# ENERGY, ENTROPY AND NUMERICAL PHYSICS - 2017/8

Module code: PHY2063

Module provider

Physics

Module Leader

ADAMS JM Dr (Physics)

Number of Credits

15

ECT Credits

15

Framework

FHEQ Level 5

JACs code

F300

Module cap (Maximum number of students)

N/A

Module Availability

Semester 1

Overall student workload

Independent Study Hours: 84

Lecture Hours: 24

Tutorial Hours: 12

Laboratory Hours: 22

Assessment pattern

Assessment type | Unit of assessment | Weighting |
---|---|---|

Examination | END OF SEMESTER 1.5HR EXAMINATION | 70% |

Coursework | COMPUTATIONAL PHYSICS COURSEWORK | 30% |

Alternative Assessment

None.

Prerequisites / Co-requisites

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 by 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 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

Attributes Developed | |
---|---|

Recall both statistical and thermodynamic descriptions of entropy and be able to assess how entropy is related to uncertainty as to the state of the system, the direction of time, and heat flow. | KC |

Compare the statistical and thermodynamic definitions of entropy. | K |

Solve problems by applying the thermodynamic method. | C |

Explain how the state variables (pressure, volume and temperature) and bulk properties (modulus and thermal expansivity) are inter-related. | K |

State Gibb's expression for the entropy and the partition function at constant temperature, | K |

Derive both the Boltzmann weight of a state at constant temperature, and also the weight of a state at constant chemical potential/Fermi level. | KC |

Assess why a statistical approach is required in the study of matter such as gases, liquids and solids. | C |

Explain the role of fluctuations, and estimate their size in a range of contexts. | C |

Calculate the properties of the two-level system | KC |

Explain how fluctuations are related to thermodynamic functions, such as the heat capacities. | C |

Recall both the partition function for a simple classical particle and the equipartition theorem, and judge which one is required for a given system. | K |

Analyse phase transitions such as the ferromagnetic phase transition using statistical physics methonds | KC |

Solve ordinary differential equations numerically using simple finite difference algorithms (in a computer language such as Fortran 95). | CT |

Solve simple partial differential equations by discretising space and solving the differential equation on a grid. In both cases, the student will be able to assess the accuracy of the solutions, judge what accuracy is required and be able to plan simple computational approaches to relevant problems in physics. | CT |

Attributes Developed

**C** - Cognitive/analytical

**K** - Subject knowledge

**T** - Transferable skills

**P** - Professional/Practical skills

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.

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

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.

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.

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

Finally, 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.

The computational part of the module will include:

Euler’s method for the solution of ordinary differential equations, plus how to use the Runge-Kutta method.

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.

The treatment of both one-point and two-point boundary conditions.

Elementary discussion of finite difference methods for the solution of partial differential equations: application to the solution of Laplace 's equation in 2D (Cartesian coordinates), the treatment of Dirichlet (defined values of the function at the boundary) and Neumann (defined derivative at the boundary) type boundary conditions.

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 tutorials as 3h/week x 11 weeks

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

Assessment Strategy

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

recall of subject knowledge

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

ability to solve mathematical problems by writing computer programs

Thus, the summative assessment for this module consists of:

Two computing coursework assignments

a final exam with 2 questions out of three to be answered

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. In addition to two summative computing coursework assignments there is a formative computing coursework assignment, this precedes the two summative assignments.

Reading list

Reading list for ENERGY, ENTROPY AND NUMERICAL PHYSICS : http://aspire.surrey.ac.uk/modules/phy2063

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 2017/8 academic year.