{"id":354,"date":"2023-09-05T21:50:42","date_gmt":"2023-09-05T21:50:42","guid":{"rendered":"https:\/\/physics.uri.edu\/muller\/?page_id=354"},"modified":"2023-09-05T23:05:47","modified_gmt":"2023-09-05T23:05:47","slug":"phy525n","status":"publish","type":"page","link":"https:\/\/physics.uri.edu\/muller\/phy525n\/","title":{"rendered":"PHY525N"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">Teaching<\/h1>\n\n\n\n<div class=\"sub_nav\"><a title=\"Electricity and Magnetism\" href=\"https:\/\/physics.uri.edu\/muller\/phy331n\/\">PHY331<\/a>|<a title=\"Mathematical Methods of Physics I\" href=\"https:\/\/physics.uri.edu\/muller\/phy510n\/\">PHY510<\/a> |<a title=\"Equilibrium Statistical Physics\" href=\"https:\/\/physics.uri.edu\/muller\/phy525n\/\">PHY525<\/a><\/div>\n\n\n\n<div>&nbsp;<\/div>\n\n\n\n<p><a rel=\"license\" href=\"http:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\"><img decoding=\"async\" style=\"border-width: 0;\" src=\"https:\/\/i.creativecommons.org\/l\/by-nc-sa\/4.0\/88x31.png\" alt=\"Creative Commons License\"><\/a>This work is licensed under a <a rel=\"license\" href=\"http:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License<\/a>.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Equilibrium Thermodynamics I: Introduction&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc1.pdf\">[tsc1]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Thermodynamic system and thermodynamic state<\/li>\n\n\n\n<li>State variables<\/li>\n\n\n\n<li>Equations of state<\/li>\n\n\n\n<li>Thermodynamic equation of state for a classical gas<\/li>\n\n\n\n<li>Encoding thermodynamic information<\/li>\n\n\n\n<li>Thermodynamic contacts<\/li>\n\n\n\n<li>Zeroth law of thermodynamics<\/li>\n\n\n\n<li>First law of thermodynamics<\/li>\n\n\n\n<li>Second law of thermodynamics<\/li>\n\n\n\n<li>Third law of themodynamics<\/li>\n\n\n\n<li>Thermodynamic processes<\/li>\n\n\n\n<li>Differentials<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Exact and inexact differentials I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex5.pdf\">[tex5]<\/a><\/li>\n\n\n\n<li>Fast heat&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex143.pdf\">[tex143]<\/a><\/li>\n\n\n\n<li>Expansion and compression of nitrogen gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex144.pdf\">[tex144]<\/a><\/li>\n\n\n\n<li>Bathtub icebreaker&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex145.pdf\">[tex145]<\/a><\/li>\n\n\n\n<li>Exact and inexact differentials II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex146.pdf\">[tex146]<\/a><\/li>\n\n\n\n<li>Exact and inexact differentials III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex168.pdf\">[tex168]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Thermodynamics overview&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln2.pdf\">[tln2]<\/a><\/li>\n\n\n\n<li>Equations of state for ideal gas and real fluid&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl12.pdf\">[tsl12]<\/a><\/li>\n\n\n\n<li>Physical constants&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl47.pdf\">[tsl47]<\/a><\/li>\n\n\n\n<li>Relevant textbooks&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln90.pdf\">[tln90]<\/a>&nbsp;&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. Equilibrium Thermodynamics II: Engines&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc2.pdf\">[tsc2]<\/a><\/h3>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Carnot engine<\/li>\n\n\n\n<li>Efficiency of Carnot engine<\/li>\n\n\n\n<li>Maximum efficiency of heat engine<\/li>\n\n\n\n<li>Absolute temperature<\/li>\n\n\n\n<li>Entropy<\/li>\n\n\n\n<li>Internal energy<\/li>\n\n\n\n<li>Reversible processes in fluid systems<\/li>\n\n\n\n<li>Gasoline engine (Otto cycle)<\/li>\n\n\n\n<li>Diesel engine<\/li>\n\n\n\n<li>Escher-Wyss gas turbine<\/li>\n\n\n\n<li>Stirling engine<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Entropy change caused by expanding ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex1.pdf\">[tex1]<\/a><\/li>\n\n\n\n<li>Heating the air in a room&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex2.pdf\">[tex2]<\/a><\/li>\n\n\n\n<li>Carnot engine of a classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex3.pdf\">[tex3]<\/a><\/li>\n\n\n\n<li>Carnot engine for an ideal paramagnet&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex4.pdf\">[tex4]<\/a><\/li>\n\n\n\n<li>Adiabates of the classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex7.pdf\">[tex7]<\/a><\/li>\n\n\n\n<li>Idealized Otto cycle&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex8.pdf\">[tex8]<\/a><\/li>\n\n\n\n<li>Work extracted from finite heat reservoir in infinite environment&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex9.pdf\">[tex9]<\/a><\/li>\n\n\n\n<li>Work extracted from finite heat reservoir in finite environment&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex10.pdf\">[tex10]<\/a><\/li>\n\n\n\n<li>Mayer&#8217;s relation for heat capacities of the classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex12.pdf\">[tex12]<\/a><\/li>\n\n\n\n<li>Room heater: electric radiator versus heat pump&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex13.pdf\">[tex13]<\/a><\/li>\n\n\n\n<li>Idealized Diesel cycle&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex16.pdf\">[tex16]<\/a><\/li>\n\n\n\n<li>Roads from 1 to 2: isothermal, isentropic, isochoric, isobaric&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex25.pdf\">[tex25]<\/a><\/li>\n\n\n\n<li>Positive and negative heat capacities&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex26.pdf\">[tex26]<\/a><\/li>\n\n\n\n<li>Ideal-gas engine with two-step cycle I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex106.pdf\">[tex106]<\/a><\/li>\n\n\n\n<li>Ideal-gas engine with two-step cycle II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex107.pdf\">[tex107]<\/a><\/li>\n\n\n\n<li>Joule cycle&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex108.pdf\">[tex108]<\/a><\/li>\n\n\n\n<li>Idealized