DOCSLIB.ORG

Teaching Thermodynamics: Chemical Potential from the Beginning G

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Teaching Thermodynamics: Chemical Potential from the Beginning G Teaching Thermodynamics: Chemical Potential from the Beginning Lecture in Taormina on 20 th February 1991 G. Job february 1991 revised 2006-07-10 Contents 1. Introduction ........................................................................................................... 1 2. First Basic Assumption .......................................................................................... 4 3. Descriptive Interpretation of the Basic Assumption ................................................ 5 4. Linear Equation ..................................................................................................... 6 5. Application in Zeroth Approximation .................................................................... 8 6. Applications in First Approximation ...................................................................... 9 7. Second Basic Assumption, Mass Action ................................................................ 11 8. Application of the Mass Action Formula ................................................................ 12 Teaching Thermodynamics: Chemical Potential from the Beginning Georg Job Lecture in Taormina on 20th February 1991 Summary: Since 1973 a new concept of chemical thermodynamics has been used in the beginner's course of chemistry at the University of Hamburg, in which the chemical potential is introduced in the first lesson. The course has the following characteristics: (1) The affinity of a reaction is introduced by using a direct measuring method (like length, time or mass) using neither energy nor entropy. The chemical potential of a substance is defined as the affinity of the decomposition reaction of this substance into the elements in their standard states. (2) The pressure, temperature, concentration dependence of the chemical potential is discussed using only linear functions in the first stage. Logarithmic equations are used in the next stage to describe the mass action of a sol- ute or gaseous substance. (3) Various applications are discussed qualitatively and quantitatively: stability of compounds, phase transitions, calculation of melting and boiling points and their dependence on pressure, vapour pressure curve, solubilities and equilibrium constants including their temperature and pressure dependence ... up to MAXWELL 's distribution law of molecular velocities (further colligative properties, diffusion and migration, chemical kinetics, multi- phase systems, elektromotive forces etc. not described here). (4) Entropy is introduced only for the description of the thermochemical phenomena (not described here). 1. Introduction Just like a description of Mesopotamia can begin with Adam and Eve in the Garden of Eden, or in medias res with the current events in Iraq, the calculation of chemical reactions can begin with an introduction to the quantum theory and quantum statistics, or in medias res with a definition of the chemical potential . The most simple way to do so is by using a direct measuring procedure as it is usual for various quantities such as length, time and mass. This method is elementary, does not require any special previous knowledge and immediately leads to results which can be utilized most practically. Even more, it has become evident that by using this method 95 ... 98% of all prob- lems for which a chemist employs thermodynamics or statistics can be accomplished. In diagram 1 this coherence is represented graphically. Different areas of chemistry are presented in key words which more or less comprise what is understood by the heading "chemical dynamics". The chemical potential forms the central turntable through which the individual areas can be reached and through which data from all directions can be distributed in all directions. Only the field of "heat effects" belongs to the sphere of thermodynamics in the original sense, constituting only a small fraction of the entire area. Historically seen, chemical dynamics have been developed from several sides. The oldest approaches had pursued the quantification of the so-called affinities A. (see diagram 1, upper part) which means from the modern point of view the determination of the potential differ- ences between the reactants