Lecture Notes on Thermodynamics UMR 8550

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Preface and bibliography 7,1 Review of basic concepts 9. 1 1 Thermodynamic systems 9,1 2 Thermodynamic equilibrium 10. 1 3 Thermodynamic variables 10,1 4 Transformations 12. 1 5 Internal energy U 13,1 6 Pressure p 16,1 7 Temperature T 18. 2 Energy transfer 19,2 1 Energy conservation work heat 19.
2 2 Some examples of energy exchange through work 21. 2 2 1 Work of pressure forces 21,2 2 2 Elastic work 22. 2 2 3 Electric work 22,2 2 4 Chemical work 22,2 3 Some examples of heat exchange 23. 2 3 1 Heat exchange by contact conduction 23,2 3 2 Heat exchange via a fluid convection 23. 2 3 3 Heat exchange by radiation 24,3 Entropy and second law of thermodynamics 25. 3 1 Necessity of the second law 25,3 1 1 Joule expansion 25.
3 1 2 Bodies in thermal contact 26,3 2 The second law 26. 3 3 Applications 29,3 3 1 Expression of dU 29,3 3 2 Positivity of CV 29. 3 3 3 Entropy of an ideal gas 30,3 3 4 Reservoirs thermostat pressostat 32. 3 4 Microscopic interpretation 33,4 Thermodynamic functions and potentials 37. 4 1 Thermodynamic potentials 37,4 1 1 Definition 37.
4 1 2 Using the potential to determine equilibrium 38. 4 1 3 First introduction of thermodynamic functions 39. 4 1 4 Internal variables 40,4 2 Legendre transformation 41. 4 2 1 Mathematical presentation 41,4 2 2 Application to thermodynamics 43. 4 2 3 Gibbs Duhem relation 45,4 3 Calorimetric coefficients of a fluid 45. 4 3 1 Definitions of calorimetric coefficients 45,4 3 2 Clapeyron equations 46. 4 3 3 Relationships between coefficients 47,4 3 4 Isentropic coefficients 49.
4 3 5 Thermodynamic inequalities 50,5 Microcanonical statistical mechanics 53. 5 1 The postulate of statistical mechanics 53,5 2 The lattice gas 54. 5 2 1 Calculation of the number of microstates 54,5 2 2 Stirling s approximation 56. 5 2 3 Lattice gas entropy and pressure 56, 5 2 4 Probability of a microscopic state of part of a system 57. 5 2 5 Probability of a macroscopic state of part of a system 58. 5 2 6 Irreversibility and fluctuations 58,5 3 Two level systems 60.
5 4 Summary 61,6 Canonical statistical mechanics 63. 6 1 The canonical ensemble 63,6 1 1 Positioning the problem 63. 6 1 2 Boltzmann s factor 64,6 2 Applications 64,6 2 1 Two level systems 64. 6 2 2 System consisting of N two level particles 65. 6 2 3 High and low temperature limits frozen states 66. 6 2 4 Energy fluctuations 67, 6 2 5 Classical systems and continuous variables 68. 6 2 6 Kinetic theory of gases 70,6 2 7 Equipartition of energy 70.
6 3 Demonstration of 6 1 71,7 Phase changes of a pure substance 73. 7 1 Equilibrium condition and evolution towards equilibrium 73. 7 2 Phase diagram 75,7 3 Isothermal diagrams 76,7 4 Latent heat 79. 8 Binary solutions 83,8 1 Gibbs phase rule 83,8 2 Single phase binary solutions 84. 8 2 1 Mixture of two ideal gases ideal mixture 84,8 2 2 Dilute solutions 86. 8 3 Phase diagram of binary solutions 90,8 3 1 Isobar diagram 90.
