory;
- Definition and use of molecular flux especially in the derivation of the ideal gas equation of state;
- Description of the relationship between average kinetic energy and temperature;
- Introduction to degrees of freedom and equipartition of energy in relation to specific heat capacity;
- Discussion of intermolecular forces and derivation of the van der Waals equation of state;
- Definition of mean free path.

Learning Outcomes:

1. Knowledge & Understanding
By the end of the study-unit the student will be able to:

Thermodynamics:
- Explain the differences between the microscopic and macroscopic scales;
- Define thermodynamic equilibrium in relation with the zeroth law of thermodynamics;
- Describe the constant volume gas thermometer, electric resistance thermometer and thermocouple;
- Define a temperature scale;
- Describe and distinguish between quasi-static, reversible and irreversible thermodynamic processes;
- Distinguish between exact and inexact differentials;
- Describe cyclic thermodynamic processes and the Carnot cycle;
- Discuss the thermodynamics processes involved in heat engines and heat pumps in relation to the second law of thermodynamics;
- Define and relate empirical and absolute (thermodynamic) temperature scales;
- Explain what is meant by entropy;
- Define the Joule coefficient and the Joule-Thomson coefficient and their empirical determination through experiment;
- Explain what is meant by thermodynamic potentials and ability to define the Helmholtz and Gibbs free energies;
- Distinguish between stable, unstable and metastable equilibrium states;
- Describe supercooling and superheating;
- Explain when a system undergoes a phase transition and ability to distinguish between first and higher-order phase transitions;
- Derive the Clausius-Clapeyron equations;
- Explain the implications of Nerst’s results and Planck’s hypothesis in relation with the third law of thermodynamics.

Kinetic Theory:
- Understand the need and implication of the assumptions needed to build kinetic theory;
- State and derive the equation of state of an ideal gas using kinetic theory;
- Describe the relationship between average kinetic energy and temperature;
- Distinguish between different degrees of freedom namely translational, vibrational and rotational modes;
- Describe the direct connection between specific heat capacity and the equipartition of energy;
- Derive the equation of state of a van der Waals gas;
- Derive the mean free path of a gas.

2. Skills
By the end of the study-unit the student will be able to:

Thermodynamics:
- Use thermodynamic equilibrium and the laws of thermodynamics including the TdS equations to solve problems;
- Analyse simple thermodynamic systems;
- State and use the equation of state of an ideal gas and of a van der Waals gas;
- Use, sketch and interpret PVT plots to identify the state of a system, the underlying thermodynamical processes and whether the system undergoes a phase transition;
- State and use the Gibbs-Helmholtz equations and Maxwell’s relations;
- Identify the nature of the phase transition;
- State and use the Clausius-Clapeyron equation.

Kinetic Theory:
- Calculate and derive expressions involving the molecular flux;
- Identify the degrees of freedom of a system;
- Use the equipartition of energy to relate the average kinetic energy with temperature;
- Solve problems involving the specific heat capacity;
- Calculate the mean free path of a gas.

Main Text/s and any supplementary readings:

Recommended Main Textbooks:

• Thermodynamics, Kinetic Theory, and Statistical Thermodynamics, F. W. Sears and G. H. Salinger (Addison-Wesley, 3rd Edition, 1975)
• Thermodynamics and Statistical Mechanics, W. Greiner, L. Neise, H. Stocker (Springer, 1997)
• Heat and Thermodynamics: An Intermediate Textbook, M. W. Zemansky and R. H. Dittman (McGraw-Hill, 7th Edition, 1997)

Supplementary Textbooks:

• A Guide to Physics Problems - Part 2: Thermodynamics, Statistical Physics and Quantum Mechanics, S. B. Cahn, G. D. Mahan and B. E. Nadgorny (Kluwer Academic, 2004)
• Thermodynamics and an introduction to Thermostatistics, H. B. Callen, (John Wiley & Sons, Singapore, 2nd Edition, 1985)
• Statistical Mechanics, K. Huang (John Wiley & Sons, 2nd Edition, 1987).

 
ADDITIONAL NOTES Pre-Requisite Study-units: Mathematical requirement follows from MAT1091

 
STUDY-UNIT TYPE Lecture and Tutorial

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Sept. Asst Session Weighting
Assignment SEM1 Yes 30%
Examination (2 Hours and 30 Minutes) SEM1 Yes 70%

 
LECTURER/S Lourdes Farrugia

 

 
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