and products of a reaction ¢ £ ¤ ¥ ¡ ¢ ¤ ¥ ¡ B + C + … D + E + …: A = ( B + C + …) – ( D + E + …). (1) 1 Motivity (Affinity): of reactions, phase transitions, Mass Action: dissolving, adsorption, diffusion, equilibrium constants, solubilities, electron or proton transfer ... Properties of Atoms, Molecules etc.: stability of complexes, electron affinity, ionization potential, distribution coefficients, degree of electronegativity, bond energy, formation, dissociation, association … stability of lattices, hydration effects, BORN -HABER cycle ... Multiphase Systems: melting, boiling, transition temperatures, vapour pressure diagrams, melting curve, Molecular Statistics: phase diagrams, tripel points, molecular partition functions, eutectic, peritectic, azeotropic points ... BOLTZMANN factor, FERMI -DIRAC Chemical and BOSE -EINSTEIN statistics, distribution of molecular velocities ... Acid Base Systems: acidity, acid and base constants, Spectroscopy and Photochemistry: HENDERSON -HASSELBALCH equation, titration curves, buffer capacity, emission and absorption of light, indicator systems ... thermal radiation, photochemical reactions, evaluation of spectroscopic data ... µ … Electrochemical Systems: galvanic cells, electromotive force, Chemical Kinetics: NERNST equation, contact equilibrium,, transition state theory, potentiometric methods ... rate constants and their temperature dependence, activation quantities ... Colligative Properties: lowering of vapour pressure, elevation of boiling point, osmotic pressure ... Solutions of Electrolytes: Dynamics interionic attraction, theory and consequences for solubility, Transport of Substances: mobility of substances, diffusion, acidity, rate of reaction, migration of ions, sedimentation, dissociation of complexes ... diffusion potential ... … Interface phenomena: Heat Effects: surface tension, heat of reaction, transition, adsorption, LANGMUIR 's adsorption isotherm, heat capacities, molar entropies, vapour pressure of small particles, CLAUSIUS -CLAPEYRON relation, surface pressure ... NERNST 's heat theorem … Diagram 1: Areas of chemistry which can be categorized by the heading “Chemical Dynamics”. The chemical potential has a central position in this entire area. Only the field of “heat effects” belongs to thermodynamics in the actual sense (see to the left at the bottom of the diagram). The first table of affinity values was published in 1786 1. As only the potential differences are of importance to chemical reactions, only these are chemically measurable. This restric- tion permits, in the reverse case, to specify the potential values of the elements to a large ex- tent arbitrarily. This can be used to simplify the potential tables 2. 1 By GUYTON DE MORVEAU , according to H. KOPP in “Geschichte der Chemie“, Braunschweig (1844), vol. 2, p. 303. Instead of using the notation “affinity”, the more neutral word “motivity” is recommendable. The notation “affinity” for the quantity A collides with the normal usage of the word in chemistry. Strictly speaking, it is only useable for reactions of the type B + C + D ... ¦ BCD... and is meaningless for processes such as dissociations, phase transitions and diffusion. 2 In chemistry only the A -values of reactions are used for which 1) the quantities of substance of the elements are preserved (in free or combined states) and 2) the temperatures of the reactants and resultants are the same and 3) the isotopic composition of the elements is not # ¦ § altered. A –values of this type are invariant towards the potential transformations § : # § ¨ ¨ ¨ § (A aBbCc…, T,…) = (A aBbCc…, T,…) + a (A, T) + b (B, T) + c (C, T) + …, whereas A aBbCc… is a compound of the elements A, B, C, ... and ¨ (E, T) is a arbitrary function of the species of the element E, the tempera- # § § © § ture T and the isotopic composition of E. If we choose, for example, ¨ (E, T) = (E, T,p0), then (E, T,p0) 0. The symbol (E, T,p0) repre- sents the potential value in its standard state. Reversely, the A -values determined from the § -values are only then uniquely defined if the function ¨ (E, T) has been stipulated in any manner. 2 In Hamburg we go back to the old approach during the beginners' courses for chemists, by no means for nostalgic reasons, but for pragmatical purposes. Under the given circumstances it is the fastest and the easiest way. In about one lesson, it is possible to reach the chemical potentials and then easily go over to many other areas. How efficiently the process can be organized can be shown in the schedule in diagram 2. 