8 4 Degree of humidity evaporation boiling 93,8 4 1 Evaporation 93. 8 4 2 Boiling 94,Preface and bibliography, Thermodynamics is a branch of physics that studies macroscopic systems i e composed. of a large number of particles using an energetic approach It is a theory that applies to. many systems and allows to establish general relations between the coefficients that describe. the various states of matter, Statistical mechanics gives a microscopic interpretation to the quantities studied in. thermodynamics In simple cases the postulates of statistical mechanics allow one to un. derstand and interpret the laws of thermodynamics, These lecture notes are intended for students who already have some notions in ther. modynamics After the first three chapters which refer to key concepts first and second. laws energy entropy work heat more advanced notions of thermodynamics are dis. cussed potentials and thermodynamic functions thermoelastic coefficients phase diagrams. binary solutions Halfway through this course two chapters outlining the fundamentals. of statistical mechanics shed light on how the macroscopic properties of matter as described. by thermodynamics are related to the microscopic behaviour of atoms and molecules we. will discuss amongst other notions the Boltzmann factor the equipartition of energy the. statistical interpretation of entropy the kinetic theory of gases. These notes are associated with about forty short videos explaining the most tricky and. important points of this course,Short bibliography.
Jancovici Statistical physics and thermodynamics Wiley 1973. A concise book ideal to review the basics of thermodynamics It also addresses statistical mechanics. Kubo Thermodynamics an advanced course with problems and solutions North Hol. Reference book with many examples and problems with complete solutions. Landau and Lifshitz Statistical Physics Elsevier 1980. More difficult advised as a second reading A classic timeless extremely concise. Callen Thermodynamics and an introduction to thermostatistics Wiley 1985. A very formal book the reading of which is strongly recommended. Reif Berkeley Physics Course Vol 5 Statistical Physics Mc Graw Hill Dunod 1967. Another classic detailed with illustrations that you will enjoy reading. Reif Fundamentals of statistical and thermal physics Waveland Press 2009. Book by the same author as the previous one more advanced and swift in its presentation. Chapter 1 Video 1,Review of basic concepts,1 1 Thermodynamic systems Video 2. Thermodynamics is the science of macroscopic systems i e of systems composed of N par. ticles atoms molecules ions etc N being very large N 1. Frame 1 1 Orders of magnitude Video 3, Under normal conditions the typical distance between particles is approximately. 3 0 3 nm 3 10 10 m for solids or liquids,3 nm for gases. In 1 cm3 of matter there are typically between,1022 to 1023 particles for solids or liquids. 1019 to 1020 particles for gases, Recall that a mole is defined as the amount of substance in 12 g of carbon 12 and the.
Avogadro constant NA gives the number of particles per mole. NA 6 022 1023 mol 1, Only a few cm3 to a few tens of cm3 of solid or liquid are required to obtain a mole. For an ideal gas at atmospheric pressure and a temperature of 0 C the volume of a mole is. Thermodynamics studies the properties of matter at a macroscopic level i e with a. number of particles so large that it is not feasible to study each individual trajectory. Frame 1 2 Thermodynamic systems, A thermodynamic system is the object of the study under review What is not in the. system is defined as the surroundings A system can be. open or closed depending on whether it can exchange matter or not with its. surroundings, non isolated or isolated depending on whether it can exchange energy or not. with its surroundings,movable or rigid, Remark if the system is open it cannot be isolated. 1 2 Thermodynamic equilibrium, If a system is left standing for a sufficiently long time it will reach a state of thermodynamic.
equilibrium,Frame 1 3 Thermodynamic equilibrium, A system is considered under thermodynamic equilibrium when there is no more macro. scopic movement nor any kind of flux, When a system is in equilibrium there is no macroscopic movement we cannot. see anything moving but considered individually particles move randomly with. high velocity, A conducting wire in which flows an electric current is not in equilibrium since. there is a flux of charges as well as thermal dissipation. A piece of metal connecting a hot source to a cold source is not in equilibrium. since there is heat transfer and hence an exchange of energy from the hot towards. the cold source,1 3 Thermodynamic variables, At thermodynamic equilibrium it is sufficient to know a small number of quantities to fully. characterise a system These quantities are called thermodynamic variables. Frame 1 4 Thermodynamic variables, Thermodynamic variables are the quantities used to characterise a system.
