ENERGY, ENTROPY AND NUMERICAL PHYSICS - 2023/4

Module Overview

This module considers develops both the thermodynamic and statistical descriptions of energy and entropy. In addition it builds on the introductory Level FHEQ 4 computing modules to develop the skills needed for computational physics. The module will explore various meanings and definitions of entropy. Knowledge of thermodynamics will then be applied to problem solving. The module will build upon the knowledge obtained of the laws of thermodynamics introduced in Properties of Matter at Level FHEQ 4. It will introduce additional thermodynamic theory and show how statistical physics allows us to calculate thermodynamic functions such as the entropy. The computational physics component will develop the student’s skills in solving both ordinary and partial differential equations, in the context of both quantum and thermal physics.

Module provider

Mathematics & Physics

Module Leader

ERKAL Denis (Maths & Phys)

Number of Credits: 15

ECTS Credits: 7.5

Framework: FHEQ Level 5

Module cap (Maximum number of students): N/A

Module Availability

Semester 1

Prerequisites / Co-requisites

None

Module content

Indicative content includes:

• 
  The module will build on the Level HE1 module “Properties of Matter” by developing our understanding of entropy within thermodynamics, and by showing how statistical physics allows us to calculate the properties of matter, such as the entropy, by averaging huge numbers of states of the matter’s constituent atoms.
  


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  The statistical nature of the 2nd Law of Thermodynamics will be shown.
  


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  The concept of a free energy and the Helmholtz and Gibb’s free energy functions will be covered. The statistical physics part of the course will introduce Shannon’s expression for the entropy, the partition function at constant temperature, the Boltzmann weight of a state at constant temperature, and also the weight of a state at constant chemical potential/Fermi level.  
  


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  Fluctuations will be studied and the Central Limit Theorem will be introduced. The relationship between fluctuations and thermodynamic quantities such as heat capacities will be shown.
  


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  An application to a simple system: a two-level system at fixed temperature, will be described in detail.
  


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  Classical statistical mechanics will be introduced, with the simple example of the partition function of a simple classical particle, as well as the equipartition theorem.
  


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  Microscopic models of Phase Transitions, and phenomenological models (Landau theory) will be introduced at the end of the course.
  

The computational part of the module will include:

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  Euler’s method for the solution of ordinary differential equations.
  


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  Applications of this method to: a single first-order differential equation; two coupled first-order differential equations; and a single second-order equation, expressed as a pair of coupled first-order equations.
  


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  The treatment of boundary conditions.
  


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  Elementary discussion of finite difference methods for the solution of partial differential equations: application to the solution of partial differential equations in two spatial dimensions, and in one spatial dimension plus time.
  


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  Introduction to the Monte Carlo numerical calculation technique.
  


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  Introduction to the use of Bayes' theorem.
  

Assessment pattern

Alternative Assessment

None.

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

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  recall of subject knowledge
  


• 
  ability to apply subject knowledge to unseen problems in mathematics and physics
  


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  ability to solve mathematical problems by writing computer programs
  

 

Thus, the summative assessment for this module consists of:

• 
  Two computing coursework assignments: In the first, the computer program (only) is assessed (10% contribution to module mark), while for the second (20% of module mark) a page-limited report plus a program is assessed.
  


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  Bi-weekly questions on Surrey Learn on the material covered in the lectures on Energy & Entropy (These total to a 10% contribution to the module mark)
  


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  A final 2-hour exam (60% contribution to the module mark) with section A consisting of compulsory questions, worth a total of 20 marks, and section B consisting of a choice of 2/3 questions for a total of 40 marks. 
  

 

Formative assessment and feedback

Students receive verbal feedback in tutorials and in the supervised computational classes.  Written feedback is given on the computational assignments, with feedback on each being given before the next is due.

 

Module aims

• introduce thermodynamic and statistical descriptions of entropy in a coherent way
• introduce the basic statistical physics ideas and tools needed to understand and to calculate the properties of matter
• develop computational and problem solving skills.

Learning outcomes

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

• 
  equip students with subject knowledge
  


• 
  develop skills in applying subject knowledge to physical situations and to solve mathematical problems
  


• 
  develop skills in writing computer programs to solve problems in mathematics and physics
  

 

The learning and teaching methods include:

• 33h of lectures and 11h of tutorials


• 22h of supervised computational labs as 2h/week x 11 weeks

 

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Reading list

https://readinglists.surrey.ac.uk
Upon accessing the reading list, please search for the module using the module code: PHY2063

Programmes this module appears in

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2023/4 academic year.