1st lesson: Motivity (Motive Power) of Chemical Reactions: Definition of quantity A, preliminary unit, measuring of A by linkage of reactions, types of reaction linkages (chemical, electri- cal or mechanical), extent and turnover of a reaction, work of reaction W = – A , SI unit of A. 2nd lesson: Chemical Potential: Descriptive meaning and main attributes, reference states for the elements, values of the chemical potentials, usage of tables, application to reactions and phase transitions. 3rd lesson: Influence of Pressure and Temperature on Material Conversions: The temperature coefficient of § , calculation of melting-, boiling-, transition-, decomposition- and reaction-temperatures; pressure coefficient of § , transition under pressure, behaviour of gases under pressure, calculation
Load more

Recommended publications
  • Thermodynamics, Flame Temperature and Equilibrium
    Thermodynamics, Flame Temperature and Equilibrium Combustion Summer School 2018 Prof. Dr.-Ing. Heinz Pitsch Course Overview Part I: Fundamentals and Laminar Flames • Introduction • Fundamentals and mass balances of combustion systems • Thermodynamic quantities • Thermodynamics, flame • Flame temperature at complete temperature, and equilibrium conversion • Governing equations • Chemical equilibrium • Laminar premixed flames: Kinematics and burning velocity • Laminar premixed flames: Flame structure • Laminar diffusion flames • FlameMaster flame calculator 2 Thermodynamic Quantities First law of thermodynamics - balance between different forms of energy • Change of specific internal energy: du specific work due to volumetric changes: δw = -pdv , v=1/ρ specific heat transfer from the surroundings: δq • Related quantities specific enthalpy (general definition): specific enthalpy for an ideal gas: • Energy balance for a closed system: 3 Multicomponent system • Specific internal energy and specific enthalpy of mixtures • Relation between internal energy and enthalpy of single species 4 Multicomponent system • Ideal gas u and h only function of temperature • If cpi is specific heat at constant pressure and hi,ref is reference enthalpy at reference temperature Tref , temperature dependence of partial specific enthalpy is given by • Reference temperature may be arbitrarily chosen, most frequently used: Tref = 0 K or Tref = 298.15 K 5 Multicomponent system • Partial molar enthalpy hi,m is and its temperature dependence is where the molar specific
    [Show full text]
  • Calculation of Chemical Potential and Activity Coefficient of Two Layers of Co2 Adsorbed on a Graphite Surface
    Physical Chemistry Chemical Physics CALCULATION OF CHEMICAL POTENTIAL AND ACTIVITY COEFFICIENT OF TWO LAYERS OF CO2 ADSORBED ON A GRAPHITE SURFACE Journal: Physical Chemistry Chemical Physics Manuscript ID: CP-ART-08-2014-003782.R1 Article Type: Paper Date Submitted by the Author: 07-Nov-2014 Complete List of Authors: Trinh, Thuat; NTNU, Department of Chemistry Bedeaux, Dick; NTNU, Chemistry Simon, Jean-Marc; Universit� de Bourgogne, Chemistry Kjelstrup, Signe; Norwegian University of Science and Technology, Natural Sciences Page 1 of 8 Physical Chemistry Chemical Physics PCCP RSC Publishing ARTICLE CALCULATION OF CHEMICAL POTENTIAL AND ACTIVITY COEFFICIENT OF TWO LAYERS Cite this: DOI: 10.1039/x0xx00000x OF CO2 ADSORBED ON A GRAPHITE SURFACE T.T. Trinh,a D. Bedeaux a , J.-M Simon b and S. Kjelstrup a,c,* Received 00th January 2014, Accepted 00th January 2014 We study the adsorption of carbon dioxide at a graphite surface using the new Small System DOI: 10.1039/x0xx00000x Method, and find that for the temperature range between 300K and 550K most relevant for CO separation; adsorption takes place in two distinct thermodynamic layers defined according www.rsc.org/ 2 to Gibbs. We calculate the chemical potential, activity coefficient in both layers directly from the simulations. Based on thermodynamic relations, the entropy and enthalpy of the CO 2 adsorbed layers are also obtained. Their values indicate that there is a trade-off between entropy and enthalpy when a molecule chooses for one of the two layers. The first layer is a densely packed monolayer of relatively constant excess density with relatively large repulsive interactions and negative enthalpy.
