PHYS20352
Statistical Mechanics
10
Semester 2
Undergraduate
Level 2
Judith McGovern
Unit coordinator
Department of Physics & Astronomy
1
FHEQ level (Framework for Higher Education Qualifications) ' Middle part of Bachelors '
European Credit Transfer & Accumulation System Rating : 5.0
<p>Statistical Mechanics</p>
<p>Statistical Mechanics</p>
<p>• To develop the statistical basis of classical thermodynamics</p><div> • To deepen the appreciation of the link between the microscopic properties of individual atoms or other particles and the macroscopic properties of many-body systems formed from them</div><div> </div><div> • To demonstrate the power of statistical methods in different areas of physics</div><div> </div><div> • To use the methods of quantum mechanics and statistical physics to calculate the behaviour of gases of identical particles, and to apply the results to a set of important physical system.</div>
<div>On completion successful students will be able to:</div><div> </div><div>1. Explain the basic concepts of statistical mechanics, including entropy, its statistical interpretation and relation to disorder, and the statistical origin of the second law of thermodynamics;</div><div> </div><div>2. Construct the canonical and grand-canonical partition functions for systems in thermal equilibrium, and use them to obtain thermodynamic quantities of interest.</div><div> </div><div>3. Demonstrate an understanding of the implications of the indistinguishability of particles for systems of non-interacting quantum particles</div><div> </div><div>4. Write down the Bose-Einstein and Fermi-Dirac distribution functions, and apply them to calculate the properties of Bose and Fermi gases, for example in the context of White Dwarf stars and black-body radiation.</div><div> </div><div>5. Explain the physical origin of Bose-Einstein condensation, to characterize it quantitatively, and to explain the experiments confirming Bose-Einstein condensation</div>
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1.The statistical theory of thermodynamics (approximately 5 lectures)</div>
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Basic of probability theory; microstates and macrostates; the concept of ensembles; the statistical interpretation of entropy and temperature; isolated systems and the microcanonical ensemble</div>
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2. Statistical physics of non-isolated systems (approximately 8 lectures)</div>
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Derivation of the Boltzmann distribution and the canonical ensemble; the independent-particle approximation; the partition function and its connection with thermodynamics; examples of non-interacting systems (paramagnet set of harmonic oscillators – quantum and classical , ideal gas, classical and quantum rotors). Equipartition theorem; Density of states. Grand-canonical ensemble and chemical potential.</div>
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3. Quantum gases (approximately 10 lectures)</div>
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Fermi-Dirac and Bose-Einstein distributions. The ideal Fermi gas: Fermi energy. Electronic heat capacity. White Dwarf stars. The ideal Bose gas: Photon gas blackbody radiation (Stefan’s Law and the Planck formula). Bose-Einstein condensation.</div>