Stirling cycle&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex131.pdf\">[tex131]<\/a><\/li>\n\n\n\n<li>Absolute temperature from measurements&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex134.pdf\">[tex134]&nbsp;<\/a><\/li>\n\n\n\n<li>Circular heat engine I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex147.pdf\">[tex147]<\/a><\/li>\n\n\n\n<li>Circular heat engine II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex148.pdf\">[tex148]<\/a><\/li>\n\n\n\n<li>Square heat engine&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex149.pdf\">[tex149]<\/a><\/li>\n\n\n\n<li>Work performance and heat transfer&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex155.pdf\">[tex155]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. Equilibrium Thermodynamics III: Free Energies&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc3.pdf\">[tsc3]<\/a>&nbsp;<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fundamental equation of thermodynamics<\/li>\n\n\n\n<li>Analogy with mechanical equilibrium<\/li>\n\n\n\n<li>Free energy in a mechanical system<\/li>\n\n\n\n<li>Free energy in a thermodynamic system<\/li>\n\n\n\n<li>Thermodynamic potentials for a fluid system<\/li>\n\n\n\n<li>Differentials of thermodynamic potentials<\/li>\n\n\n\n<li>Facts about thermodynamic potentials<\/li>\n\n\n\n<li>Thermodynamic functions for fluid system<\/li>\n\n\n\n<li>Substitutions for magnetic system<\/li>\n\n\n\n<li>Maxwell&#8217;s relations<\/li>\n\n\n\n<li>Free energy stored and retrieved<\/li>\n\n\n\n<li>Response functions<\/li>\n\n\n\n<li>Thermal response functions<\/li>\n\n\n\n<li>Mechanical response functions<\/li>\n\n\n\n<li>Magnetic response functions<\/li>\n\n\n\n<li>Isothermal and adiabatic processes<\/li>\n\n\n\n<li>Conditions for thermal equilibrium<\/li>\n\n\n\n<li>Stability of thermal equilibrium<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Retrievable and irretrievable energy put in heat reservoir&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex6.pdf\">[tex6]<\/a>&nbsp;<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Legendre transform&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln77.pdf\">[tln77]<\/a>&nbsp;<\/li>\n\n\n\n<li>Alternative set of thermodynamic potentials&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln9.pdf\">[tln9]<\/a><\/li>\n\n\n\n<li>Useful relations between partial derivatives&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln6.pdf\">[tln6]<\/a><\/li>\n\n\n\n<li>Jacobi transformations&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln21.pdf\">[tln21]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4. Equilibrium Thermodynamics IV: Applications&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc4.pdf\">[tsc4]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Classical ideal gas<\/li>\n\n\n\n<li>Van der Waals gas<\/li>\n\n\n\n<li>Cooling a gas by free expansion (Joule effect)<\/li>\n\n\n\n<li>Cooling a gas by throttling (Joule-Thomson effect)<\/li>\n\n\n\n<li>Entropy of mixing in classical ideal gas<\/li>\n\n\n\n<li>Ideal paramagnet<\/li>\n\n\n\n<li>Adiabatic demagnetization<\/li>\n\n\n\n<li>Ideal paramagnetic gas<\/li>\n\n\n\n<li>Photon gas<\/li>\n\n\n\n<li>Rubber band elasticity<\/li>\n\n\n\n<li>Inhomogeneous systems<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>How not to modify the ideal gas equation of state&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex11.pdf\">[tex11]<\/a><\/li>\n\n\n\n<li>Entropy and internal energy of the classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex14.pdf\">[tex14]<\/a><\/li>\n\n\n\n<li>Thermodynamic potentials of the classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex15.pdf\">[tex15]<\/a><\/li>\n\n\n\n<li>Chemical potential of the classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex17.pdf\">[tex17]<\/a><\/li>\n\n\n\n<li>Sound velocity in the classical ideal gas I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex18.pdf\">[tex18]<\/a><\/li>\n\n\n\n<li>Thermodynamics of an ideal paramagnet I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex19.pdf\">[tex19]<\/a><\/li>\n\n\n\n<li>Thermodynamics of an ideal paramagnet II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex20.pdf\">[tex20]<\/a><\/li>\n\n\n\n<li>Thermodynamics of an ideal paramagnet III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex21.pdf\">[tex21]<\/a><\/li>\n\n\n\n<li>Thermodynamics of a classical ideal paramagnetic gas I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex22.pdf\">[tex22]<\/a><\/li>\n\n\n\n<li>Thermodynamics of black-body radiation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex23.pdf\">[tex23]<\/a><\/li>\n\n\n\n<li>Carnot cycle of thermal radiation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex24.pdf\">[tex24]<\/a><\/li>\n\n\n\n<li>Heat capacities of the van der Waals gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex27.pdf\">[tex27]<\/a><\/li>\n\n\n\n<li>Determining C<sub>V<\/sub>&nbsp;of condensed matter&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex28.pdf\">[tex28]<\/a><\/li>\n\n\n\n<li>Assembling thermodyamic information&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex29.pdf\">[tex29]<\/a><\/li>\n\n\n\n<li>Joule coefficient of van der Waals gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex31.pdf\">[tex31]<\/a><\/li>\n\n\n\n<li>Joule-Thomson coefficient of van der Waals gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex32.pdf\">[tex32]<\/a><\/li>\n\n\n\n<li>Effects of first virial correction on ideal gas properties&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex33.pdf\">[tex33]<\/a><\/li>\n\n\n\n<li>Ideal gas heat capacity by design&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex35.pdf\">[tex35]<\/a><\/li>\n\n\n\n<li>Thermodynamics of a real paramagnet&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex36.pdf\">[tex36]<\/a><\/li>\n\n\n\n<li>Internal energy and entropy of van der Waals gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex38.pdf\">[tex38]<\/a><\/li>\n\n\n\n<li>Rubber band heat engine&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex39.pdf\">[tex39]<\/a><\/li>\n\n\n\n<li>Equation of state and adiabate of an elastic band&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex40.pdf\">[tex40]<\/a><\/li>\n\n\n\n<li>Reconstructing the equation of state of a fluid system&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex42.pdf\">[tex42]<\/a><\/li>\n\n\n\n<li>Reconstructing the equation of state of a gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex43.pdf\">[tex43]<\/a><\/li>\n\n\n\n<li>Sound velocity in the classical ideal gas II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex99.pdf\">[tex99]<\/a><\/li>\n\n\n\n<li>Hydrostatic pressure&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex132.pdf\">[tex132]<\/a><\/li>\n\n\n\n<li>Thermodynamics of a classical ideal paramagnetic gas II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex133.pdf\">[tex133]<\/a><\/li>\n\n\n\n<li>Polytropic process of classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex138.pdf\">[tex138]<\/a><\/li>\n\n\n\n<li>Heavy piston I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex141.pdf\">[tex141]<\/a><\/li>\n\n\n\n<li>Isothermal atmosphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex150.pdf\">[tex150]<\/a><\/li>\n\n\n\n<li>Adiabatic atmosphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex151.pdf\">[tex151]<\/a><\/li>\n\n\n\n<li>Homogeneous atmosphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex152.pdf\">[tex152]<\/a><\/li>\n\n\n\n<li>Heavy piston II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex170.pdf\">[tex170]<\/a>&nbsp;<\/li>\n\n\n\n<li>Effect of mixing on chemical potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex173.pdf\">[tex173]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Joule-Thomson inversion curves&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl1.pdf\">[tsl1]<\/a><\/li>\n\n\n\n<li>Osmotic pressure&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln26.pdf\">[tln26]<\/a><\/li>\n\n\n\n<li>Entropy landscape of paramagnetic salt&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl2.pdf\">[tsl2]<\/a><\/li>\n\n\n\n<li>Mechanocaloric and thermomechanical effects&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln34.pdf\">[tln34]<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">5. Thermodynamics of Phase Transitions I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc5.pdf\">[tsc5]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Typical solid-liquid-gas phase diagram<\/li>\n\n\n\n<li>Additional and alternative phases<\/li>\n\n\n\n<li>Classification of phase transitions<\/li>\n\n\n\n<li>Discontinuous transition<\/li>\n\n\n\n<li>Continuous transition<\/li>\n\n\n\n<li>Order parameter<\/li>\n\n\n\n<li>Phase coexistence: Gibbs&#8217; phase rule<\/li>\n\n\n\n<li>Clausius-Clapeyron equation<\/li>\n\n\n\n<li>Effects of a uniform gravitational field<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Entropy of supercooled liquid&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex30.pdf\">[tex30]<\/a><\/li>\n\n\n\n<li>Coexistence line of continuous phase transition&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex37.pdf\">[tex37]<\/a><\/li>\n\n\n\n<li>Heat capacity of vapor in equilibrium with liquid phase&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex41.pdf\">[tex41]<\/a><\/li>\n\n\n\n<li>Melting or freezing?&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex51.pdf\">[tex51]<\/a><\/li>\n\n\n\n<li>Triple-point phase changes I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex52.pdf\">[tex52]<\/a><\/li>\n\n\n\n<li>Abnormal phase behavior&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex54.pdf\">[tex54]<\/a><\/li>\n\n\n\n<li>Phase coexistence of ammonia&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex55.pdf\">[tex55]<\/a><\/li>\n\n\n\n<li>Discontinuous transition: change in internal energy&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex123.pdf\">[tex123]<\/a><\/li>\n\n\n\n<li>Latent heat and response functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex124.pdf\">[tex124]<\/a><\/li>\n\n\n\n<li>Dry ice&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex125.pdf\">[tex125]<\/a><\/li>\n\n\n\n<li>Cooling down? Heating up?&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex153.pdf\">[tex153]<\/a><\/li>\n\n\n\n<li>Triple-point phase changes II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex156.pdf\">[tex156]<\/a><\/li>\n\n\n\n<li>Effects of heat input&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex159.pdf\">[tex159]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Phase diagram of H<sub>2<\/sub>O&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl4.pdf\">[tsl4]<\/a><\/li>\n\n\n\n<li>Liquid crystal phases&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl51.pdf\">[tsl51]<\/a><\/li>\n\n\n\n<li>Ferrimagnetic phases&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl49.pdf\">[tsl49]<\/a><\/li>\n\n\n\n<li>Ordering of surfactant molecules&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl50.pdf\">[tsl50]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">6. Thermodynamics of Phase Transitions II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc6.pdf\">[tsc6]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Law of corresponding states (using van der Waals equation of state)<\/li>\n\n\n\n<li>Maxwell construction (using Gibbs potential or Helmholtz potential)<\/li>\n\n\n\n<li>Nucleation of droplets or bubbles (coexistence line, spinodal line)<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Dieterici equation of state&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex34.pdf\">[tex34]<\/a><\/li>\n\n\n\n<li>Latent heat and heat capacies at superconducting transition&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex44.pdf\">[tex44]<\/a><\/li>\n\n\n\n<li>Mean-field