    [Show full text]
  • Chapter 4 Solution Theory
    SMA5101 Thermodynamics of Materials Ceder 2001 Chapter 4 Solution Theory In the first chapters we dealt primarily with closed systems for which only heat and work is transferred between the system and the environment. In the this chapter, we study the thermodynamics of systems that can also exchange matter with other systems or with the environment, and in particular, systems with more than one component. First we focus on homogeneous systems called solutions. Next we consider heterogeneous systems with emphasis on the equilibrium between different multi-component phases. 4.1 WHAT IS A SOLUTION? A solution in thermodynamics refers to a system with more than one chemical component that is mixed homogeneously at the molecular level. A well-known example of a solution is salt water: The Na+, Cl- and H2O ions are intimately mixed at the atomic level. Many systems can be characterized as a dispersion of one phase within another phase. Although such systems typically contain more than one chemical component, they do not form a solution. Solutions are not limited to liquids: for example air, a mixture of predominantly N2 and O2, forms a vapor solution. Solid solutions such as the solid phase in the Si-Ge system are also common. Figure 4.1. schematically illustrates a binary solid solution and a binary liquid solution at the atomic level. Figure 4.1: (a) The (111) plane of the fcc lattice showing a cut of a binary A-B solid solution whereby A atoms (empty circles) are uniformly mixed with B atoms (filled circles) on the atomic level.
    [Show full text]
  • Chapter 2: Equation of State
    Chapter 2: Equation of State Introduction The Local Thermodynamic Equilibrium The Distribution Function Black Body Radiation Fermi-Dirac EoS The Complete Degenerate Gas Application to White Dwarfs Temperature Effects Ideal Gas The Saha Equation “Almost Perfect” EoS Adiabatic Exponents and Other Derivatives Outline Introduction The Local Thermodynamic Equilibrium The Distribution Function Black Body Radiation Fermi-Dirac EoS The Complete Degenerate Gas Application to White Dwarfs Temperature Effects Ideal Gas The Saha Equation “Almost Perfect” EoS Adiabatic Exponents and Other Derivatives The EoS, together with the thermodynamic equation, allows to study how the stellar material properties react to the heat, changing density, etc. Introduction Goal of the Chapter: derive the equation of state (or the mutual dependencies among local thermodynamic quantities such as P; T ; ρ, and Ni ), not only for the classic ideal gas, but also for photons and fermions. Introduction Goal of the Chapter: derive the equation of state (or the mutual dependencies among local thermodynamic quantities such as P; T ; ρ, and Ni ), not only for the classic ideal gas, but also for photons and fermions. The EoS, together with the thermodynamic equation, allows to study how the stellar material properties react to the heat, changing density, etc. Thermodynamics Thermodynamics is defined as the branch of science that deals with the relationship between heat and other forms of energy, such as work. The Laws of Thermodynamics: I First law: Energy can be neither created nor destroyed. This is a version of the law of conservation of energy, adapted for (isolated) thermodynamic systems. I Second law: In an isolated system, natural processes are spontaneous when they lead to an increase in disorder, or entropy, finally reaching an equilibrium.
    [Show full text]
  • Thermodynamics.Pdf
    1 Statistical Thermodynamics Professor Dmitry Garanin Thermodynamics February 24, 2021 I. PREFACE The course of Statistical Thermodynamics consist of two parts: Thermodynamics and Statistical Physics. These both branches of physics deal with systems of a large number of particles (atoms, molecules, etc.) at equilibrium. 3 19 One cm of an ideal gas under normal conditions contains NL = 2:69×10 atoms, the so-called Loschmidt number. Although one may describe the motion of the atoms with the help of Newton's equations, direct solution of such a large number of differential equations is impossible. On the other hand, one does not need the too detailed information about the motion of the individual particles, the microscopic behavior of the system. One is rather interested in the macroscopic quantities, such as the pressure P . Pressure in gases is due to the bombardment of the walls of the container by the flying atoms of the contained gas. It does not exist if there are only a few gas molecules. Macroscopic quantities such as pressure arise only in systems of a large number of particles. Both thermodynamics and statistical physics study macroscopic quantities and relations between them. Some macroscopics quantities, such as temperature and entropy, are non-mechanical. Equilibruim, or thermodynamic equilibrium, is the state of the system that is achieved after some time after time-dependent forces acting on the system have been switched off. One can say that the system approaches the equilibrium, if undisturbed. Again, thermodynamic equilibrium arises solely in macroscopic systems. There is no thermodynamic equilibrium in a system of a few particles that are moving according to the Newton's law.