<h4 class="ui header" style="border-style:none;box-sizing:inherit;color:rgba(0, 0, 0, 0.87);font-family:"Segoe UI", Lato, "Helvetica Neue", Arial, Helvetica, sans-serif;font-size:1.1rem !important;line-height:1.28571em;margin:-0.142857em 0px 1rem;padding:0px;scrollbar-color:auto;text-transform:none;"><strong>CUIP Teaching Methods</strong></h4><div class="ui grid" style="-webkit-box-align:stretch;-webkit-box-direction:normal;-webkit-box-orient:horizontal;align-items:stretch;box-sizing:inherit;display:flex;flex-flow:wrap;margin:-1rem;padding:0px;scrollbar-color:auto;"><div class="five wide column" style="-webkit-text-stroke-width:0px;background-color:rgb(255, 255, 255);box-sizing:inherit;color:rgba(0, 0, 0, 0.87);display:inline-block;font-family:"Segoe UI", Lato, "Helvetica Neue", Arial, Helvetica, sans-serif;font-size:14px;font-style:normal;font-variant-caps:normal;font-variant-ligatures:normal;font-weight:400;letter-spacing:normal;orphans:2;padding:1rem;position:relative;text-align:start;text-decoration-color:initial;text-decoration-style:initial;text-decoration-thickness:initial;text-indent:0px;text-transform:none;vertical-align:top;white-space:normal;widows:2;width:333.854px;word-spacing:0px;"><figure class="table" style="width:305.854px;"><table class="ui table" style="background-color:rgb(255, 255, 255);border-collapse:separate;border-radius:0.285714rem;border-spacing:0px;border:1px solid rgba(34, 36, 38, 0.15);box-shadow:none;box-sizing:inherit;color:rgba(0, 0, 0, 0.87);font-size:1em;margin:0px;scrollbar-color:auto;text-align:left;vertical-align:middle;" id="teaching_table"><thead class="mobile hidden" style="box-shadow:none;box-sizing:inherit;text-align:inherit;vertical-align:inherit;"><tr style="box-sizing:inherit;"><th style="background-color:rgb(249, 250, 251);border-bottom:1px solid rgba(34, 36, 38, 0.1);border-left-style:none;border-radius:0.285714rem 0px 0px;border-right-color:!important;box-sizing:inherit;color:rgba(0, 0, 0, 0.87);cursor:auto;padding:0.928571em 0.785714em;text-align:inherit;text-transform:none;transition:background 0.1s, color 0.1s;vertical-align:inherit;"><strong>Activity</strong></th><th class="right aligned" style="background-color:rgb(249, 250, 251);border-bottom:1px solid rgba(34, 36, 38, 0.1);border-left-style:none;border-radius:0px 0.285714rem 0px 0px;box-sizing:inherit;color:rgba(0, 0, 0, 0.87);cursor:auto;padding:0.928571em 0.785714em;text-align:right;text-transform:none;transition:background 0.1s, color 0.1s;vertical-align:inherit;"><strong>Hours</strong></th></tr></thead><tbody style="box-sizing:inherit;counter-reset:numdivcounter 0;text-align:inherit;vertical-align:inherit;"><tr style="box-sizing:inherit;"><td style="border-right-color:!important;border-top-style:none;box-sizing:inherit;padding:0.785714em;text-align:inherit;transition:background 0.1s, color 0.1s;">Tutorials</td><td class="right aligned" style="border-top-style:none;box-sizing:inherit;padding:0.785714em;text-align:right;transition:background 0.1s, color 0.1s;">4</td></tr><tr style="box-sizing:inherit;"><td style="border-right-color:!important;border-top:1px solid rgba(34, 36, 38, 0.1);box-sizing:inherit;padding:0.785714em;text-align:inherit;transition:background 0.1s, color 0.1s;">Lectures</td><td class="right aligned" style="border-top:1px solid rgba(34, 36, 38, 0.1);box-sizing:inherit;padding:0.785714em;text-align:right;transition:background 0.1s, color 0.1s;">24</td></tr></tbody></table></figure></div></div><p><br> </p>
0
Other
10%
1
Written exam
90%
<p>* Other 10% Tutorial Work/attendance </p>
<p>Feedback is through weekly tutorials and marked tutorial work.</p>
PHYS20101
Introduction to Quantum Mechanics
Pre-Requisite
Compulsory
PHYS20151
Properties of Matter
Pre-Requisite
Compulsory
N
<p>Mandl, F., <em>Statistical Physics</em>, 2nd edition (Wiley) </p><p>Bowley, R. & Sanchez, M. <em>Introductory Statistical Mechanics</em>, 2nd edition (Oxford)</p><p>Zemansky, M.W. & Dittman, R.H., <em>Heat and Thermodynamics</em>, 7th edition (McGraw Hill)</p><p>Steane, A.M., <em>A complete undergraduate course Thermodynamics</em> (Oxford University Press)</p><p>Blundell, S.J. Blundell, K.M. <em>Concepts in Thermal Physics</em> (Oxford University Press)</p><p> </p>
Assessment written exam
1.5
Lectures
24
Tutorials
4
0
70.5