ferromagnet I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex45.pdf\">[tex45]<\/a><\/li>\n\n\n\n<li>Mean-field ferromagnet II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex46.pdf\">[tex46]<\/a><\/li>\n\n\n\n<li>Structural transition of iron&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex53.pdf\">[tex53]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Helium liquids and superfluidity&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln33.pdf\">[tln33]<\/a><\/li>\n\n\n\n<li>Superconducting transition&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln35.pdf\">[tln35]<\/a><\/li>\n\n\n\n<li>Thermodynamics of a ferromagnet&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl5.pdf\">[tsl5]<\/a><\/li>\n\n\n\n<li>Mean-field ferromagnet&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln84.pdf\">[tln84]<\/a>&nbsp;&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">7. Kinetic Theory I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc7.pdf\">[tsc7]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Statistical concept of uncertainty<\/li>\n\n\n\n<li>Statistical concept of information<\/li>\n\n\n\n<li>Statistical uncertainty and entropy<\/li>\n\n\n\n<li>Kinetics of classical ideal gas<\/li>\n\n\n\n<li>Maxwell velocity distribution<\/li>\n\n\n\n<li>Boltzmann equation<\/li>\n\n\n\n<li>H-function<\/li>\n\n\n\n<li>H-theorem<\/li>\n\n\n\n<li>H-theorem and irreversibility<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Statistical uncertainty: verification of criteria&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex47.pdf\">[tex47]<\/a><\/li>\n\n\n\n<li>Information regarding a census of birds&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex48.pdf\">[tex48]<\/a><\/li>\n\n\n\n<li>Information of sequenced messages&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex61.pdf\">[tex61]<\/a><\/li>\n\n\n\n<li>Pressure and mean-square velocity in classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex49.pdf\">[tex49]<\/a><\/li>\n\n\n\n<li>Maxwell velocity distribution (Maxwell&#8217;s derivation)&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex50.pdf\">[tex50]<\/a><\/li>\n\n\n\n<li>Maxwell distribution in D dimensions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex56.pdf\">[tex56]<\/a><\/li>\n\n\n\n<li>Energy distribution for N ideal gas atoms&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex57.pdf\">[tex57]<\/a><\/li>\n\n\n\n<li>Maxwell velocity distribution (Boltzmann&#8217;s derivation)&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex58.pdf\">[tex58]<\/a><\/li>\n\n\n\n<li>Ideal-gas entropy and Boltzmann&#8217;s H-function&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex59.pdf\">[tex59]<\/a><\/li>\n\n\n\n<li>Maxwell distribution from variational principle&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex60.pdf\">[tex60]<\/a><\/li>\n\n\n\n<li>Doppler broadening of atomic spectral lines&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex63.pdf\">[tex63]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">8. Kinetic Theory II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc9.pdf\">[tsc9]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Gas container with tiny hole<\/li>\n\n\n\n<li>Leakage from container with heat conducting walls<\/li>\n\n\n\n<li>Leakage from container with insulating walls<\/li>\n\n\n\n<li>Particle flow and energy flow between containers<\/li>\n\n\n\n<li>Kinematic pressure and interaction pressure<\/li>\n\n\n\n<li>Kinetic forces and mobility<\/li>\n\n\n\n<li>Collision rate and mean free path<\/li>\n<\/ul>\n\n\n\n<p>Exercises<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ideal gas atoms escaping from a container I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex62.pdf\">[tex62]<\/a><\/li>\n\n\n\n<li>Isotope separation via diffusion&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex65.pdf\">[tex65]<\/a><\/li>\n\n\n\n<li>Ideal gas atoms escaping from a container II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex176.pdf\">[tex176]<\/a><\/li>\n\n\n\n<li>Ideal gas atoms escaping from a container III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex177.pdf\">[tex177]<\/a><\/li>\n\n\n\n<li>Toward thermal equilibrium via particle transfer&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex64.pdf\">[tex64]<\/a><\/li>\n\n\n\n<li>Interaction pressure produced by Gaussian interparticle potential&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex66.pdf\">[tex66]<\/a><\/li>\n\n\n\n<li>Average force of particle beam on heavy hard sphere&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex68.pdf\">[tex68]<\/a><\/li>\n\n\n\n<li>Mobility of a hard sphere in a dilute gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex69.pdf\">[tex69]<\/a><\/li>\n\n\n\n<li>Collision rate in a classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex70.pdf\">[tex70]<\/a><\/li>\n\n\n\n<li>Mean free path of particle in classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex71.pdf\">[tex71]<\/a><\/li>\n\n\n\n<li>Rate of chemical reaction in gas phase&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex67.pdf\">[tex67]<\/a><\/li>\n\n\n\n<li>Effect of escaping particles on temperature of 1D ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex72.pdf\">[tex72]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">9. Microcanonical Ensemble&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc10.pdf\">[tsc10]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Classical Hamiltonian systems<\/li>\n\n\n\n<li>Points and trajectories in phase space<\/li>\n\n\n\n<li>Probability density in phase space<\/li>\n\n\n\n<li>Probability flow in phase space<\/li>\n\n\n\n<li>Classical Liouville operator<\/li>\n\n\n\n<li>Stationarity condition for phase-space probability density<\/li>\n\n\n\n<li>Density operator<\/li>\n\n\n\n<li>Quantum time evolution<\/li>\n\n\n\n<li>Stationarity condition for density operator<\/li>\n\n\n\n<li>Gibbs entropy<\/li>\n\n\n\n<li>Phase-space