    [Show full text]
  • Derivation of the Chemical Potential Equation
    X - 8 DELGADO-BONAL ET AL.: DISEQUILIBRIUM ON MARS T Appendix A: Derivation of the chemical −CpT ln( ) + RT ln(p=p0) (A7) potential equation T0 When the temperature is T=T0, the above expression is The expression that is commonly used in planetary at- reduced to the more familiar equation: mospheres is usually written as (Kodepudi and Prigogine [1998], Eq. 5.3.6): µ(p; T0) = µ(p0;T0) + RT0 ln(p=p0) (A8) However, as has been explained in Section 2, this expres- µ(p; T ) = µ(p0;T ) + RT ln(p=p0) (A1) sion is only useful for situations where the temperature is where µ0 is the chemical potential at unit pressure (1 close to the standard temperature of reference (usually 298 atm), p0 is the pressure at standard conditions and R the K), i.e., the Earth environment. When the temperatures are gas constant. different, the complete expression for the chemical potential In order to calculate the chemical potential for arbitrary is needed. p and T, the knowledge of the chemical potential at (p0,T) The temperature dependence of the heat capacity is usu- is needed. This previous step, usually omitted, can be per- ally expressed as a polynomial function with tabulated con- formed as (Eq. (5.3.3) in (Kodepudi and Prigogine [1998])): stants: 2 Cp(T ) = a + bT + cT (A9) T Z T −H (p ;T 0) µ(p ;T ) = µ(p ;T ) + T · m 0 dT 0 (A2) If the coefficients b and c are much smaller than a, as usu- 0 T 0 0 T 02 0 T0 ally happens, Equation A7 represents an useful approxima- tion, useful for those environments where the temperature where T0 is the temperature at standard conditions and variations are not large and the heat capacity can be con- Hm is the molar enthalpy of the compound.
    [Show full text]
  • Equation of State
    EQUATION OF STATE Consider elementary cell in a phase space with a volume 3 ∆x ∆y ∆z ∆px ∆py ∆pz = h , (st.1) where h =6.63×10−27 erg s is the Planck constant, ∆x ∆y ∆z is volume in ordinary space measured 3 −1 3 in cm , and ∆px ∆py ∆pz is volume in momentum space measured in ( g cm s ) . According to quantum mechanics there is enough room for approximately one particle of any kind within any elementary cell. More precisely, an average number of particles per cell is given as g n = , (st.2) av e(E−µ)/kT ± 1 with a ”+” sign for fermions, and a ”−” sign for bosons. The corresponding distributions are called Fermi-Dirac and Bose-Einstein, respectively. Particles with a spin of 1/2 are called fermions, while those with a spin 0, 1, 2... are called bosons. Electrons and protons are fermions, photons are bosons, while larger nuclei or atoms may be either fermions or bosons, depending on the total spin of such − a composite particle. In the equation (st.2) E is the particle energy, k = 1.38 × 10−16 erg K 1 is the Boltzman constant, T is temperature, µ is chemical potential, and g is a number of different quantum states a particle may have within the cell. The meaning of temperature is obvious, while chemical potential will become more familiar later on. In most cases it will be close to the rest mass of a particle under consideration. If there are anti-particles present in equilibrium with particles, and particles have chemical potential µ then antiparticles have chemical potential µ − 2m, where m is their rest mass.