Some variables have a meaning even when the number of particles in the system. is small Such variables are derived from geometry mechanics electromagnetism. etc e g volume V surface S number of particles N amount of substance n in. moles applied force internal energy U magnetisation M etc. Other variables only have a meaning for systems with a large number of particles. e g gas pressure p temperature T chemical potential entropy S etc. A thermodynamic variable is said to be extensive if it is proportional to the amount of. substance in the system and intensive if it is independent A thermodynamic variable. is additive if the value associated with a system composed of several parts is equal to. the sum of the values associated with each individual part. Example 1 A glass of 10 c is taken from a bathtub filled with 100 of water In the. glass there is a thousand times less particles moles volume energy entropy than in the. bathtub these quantities are extensive On the other hand the temperature pressure and. chemical potential of the water are the same in the bathtub and in the glass these quantities. are intensive The contact surface between water and air has a complicated dependence on. the geometry of the glass and the bathtub this surface is a quantity that is neither intensive. nor extensive, Example 2 The system considered is the content of a half filled bottle i e a liquid. bottom part and a gas top part The energy of the system is equal to the energy of the. liquid plus the energy of the gas this quantity is additive It is also the case for volume. entropy etc, Remark In general additive and extensive variables are the same. Some variables are easy to measure volume temperature pressure in a fluid etc and. others can only be obtained through a calculation internal energy entropy chemical poten. tial etc We distinguish external and internal variables. External variables are those controlled by the operator either by maintaining them. fixed e g mass m of a closed system volume V of a rigid system or by exerting an. action on the system e g pressure of a pressostat p0 temperature of a thermostat T0. The variable is internal or free when the operator does not have direct access to it. even if he can define it or measure it For example this is the case of the number of. reagent particles in a closed system in which a chemical reaction occurs The value of. these variables is fixed only by the thermodynamic equilibrium conditions. For a pure single phase fluid the equilibrium state of the system is entirely determined. by three thermodynamic variables for example n V and T or n V and U The values of. the other variables can then be obtained using the equation of state relationship between. p n V and T and other relationships see the example of the ideal gas in frame 1 5 or of. the van der Waals gas in frame 1 10,Frame 1 5 The ideal gas. The ideal gas is an ideal thermodynamic system where the interactions between parti. cles are neglected For a classical ideal gas where quantum effects are neglected the. equation of state ideal gas law is,p pressure Pa V volume m3. pV nRT n amount of substance mol T temperature K, where R 8 31 J K mol is the ideal gas constant We can also write.
pV N kB T N number of particles, where kB 1 38 10 23 J K is the Boltzmann constant Since N nNA we have. When the ideal gas is monoatomic we also have the relationship. U nRT N kB T U internal energy J, The ideal gas is a very good approximation of the usual real gases at ordinary tempera. tures and pressures However when the molar density n V becomes high the ideal gas. approximation is no longer satisfactory the mean distance between particles decreases. and the interaction potential between them makes for a sizeable contribution to the. total energy of the gas On can then use a better approximation such as the van der. Waals gas see frame 1 10,Video 4 1 4 Transformations. In thermodynamics one is interested in the transformations of a system and most often in. transformations between two equilibrium states Let us consider a system transiting between. two equilibrium states i to f and X a state variable passing from the value Xi to Xf e g. the temperature T which would change from Ti 20 C to Ti 60 C The variation of X. during the transformation is defined by X Xf Xi i e T Tf Ti 40 C in our. example By definition this variation only depends on the initial and final states and not. on the sequence of intermediate states In short X does not depend on the path of the. process followed, Some transformations are brutal which can lead to intermediate states being poorly. defined this is the case of a gas expansion in vacuum or an explosive chemical reaction In. thermodynamics we are more often interested in slower transformations for which the state. of the system is well defined at each moment In particular quasistatic transformations and. reversible transformations are of crucial importance. Frame 1 6 Quasistatic transformation, A transformation is said to be quasistatic when it evolves slowly enough for the system.
to be described by a continuous succession of internal equilibrium states During a. quasistatic transformation all the state variables X1 X2 of the system are defined. and vary continuously We can then express the differential of any state function. Lecture Notes on Thermodynamics ric Brunet1 Thierry Hocquet2 Xavier Leyronas3 February13 2019 Atheoryisthemoreimpressivethegreaterthesimplicityofitspremisesis

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