1. 1.Introduction 2.Postulates of thermodynamics 3.Thermodynamic equilibrium in isolated and isentropic systems 4.Thermodynamic equilibrium in systems with other constraints 5.Thermodynamic processes and engines pp. 1–92 6.Thermodynamics of mixtures (multicomponent systems) 7.Phase equilibria 8.Equilibria of chemical reactions 9.Extension of thermodynamics for additional interactions (non-simple systems) 10. Elements of equilibrium statistical thermodynamics 11.Towards equilibrium – elements of transport phenomena pp. 92–303 Appendix pp. 305-328

2. Table of contents 1.Introduction 2.Postulates of thermodynamics 3.Thermodynamic equilibrium in isolated and isentropic systems 4.Thermodynamic equilibrium in systems with other constraints 5.Thermodynamic processes and engines pp. 1–92 6.Thermodynamics of mixtures (multicomponent systems) 7.Phase equilibria 8.Equilibria of chemical reactions 9.Extension of thermodynamics for additional interactions (non-simple systems) 10.Elements of equilibrium statistical thermodynamics 11.Towards equilibrium – elements of transport phenomena pp. 92–303 Appendix pp. 305–328

3. Table of contents Appendix F1. Useful relations of multivariate calculus F2. Changing extensive variables to intensive ones: Legendre transformation F3. Classical thermodynamics: the laws

4. Fundamentals of postulatory thermodynamics An important definition: the thermodynamic system The objects described by thermodynamics are called thermodynamic systems. These are not simply “the part of the physical universe that is under consideration ” (or in which we have special interest ), rather material bodies having a special property; they are in equilibrium. The condition of equilibrium can also be formulated so that thermodynamics is valid for those bodies at rest for which the predictions based on thermodynamic relations coincide with reality (i. e. with experimental results). This is an a posteriori definition; the validity of thermodynamic description can be verified after its actual application. However, thermodynamics offers a valid description for an astonishingly wide variety of matter and phenomena.

5. Postulatory thermodynamics A practical simplification: the simple system Simple systems are pieces of matter that are macroscopically homogeneous and isotropic, electrically uncharged, chemically inert, large enough so that surface effects can be neglected, and they are not acted on by electric, magnetic or gravitational fields. Postulates will thus be more compact, and these restrictions largely facilitate thermodynamic description without limitations to apply it later to more complicated systems where these limitations are not obeyed. Postulates will be formulated for physical bodies that are homogeneous and isotropic, and their only possibility to interact with the surroundings is mechanical work exerted by volume change, plus thermal and chemical interactions.

6. Postulates of thermodynamics 1. There exist particular states (called equilibrium states) of simple systems that, macroscopically, are characterized completely by the internal energy U, the volume V, and the amounts of the K chemical components n 1, n 2,…, n K. 2. There exists a function (called the entropy, denoted by S ) of the extensive parameters of any composite system, defined for all equilibrium states and having the following property: The values assumed by the extensive parameters in the absence of an internal constraint are those that maximize the entropy over the manifold of constrained equilibrium states. 3. The entropy of a composite system is additive over the constituent subsystems. The entropy is continuous and differentiable and is a strictly increasing function of the internal energy. 4. The entropy of any system is non-negative and vanishes in the state for which the derivative ( ∂U / ∂S ) V, n = 0. (I. e., at T = 0.)

7. Summary of the postulates (Simple) thermodynamic systems can be described by K + 2 extensive variables. Extensive quantities are their homogeneous linear functions. Derivatives of these functions are homogeneous zero order. Solving thermodynamic problems can be done using differential- and integral calculus of multivariate functions. Equilibrium calculations – knowing the fundamental equations – can be reduced to extremum calculations. Postulates together with fundamental equations can be used directly to solve any thermodynamical problems.

8. Relations of the functions S and U S (U, V, n 1, n 2,… n K ) is concave, and a strictly monotonous function of U

9. Identifying (first order) derivatives We know: at constantS and n (in closed, adiabatic systems): (This is the volume work.) Similarly: at constantV and n (in closed, rigid wall systems): (This is the absorbed heat.) Properties of the derivative confirm: at constant S andV (in rigid, adiabatic systems): (This is energy change due to material transport) The relevant derivative is called chemical potential:

10. Identifying (first order) derivatives is negative pressure, is temperature, is chemical potential. The total differential can thus be written (in a simpler notation) as:

11. Equilibrium calculations isentropic, rigid, closed system impermeable, initially fixed, thermally isolated piston, then freely moving, diathermal S α, V α, n α S β, V β, n β S α + S β = constant; – dS α = dS β Consequences of impermeability (piston): n α = constant; n β = constant → dn α = 0; dn β = 0 V α + V β = constant; – dV α = dV β Equilibrium condition: dU= dU α + dU β = 0 U αU α U βU β Equilibrium: T α = T β and P α = P β