    [Show full text]
  • Energy & Chemical Reactions
    Energy & Chemical Reactions Chapter 6 The Nature of Energy Chemical reactions involve energy changes • Kinetic Energy - energy of motion – macroscale - mechanical energy – nanoscale - thermal energy – movement of electrons through conductor - electrical energy 2 – Ek = (1/2) mv • Potential Energy - stored energy – object held above surface of earth - gravitational energy – energy of charged particles - electrostatic energy – energy of attraction or repulsion among electrons and nuclei - chemical potential energy The Nature of Energy Energy Units • SI unit - joule (J) – amount of energy required to move 2 kg mass at speed of 1 m/s – often use kilojoule (kJ) - 1 kJ = 1000 J • calorie (cal) – amount of energy required to raise the temperature of 1 g of water 1°C – 1 cal = 4.184 J (exactly) – nutritional values given in kilocalories (kcal) First Law of Thermodynamics The First Law of Thermodynamics says that energy is conserved. So energy that is lost by the system must be gained by the surrounding and vice versa. • Internal Energy – sum of all kinetic and potential energy components of the system – Einitial → Efinal – ΔE = Efinal - Einitial – not possible to know the energy of a system but easy to measure energy changes First Law of Thermodynamics • ΔE and heat and work – internal energy changes if system loses or gains heat or if it does work or has work done on it – ΔE = q + w – sign convention to keep track of heat (q > 0) system work (w > 0) – both heat added to system and work done on system increase internal energy First Law of Thermodynamics First Law of Thermodynamics Divide the universe into two parts • system - what we are studying • surroundings - everything else ∆E > 0 system gained energy from surroundings ∆E < 0 system lost energy to surroundings Work and Heat Energy can be transferred in the form of work, heat or a combination of the two.
    [Show full text]
  • Linking up Pressure, Chemical Potential and Thermal Gradients François Montel, Hai Hoang, Guillaume Galliero
    Linking up pressure, chemical potential and thermal gradients François Montel, Hai Hoang, Guillaume Galliero To cite this version: François Montel, Hai Hoang, Guillaume Galliero. Linking up pressure, chemical potential and thermal gradients. European Physical Journal E: Soft matter and biological physics, EDP Sciences: EPJ, 2019, 42 (5), pp.65. 10.1140/epje/i2019-11821-0. hal-02478640 HAL Id: hal-02478640 https://hal.archives-ouvertes.fr/hal-02478640 Submitted on 17 Feb 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Linking up Pressure, Chemical Potential and Thermal Gradients François Montel1§, Hai Hoang2, Guillaume Galliero1 1Laboratoire des Fluides Complexes et leurs Réservoirs, UMR-5150 CNRS/TOTAL/Univ Pau & Pays Adour, E2S, 64000, Pau, France 2 Institute of Fundamental and Applied Sciences, Duy Tan University, 10C Tran Nhat Duat Street, District 1, Ho Chi Minh City 700000, Viet Nam §[email protected] Abstract Petroleum reservoirs are remarkable illustrations of the impact of a thermal gradient on fluid pressure and composition. This topic has been extensively studied during the last decades to build tools that are required by reservoir engineers to populate their models. However, one can get only a very limited number of representative samples from a given reservoir and assessing connectivity between all sampling points is often a key issue.