volume allocated per quantum state<\/li>\n\n\n\n<li>Microcanonical ensemble<\/li>\n\n\n\n<li>Aspects of significance<\/li>\n\n\n\n<li>Simple applictions<\/li>\n\n\n\n<li>Entropy of mixing revisited<\/li>\n\n\n\n<li>Negative temperatures<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex73.pdf\">[tex73]<\/a><\/li>\n\n\n\n<li>Array of classical harmonic oscillators&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex74.pdf\">[tex74]<\/a><\/li>\n\n\n\n<li>Array of quantum harmonic oscillators I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex75.pdf\">[tex75]<\/a><\/li>\n\n\n\n<li>Array of quantum harmonic oscillators II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex126.pdf\">[tex126]<\/a><\/li>\n\n\n\n<li>Quantum paramagnet&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex127.pdf\">[tex127]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">10. Canonical Ensemble I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc11.pdf\">[tsc11]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Extremum principle<\/li>\n\n\n\n<li>Canonical partition function<\/li>\n\n\n\n<li>Systems of noninteracting particles<\/li>\n\n\n\n<li>From phase-space density to Maxwell velocity distribution<\/li>\n\n\n\n<li>Ensemble averages<\/li>\n\n\n\n<li>Energy fluctuations and heat capacity<\/li>\n\n\n\n<li>Classical ideal gas (relativistic)<\/li>\n\n\n\n<li>Inhomogeneous systems<\/li>\n\n\n\n<li>Partition function and density of states<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Nonrelativistic ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex76.pdf\">[tex76]<\/a><\/li>\n\n\n\n<li>Ultrarelativistic ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex77.pdf\">[tex77]<\/a><\/li>\n\n\n\n<li>Ultrarelativistic ideal gas in two dimensions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex154.pdf\">[tex154]<\/a><\/li>\n\n\n\n<li>Relativistic ideal gas I: canonical partition function&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex91.pdf\">[tex91]<\/a><\/li>\n\n\n\n<li>Relativistic ideal gas II: entropy and internal energy&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex92.pdf\">[tex92]<\/a><\/li>\n\n\n\n<li>Relativistic ideal gas III: heat capacity&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex93.pdf\">[tex93]<\/a><\/li>\n\n\n\n<li>Classical ideal gas in uniform gravitational field&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex79.pdf\">[tex79]<\/a><\/li>\n\n\n\n<li>Gas pressure and density inside centrifuge&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex135.pdf\">[tex135]<\/a><\/li>\n\n\n\n<li>Irreversible decompression&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex136.pdf\">[tex136]<\/a><\/li>\n\n\n\n<li>Irreversible heat exchange&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex137.pdf\">[tex137]<\/a><\/li>\n\n\n\n<li>Reversible decompression&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex139.pdf\">[tex139]<\/a><\/li>\n\n\n\n<li>Reversible heat exchange&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex140.pdf\">[tex140]<\/a><\/li>\n\n\n\n<li>Heavy piston I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex141.pdf\">[tex141]<\/a><\/li>\n\n\n\n<li>Ideal gas partition function and density of states&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex81.pdf\">[tex81]<\/a><\/li>\n\n\n\n<li>Relative momentum of two ideal-gas particles&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex80.pdf\">[tex80]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">11. Canonical Ensemble II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc12.pdf\">[tsc12]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Vibrational heat capacities of solids<\/li>\n\n\n\n<li>Theory of Dulong and Petit<\/li>\n\n\n\n<li>Theory of Einstein<\/li>\n\n\n\n<li>Atoms interacting via harmonic forces<\/li>\n\n\n\n<li>Theory of Debye<\/li>\n\n\n\n<li>Paramagnetism of localized magnetic dipoles<\/li>\n\n\n\n<li>Langevin paramagnetism<\/li>\n\n\n\n<li>Two-level system<\/li>\n\n\n\n<li>Brillouin paramagnetism<\/li>\n\n\n\n<li>Fluctuations in a magnetic system<\/li>\n\n\n\n<li>Gases with internal degrees of freedom<\/li>\n\n\n\n<li>Translational motion (classical)<\/li>\n\n\n\n<li>Rotational motion (classical)<\/li>\n\n\n\n<li>Rotational motion (quantum)<\/li>\n\n\n\n<li>Vibrational motion (quantum)<\/li>\n\n\n\n<li>Fine structure<\/li>\n\n\n\n<li>Orthohydrogen and parahydrogen<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Array of classical harmonic oscillators&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex78.pdf\">[tex78]<\/a><\/li>\n\n\n\n<li>Array of quantum harmonic oscillators&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex82.pdf\">[tex82]<\/a><\/li>\n\n\n\n<li>Vibrational heat capacity of a solid&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex83.pdf\">[tex83]<\/a><\/li>\n\n\n\n<li>Anharmonic oscillator and thermodynamic perturbation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex104.pdf\">[tex104]<\/a><\/li>\n\n\n\n<li>Classical paramagnet&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex84.pdf\">[tex84]<\/a><\/li>\n\n\n\n<li>Quantum paramagnet (two-level system)&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex85.pdf\">[tex85]<\/a><\/li>\n\n\n\n<li>Quantum paramagnet (three-level system)&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex157.pdf\">[tex157]<\/a><\/li>\n\n\n\n<li>Quantum paramagnet (Brillouin function)&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex86.pdf\">[tex86]<\/a><\/li>\n\n\n\n<li>Ising trimer&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex142.pdf\">[tex142]<\/a><\/li>\n\n\n\n<li>Fluctuation in a magnetic system&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex109.pdf\">[tex109]<\/a><\/li>\n\n\n\n<li>Classical rotational entropies of HCl and N<sub>2<\/sub>&nbsp;gases&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex88.pdf\">[tex88]<\/a><\/li>\n\n\n\n<li>Classical rotational free energies of