12. Equilibrium calculations isentropic, rigid, closed system S α, V α, n α S β, V β, n β Condition of thermal and mechanical equilibrium in the composit system: U αU α U βU β T α = T β and P α = P β 4 variables S α, V α, S β and V β are to be known at equilibrium. They can be calculated by solving the 4 equations: T α (S α, V α, n α ) = T β (S β, V β, n β ) P α (S α, V α, n α ) = P β (S β, V β, n β ) S α + S β = S ( constant ) V α + V β = V ( constant )

13. Equilibrium at constant temperature and pressure isentropic, rigid, closed system T = T r and P = P r (constants) S r, V r, n r T r, P r S, V, n T, P equilibrium condition: the „internal system” is closed n r = constant and n = constant d (U+U r ) = d U + T r dS r – P r dV r = 0 S r + S = constant; – dS r = dS V r + V = constant; – dV r = dV d (U+U r ) = d U + T r dS r – P r dV r = d U + T r dS – P r dV = 0 T = T r and P = P r d (U+U r ) = d U – TdS + PdV = d (U – TS + PV ) = 0 minimizing U + U r is equivalent to minimizing U – TS + PV Equilibrium condition at constant temperature and pressure: minimum of the Gibbs potential G = U – TS + PV

14. Rankine vapor cycle and engines refrigerator heat engine

15. Fugacty and interrelation of activities Illustration of the thermodynamic definition of fugacity

16. Fugacity and interrelation of activities Relation of the activities f i (referenced to infinite dilution) and γ i (referenced to pure substance for the same system

17. Overview of different activities activity a i name meaning of the standardcondition f i x i relative activity (activity referenced to Raoult’s law) (chemical potential of the pure substance) at any concentration 0 ≤ x i ≤ 1 rational activity (activity referenced to Henry’s law) (chemical potential of the hypothetical pure substance in the state identical to that at infinite dilution) at any concentration in existing mixtures molality basis activity (chemical potential of the hypothetical ideal mixture at concentration = 1 mol/kg in the state identical to that at infinite dilution) in solutions concentration basis activity (chemical potential of the hypothetical ideal mixture at concentration = 1 mol/dm 3 in the state identical to that at infinite dilution) in solutions fugacity (chemical potential of the hypothetical ideal mixture at a reference pressure φ i p i = P, ) in every gaseous mixture

18. Phase diagram of a van der Waals fluid Equilibrium condition: and

19. phase diagram of a pure substance P ( V, T ) phase diagram of a pure substance contracting when freezing

20. phase diagram of a pure substance P ( V, T ) phase diagram of a pure substance expanding when freezing

21. Thermodynamics of phase separation molar Gibbs potential ( g ) of (heterogeneous) mechanical dispersion and (homogeneous) mixture Common tangents 2 components, liquid-liquid

22. Thermodynamics of phase separation 2 components, solid-liquid

23. Thermodynamics of phase separation 2 components, solid-liquid

24. Other binary solid-liquid phase diagrams peritectic reaction compound formation monotectic reaction syntectic reaction

25. Three-component phase diagrams 3D diagram 2D projection

26. Factors influencing chemical equilibria Example: 1 ½ H 2 + ½ N 2  NH 3 mixing reaction

27. Extension for additional interactions surface effects (elements of surface chemistry) electrically charged phases (elements of electrochemistry)

28. Energy distribution in canonical ensembles density function of multiparticle energy distribution density function of single particle energy distribution

29. General interpretation of entropy disordered ordered smaller entropy greater entropy Misunderstandings due to the interpretation as “order–disorder”

30. Viscuous flow as momentum transfer

31. Lagrange-transformation (Appendix) the envelope of the tangent lines determines the curve

32. Special terms and notation explained The name comes from the German freie Energie (free energy). It also has another name, Helmholtz potential, to honor Hermann Ludwig Ferdinand von Helmholtz (1821-1894) German physician and physicist. Apart from F, it is denoted sometimes by A, the first letter of the German word Arbeit = work, referring to the available useful work of a system. The words diabatic, adiabatic and diathermal have Greek origin. The Greek noun διαßασις [diabasis] designates a pass through, e. g., a river, and its derivative διαßατικος [diabatikos] means the possibility that something can be passed through. Adding the prefix α - expressing negation, we get the adjective αδιαßατικος [adiabatikos] meaning non-passability. In thermodynamic context, diabatic means the possibility for heat to cross the wall of the container, while adiabatic has the opposite meaning, i. e. the impossibility for heat to cross. ….

33. Összefoglalás easy-to-follow basis of thermodynamics postulates ready-to-use in equilibrium calculations detailed discussion of multicomponent systems sound thermodynamic foundations of phase transitions & related equilibria chemical reactions (homogeneous & heterogeneous) surface chemistry electrochemistry exact explanation of statistical thermodynamics elements of nonequilibrium thermodynamics (transport) Appendix: calculus + laws of classical thermodynamics Summing up

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