    [Show full text]
  • Lecture 10: 10.14.05 Chemical Potentials and the Gibbs Free Energy
    3.012 Fundamentals of Materials Science Fall 2005 Lecture 10: 10.14.05 Chemical potentials and the Gibbs free energy Today: LAST TIME........................................................................................................................................... 2 APPLICATION EXAMPLE: PREDICTING SPONTANEOUS WETTING ............................................................. 3 DESCRIBING MULTI-PHASE/MULTI-COMPONENT SYSTEMS ..................................................................... 4 Molar and Partial molar quantities............................................................................................................................................4 The partial molar free energy .....................................................................................................................................................7 CHEMICAL POTENTIALS IN MULTI-PHASE MATERIALS AT EQUILIBRIUM ................................................. 8 Materials that rearrange their components to reach equilibrium............................................................................................8 REFERENCES ..................................................................................................................................... 10 Reading: Engel and Reid, Ch. 6.4. Supplementary Reading: - Lecture 10 – chemical potentials at equilibrium 1 of 10 10/14/05 3.012 Fundamentals of Materials Science Fall 2005 Last time A summary of fundamental equations: Experimental Key Fundamental At equilibrium, this Mathematical
    [Show full text]
  • The Elusive Chemical Potential Ralph Baierlein
    The elusive chemical potential Ralph Baierlein Citation: American Journal of Physics 69, 423 (2001); doi: 10.1119/1.1336839 View online: https://doi.org/10.1119/1.1336839 View Table of Contents: https://aapt.scitation.org/toc/ajp/69/4 Published by the American Association of Physics Teachers ARTICLES YOU MAY BE INTERESTED IN Making sense of the Legendre transform American Journal of Physics 77, 614 (2009); https://doi.org/10.1119/1.3119512 Light with nonzero chemical potential American Journal of Physics 73, 717 (2005); https://doi.org/10.1119/1.1904623 Thermodynamically reversible processes in statistical physics American Journal of Physics 85, 135 (2017); https://doi.org/10.1119/1.4966907 Understanding temperature and chemical potential using computer simulations American Journal of Physics 73, 708 (2005); https://doi.org/10.1119/1.1834923 Insight into entropy American Journal of Physics 68, 1090 (2000); https://doi.org/10.1119/1.1287353 How batteries work: A gravitational analog American Journal of Physics 51, 829 (1983); https://doi.org/10.1119/1.13128 The elusive chemical potential Ralph Baierlein Department of Physics and Astronomy, Northern Arizona University, Flagstaff, Arizona 86011-6010 ͑Received 12 April 2000; accepted 10 October 2000͒ This paper offers some qualitative understanding of the chemical potential, a topic that students invariably find difficult. Three ‘‘meanings’’ for the chemical potential are stated and then supported by analytical development. Two substantial applications—depression of the melting point and batteries—illustrate the chemical potential in action. The origin of the term ‘‘chemical potential’’ has its surprises, and a sketch of the history concludes the paper.
    [Show full text]
  • Entropy. Temperature. Chemical Potential. Thermodynamic Identities
    Entropy. Temperature. Chemical Potential. Thermodynamic Identities. Third Law. Physics 3700 Entropy. Temperature. Chemical Potential. Thermodynamic Identities. Third Law. Relevant sections in text: x2.6, 3.1, 3.2, 3.4, 3.5 Entropy We have seen that the equilibrium state for an isolated macroscopic thermal system is the one with the highest multiplicity. Obviously, the multiplicity of a macrostate is an important observable of the system. This is, of course, a huge number in general. To keep things manageable | and to give us other important properties, to be discussed later | we define a corresponding observable using the natural logarithm of the multiplicity times Boltzmann's constant. This is the entropy* S = k ln Ω: The SI units of entropy are J/K. For the Einstein solid (with our macroscopic, high temperature approximation) the entropy is eq N q S = k ln = Nk(ln + 1): N N With N = 1022 and q = 1024 we have S = 0:77J=K. This is a typical result. In SI units Boltzmann's constant is around 10−23, and the logarithm of the multiplicity for a macroscopic system is typically around 1023, so the entropy | which is on the order of Nk | is typically on the order of unity in SI units. Note that the more particles there are, the higher the entropy. The more energy there is, the higher the entropy. Both of these stem from the increased multiplicity that occurs when these observables are increased. The entropy is an extensive observable. This is one of the key features of using the logarithm of the multiplicity to define entropy.
    [Show full text]