NH<sub>3<\/sub>&nbsp;gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex87.pdf\">[tex87]<\/a><\/li>\n\n\n\n<li>Quantum rotational heat capacity of a gas at low temperature&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex89.pdf\">[tex89]<\/a><\/li>\n\n\n\n<li>Quantum rotational heat capacity of a gas at high temperature&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex90.pdf\">[tex90]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Vibrational heat capacities of solids&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl29.pdf\">[tsl29]<\/a><\/li>\n\n\n\n<li>Paramagnetic salts&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl30.pdf\">[tsl30]<\/a><\/li>\n\n\n\n<li>Thermodynamic perturbation expansion&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln80.pdf\">[tln80]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">12. Grandcanonical Ensemble&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc13.pdf\">[tsc13]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Extremum principle<\/li>\n\n\n\n<li>Grandcanonical partition function<\/li>\n\n\n\n<li>Density fluctuations and compressibility<\/li>\n\n\n\n<li>Gentle introduction to quantum statistics<\/li>\n\n\n\n<li>Permutation symmetry<\/li>\n\n\n\n<li>Occupation number representation<\/li>\n\n\n\n<li>Canonical partition function (for quantum gases)<\/li>\n\n\n\n<li>Grandcanonical partition function (for quantum gases)<\/li>\n\n\n\n<li>Grand potential<\/li>\n\n\n\n<li>Average number of particles and state occupancies<\/li>\n\n\n\n<li>Entropy and state occupancies<\/li>\n\n\n\n<li>Internal energy and state occupancies<\/li>\n\n\n\n<li>Fluctuations of state occupanices<\/li>\n\n\n\n<li>Density of states<\/li>\n\n\n\n<li>Occupancy of 1-particle states<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Classical ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex94.pdf\">[tex94]<\/a><\/li>\n\n\n\n<li>Ultrarelativistic ideal gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex169.pdf\">[tex169]<\/a><\/li>\n\n\n\n<li>Density fluctuations&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex95.pdf\">[tex95]<\/a><\/li>\n\n\n\n<li>Density fluctuations and compressibility&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex96.pdf\">[tex96]<\/a><\/li>\n\n\n\n<li>Energy fluctuations and thermal response functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex103.pdf\">[tex103]<\/a><\/li>\n\n\n\n<li>Occupation number fluctuations&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex110.pdf\">[tex110]<\/a><\/li>\n\n\n\n<li>Density of 1-particle states&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex111.pdf\">[tex111]<\/a><\/li>\n\n\n\n<li>Maxwell-Boltzmann gas in&nbsp;<em>D<\/em>&nbsp;dimensions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex112.pdf\">[tex112]<\/a><\/li>\n\n\n\n<li>Some fantasy gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex171.pdf\">[tex171]<\/a><\/li>\n\n\n\n<li>Ideal lattice gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex172.pdf\">[tex172]<\/a><\/li>\n\n\n\n<li>Entropy and internal energy from state occupancies&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex178.pdf\">[tex178]<\/a>&nbsp;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">13. Ideal Quantum Gases I: Bosons&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc14.pdf\">[tsc14]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Equation of state<\/li>\n\n\n\n<li>Reference values<\/li>\n\n\n\n<li>Isochores<\/li>\n\n\n\n<li>Coexistence of gas and condensate<\/li>\n\n\n\n<li>Isotherms<\/li>\n\n\n\n<li>Isobars<\/li>\n\n\n\n<li>Phase diagrams<\/li>\n\n\n\n<li>Entropy<\/li>\n\n\n\n<li>Internal energy<\/li>\n\n\n\n<li>Heat capacity<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fundamental relations&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex113.pdf\">[tex113]<\/a><\/li>\n\n\n\n<li>Isochores&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex114.pdf\">[tex114]<\/a><\/li>\n\n\n\n<li>Isotherms and isobars&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex115.pdf\">[tex115]<\/a><\/li>\n\n\n\n<li>Entropy and internal energy&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex179.pdf\">[tex179]<\/a><\/li>\n\n\n\n<li>Heat capacity at high temperature&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex97.pdf\">[tex97]<\/a><\/li>\n\n\n\n<li>Heat capacity at low temperature&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex116.pdf\">[tex116]<\/a><\/li>\n\n\n\n<li>Isothermal compressibility&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex128.pdf\">[tex128]<\/a><\/li>\n\n\n\n<li>Isobaric expansivity&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex129.pdf\">[tex129]<\/a><\/li>\n\n\n\n<li>Speed of sound&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex130.pdf\">[tex130]<\/a><\/li>\n\n\n\n<li>Ultrarelativistic Bose-Einstein gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex98.pdf\">[tex98]<\/a><\/li>\n\n\n\n<li>Statistical mechanics of blackbody radiation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex105.pdf\">[tex105]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bose-Einstein functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl36.pdf\">[tsl36]<\/a><\/li>\n\n\n\n<li>Blackbody radiation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln68.pdf\">[tln68]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">14. Ideal Quantum Gases II: Fermions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc15.pdf\">[tsc15]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Equation of state<\/li>\n\n\n\n<li>Chemical potential<\/li>\n\n\n\n<li>Level occupancies<\/li>\n\n\n\n<li>Isochores<\/li>\n\n\n\n<li>Phase transition<\/li>\n\n\n\n<li>Isotherms<\/li>\n\n\n\n<li>Entropy<\/li>\n\n\n\n<li>Internal energy<\/li>\n\n\n\n<li>Heat capacity<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Chemical potential I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex117.pdf\">[tex117]<\/a><\/li>\n\n\n\n<li>Chemical potential II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex118.pdf\">[tex118]<\/a><\/li>\n\n\n\n<li>Statistical interaction pressure&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex119.pdf\">[tex119]<\/a><\/li>\n\n\n\n<li>Isotherm and adiabate&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex120.pdf\">[tex120]<\/a><\/li>\n\n\n\n<li>Ground-state energy&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex102.pdf\">[tex102]<\/a><\/li>\n\n\n\n<li>Heat capacity at high temperature&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex100.pdf\">[tex100]<\/a><\/li>\n\n\n\n<li>Heat capacity at low temperature&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex101.pdf\">[tex101]<\/a><\/li>\n\n\n\n<li>Stable white dwarf star&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex121.pdf\">[tex121]<\/a><\/li>\n\n\n\n<li>Unstable white dwarf star&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex122.pdf\">[tex122]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fermi-Dirac functions&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsl42.pdf\">[tsl42]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">15. Nearly Free Electrons&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc16.pdf\">[tsc16]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Thermionic emission (Richardson effect)<\/li>\n\n\n\n<li>Schottky effect<\/li>\n\n\n\n<li>Photoelectric emission (Hallwachs effect)<\/li>\n\n\n\n<li>Pauli paramagnetism (PPM)<\/li>\n\n\n\n<li>PPM analyzed in canonical ensemble<\/li>\n\n\n\n<li>PPM thermodynamic potentials and functions<\/li>\n\n\n\n<li>PPM response functions<\/li>\n\n\n\n<li>PPM magnetization curves (numerical analysis)<\/li>\n\n\n\n<li>PPM magnetization curves at T = 0 (exact results)<\/li>\n\n\n\n<li>PPM magnetization curves in D = 2 (exact analysis)<\/li>\n\n\n\n<li>PPM isothermal susceptibility at H = 0<\/li>\n\n\n\n<li>PPM correction to Langevin-Brillouin result at high T<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Paramagnetic FD gas I: pressure and entropy&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex161.pdf\">[tex161]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas II: internal energy&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex162.pdf\">[tex162]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas III: heat capacity C<sub>VM<\/sub>&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex163.pdf\">[tex163]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas IV: heat capacity C<sub>VH<\/sub>&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex164.pdf\">[tex164]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas V: isothermal susceptibility&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex165.pdf\">[tex165]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas VI: isothermal compressibilities&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex166.pdf\">[tex166]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas VII: isobaric expansivity&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex167.pdf\">[tex167]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas VIII: magnetization curves at T &gt; 0&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex180.pdf\">[tex180]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas IX: magnetization curves at T = 0&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex181.pdf\">[tex181]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas X: exact magnetization curve for D = 2&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex182.pdf\">[tex182]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas XI: isothermal susceptibility at H = 0&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex183.pdf\">[tex183]<\/a><\/li>\n\n\n\n<li>Paramagnetic FD gas XII: Langevin-Brillouin limit at high T&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex184.pdf\">[tex184]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">16. Thermodynamics of Phase Transitions III&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc8.pdf\">[tsc8]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ginzburg-Landau theory for secon-order phase transition<\/li>\n\n\n\n<li>Ginzburg-Landau theory for first-order phase transition<\/li>\n\n\n\n<li>Ornstein-Zernike theory for correlations<\/li>\n\n\n\n<li>Critical-point exponents<\/li>\n\n\n\n<li>Critical singularities of magnetic system<\/li>\n\n\n\n<li>Critical singularities of fluid system<\/li>\n\n\n\n<li>Inequalities of critical-point exponents<\/li>\n\n\n\n<li>Test of scaling laws<\/li>\n\n\n\n<li>Marginal dimensionality<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Order parameter of first-order Ginzburg-Landau transition&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex174.pdf\">[tex174]<\/a><\/li>\n\n\n\n<li>Critical singularities of van der Waals gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex175.pdf\">[tex175]<\/a><\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">&nbsp;17. Interacting Degrees of Freedom [tsc17]<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Nearly ideal classical gas<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">18. Ising model I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc18.pdf\">[tsc18]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ising magnet<\/li>\n\n\n\n<li>Ising lattice gas<\/li>\n\n\n\n<li>Mapping between magnet and lattice gas<\/li>\n\n\n\n<li>Transfer matrix solution of 1D Ising magnet<\/li>\n\n\n\n<li>Expectation values via transfer matrix<\/li>\n\n\n\n<li>Correlation functions via transfer matrix<\/li>\n\n\n\n<li>Ising lattice gas in D=1<\/li>\n\n\n\n<li>Ideal lattice gas limit<\/li>\n\n\n\n<li>Ising lattice gas equation of state in D=1<\/li>\n\n\n\n<li>Ising lattice gas entropy in D=1<\/li>\n\n\n\n<li>Ising lattice gas internal energy in D=1<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ideal lattice gas&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex172.pdf\">[tex172]<\/a><\/li>\n\n\n\n<li>Ising chain: transfer matrix solution I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex185.pdf\">[tex185]<\/a><\/li>\n\n\n\n<li>Ising chain: transfer matrix solution II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex189.pdf\">[tex189]<\/a><\/li>\n\n\n\n<li>Ising lattice gas in D=1: equation of state&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex194.pdf\">[tex194]<\/a><\/li>\n\n\n\n<li>Ising lattice gas in D=1: entropy I&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex195.pdf\">[tex195]<\/a><\/li>\n\n\n\n<li>Ising lattice gas in D=1: entropy II&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex201.pdf\">[tex201]<\/a><\/li>\n\n\n\n<li>Ising model in Bethe approximation&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex203.pdf\">[tex203]<\/a>&nbsp;<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Additional materials:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ising model and descendents&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln93.pdf\">[tln93]<\/a><\/li>\n\n\n\n<li>Exchange interaction&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln94.pdf\">[tln94]<\/a><\/li>\n\n\n\n<li>Metallic alloys&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln95.pdf\">[tln95]<\/a><\/li>\n\n\n\n<li>T=0 phase diagrams of Ising chains&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln96.pdf\">[tln96]<\/a><\/li>\n\n\n\n<li>Approximating the Ising model&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln97.pdf\">[tln97]<\/a>&nbsp;<\/li>\n\n\n\n<li>Equivalent-neighbor Ising model&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln98.pdf\">[tln98]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">19. Coordinate Bethe Ansatz [tsc19]<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>NLS model<\/li>\n\n\n\n<li>Free bosons<\/li>\n\n\n\n<li>Impenetrable bosons and free fermions<\/li>\n\n\n\n<li>Two bosons with finite contact repulsion<\/li>\n\n\n\n<li>Three bosons subject to finite two-body contact repulsion<\/li>\n\n\n\n<li>General Bethe ansatz equations of the NLS model<\/li>\n\n\n\n<li>Trigonometric Bethe ansatz equations<\/li>\n\n\n\n<li>Iterative solutions<\/li>\n\n\n\n<li>Particles and holes<\/li>\n\n\n\n<li>Densities of particle momenta and hole momenta<\/li>\n\n\n\n<li>Ground state of the NLS model from Lieb-Liniger equation<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Wave function of impenetrable bosons for&nbsp;<em>N<\/em>=2 and&nbsp;<em>N<\/em>=3 [tex190]<\/li>\n\n\n\n<li>Two-boson Bethe wave functions [tex191]<\/li>\n\n\n\n<li>Three-boson Bethe ansatz equations [tex192]<\/li>\n\n\n\n<li>Trigonometric Bethe ansatz equations for the NLS model [tex193]<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">20. Statistical Interactions I: Combinatorics&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tsc20.pdf\">[tsc20]<\/a><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Fermions<\/li>\n\n\n\n<li>BosonsC<\/li>\n\n\n\n<li>Size L and XL particles<\/li>\n\n\n\n<li>Semions<\/li>\n\n\n\n<li>Particles with internal degrees of freedom<\/li>\n\n\n\n<li>Distinguishable species of particles in shared orbitals<\/li>\n\n\n\n<li>Hosts and caps<\/li>\n\n\n\n<li>Hosts, hybrids, and caps<\/li>\n\n\n\n<li>Hosts, hybrids, and tags<\/li>\n\n\n\n<li>Configurational entropy<\/li>\n\n\n\n<li>Examples with one species<\/li>\n\n\n\n<li>Example with two species<\/li>\n\n\n\n<li>Semions versus hosts and caps<\/li>\n<\/ul>\n\n\n\n<p>Exercises:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Configurational entropy of statistically interacting particles&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex186.pdf\">[tex186]<\/a><\/li>\n\n\n\n<li>Hosts and tags at level 1&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex187.pdf\">[tex187]<\/a><\/li>\n\n\n\n<li>Hosts and tags at level 2&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/wtex188.pdf\">[tex188]<\/a><\/li>\n<\/ul>\n\n\n\n<p>Additional materials<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Particles at two levels&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln91.pdf\">[tln91]<\/a><\/li>\n\n\n\n<li>Merging particle species&nbsp;<a href=\"https:\/\/penrose.uri.edu\/Gerhard\/PHY525N\/tln92.pdf\">[tln92]<\/a><\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">&nbsp;21. Statistical Interactions II: Partition Functions [tsc21]<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Conversion of dynamical interactions into statistical interactions<\/li>\n\n\n\n<li>Partition function, average occupancies, and entropy<\/li>\n\n\n\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">22. Ergodic Theory [tsc22]<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#8230;<\/li>\n<\/ul>\n\n\n\n<p><small>Last updated 08\/07\/22<\/small><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Teaching PHY331|PHY510 |PHY525 &nbsp; This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. 1. Equilibrium Thermodynamics I: Introduction&nbsp;[tsc1] Exercises: Additional materials: 2. Equilibrium Thermodynamics II: Engines&nbsp;[tsc2] Exercises: 3. Equilibrium Thermodynamics III: Free Energies&nbsp;[tsc3]&nbsp; Exercises: Additional materials: 4. Equilibrium Thermodynamics IV: Applications&nbsp;[tsc4] Exercises: Additional materials: 5. Thermodynamics of Phase Transitions I&nbsp;[tsc5] Exercises: Additional [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"page-twocol.php","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-354","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages\/354","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/comments?post=354"}],"version-history":[{"count":7,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages\/354\/revisions"}],"predecessor-version":[{"id":516,"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/pages\/354\/revisions\/516"}],"wp:attachment":[{"href":"https:\/\/physics.uri.edu\/muller\/wp-json\/wp\/v2\/media?parent=354"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}