Phase equilibria, phase diagrams and phase transformations second edition thermodynamic principles are central to understanding material behaviour, particularly as the application of these concepts underpins phase equilibrium, transformation and state. Introduction to chemical engineering for lectures 36. Equilibrium phase diagrams represent the relationships between temperature and the compositions and the quantities of phases at equilibrium. Phase equilibrium various heterogeneous equilibria box 10. Your support will help mit opencourseware continue to offer high quality educational resources for free. Max concentration for which only a single phase solution occurs.
A plot of g versus temperature for any given phase will be a straight line with a slope of s g h. So of course you saw the whole delta g0 as minus rt log kp and so forth. G ng m 2 ng m 1 ng m 2 g m 1 equilibrium is termed as phase diagram. Thermodynamics and phase equilibria stanford online. According to gibbs, the phase rule is a general relation between the variance f no. Four laws that drive the universe related presentation on free energy peter atkins, 2007. Lecture 10 phase equilibria and polymer blends february 7, 2001. As we decrease the pressure, we eventually reach 2 on the coexistence line. This equation can be solved for t and p if know the complete form of the analytical expression. Mech 6661 thermodynamics of materials and phase equilibria. Phase equilibria and phase diagram nilesh prakash gurao associate professor department of materials science and engineering indian institute. Chemical engineering 160260 polymer science and engineering. In fact, there is a road map that, once understood, allows. The composition of the liquid phase at this point is x 0 y b2 x b2 1 liquid phase gas phase p b x b,y b p a p 1 2 2 b2.
To develop the classical floryhuggins theory for the free. Non equilibrium molecular dynamics, linearresponse theory. Phase equilibria of pure substances atkins, chapter 5 phase transition. Pdf pdf phase equilibrium dhiren kathiriya academia. Second law second law of thermodynamics and its consequences, combined statement of first and second laws 5 4. Jun 17, 2020 d4, july 16, 2020 renewable energy application in smart grid, micro grid and evs, reasgmgev 2020 bharani chandra 231 watching live now. To develop the classical floryhuggins theory for the free energy of mixing of polymer solutions based on a statistical approach on a regular lattice. Thermodynamics of fluidphase equilibria for standard chemical. Drude theory of metals department of chemistry uci. S this means that at the phase transition temperature. Mass, species a mass, energy balances, fluid flow fundamentals 3. Chapter 8, acidbase equilibria road map of acidbase equilibria on first encounter, the study of acidbase equilibria is a little like a strange land with seemingly confusing trails that make passage difficult. Request pdf thermodynamics of fluidphase equilibria for standard chemical engineering operations thermodynamics provides one of. Phase equilibria diagram of the system baotio2zno 62.
In general practice it is sufficient to consider only solid and liquid phases, thus pressure is assumed to be constant 1 atm. The solution is at saturation equilibrium solid phase will precipitate and dissolve at same rate. If they all intersect, called triple point, three phases in equilibrium. P i x i h i where p i partial pressure of component i in the vapor phase. Note that the condition of equilibrium implies that there is a temperature and pressure. Lecture notes on phase transformations ju li, university of pennsylvania, 20082010 equilibrium. They refer to the independent chemical species that comprise the system. This means something from the thermodynamics standpoint. Phase equilibria lectures click to view phase equilibria problems click to view. The modules are available for students in future classes and for anyone else that needs to learn to interpret or analyze phase diagrams. Thus a phase diagram can be constructed for a one component system. While this is a complex and challenging area, the use of computational tools has. Tutorial modules for the study of phase equilibrium diagrams. Chem 340 lecture notes 9 fall 20 phase equilibria chap.
This condition, called univariant equilibrium or monovariant equilibrium, is illus trated as lines 1, 2, and 3 separating the single phase fields in fig. Phase equilibria and electrochemical cells notes pdf download. When this point is reached, the temperature must remain constant until one of the phases disappears. In these phase equilibria and electrochemical cells notes pdf, we will study the phase, coexistence of phases, phase diagram, cst and distribution law and concepts of electrochemical cells, electrode potential, electrochemical series and learn about the surface phenomenon, adsorption isotherms, bet equation.
Why shouldnt we be able to calculate phase diagrams. Phase equilibria, phase diagrams and phase transformations. Filled circles represent compounds stable at 1250 c. A typical trajectory of the system solution in the is phase plane is given in fig. Phase equilibria phase equilibria phase equilibrium describes the way phases such as solid, liquid andor gas coexist at some temperatures and pressure, but interchange at others. Introduction introduction, thermodynamics terminology 1 2. So in the earlier part of the course, you went through and saw the macroscopic thermodynamic treatment.
The value of these variables is fixed only by the thermodynamic equilibrium conditions. It is intended for a general audience, and is especially useful as a preparatory course for undergarduate and graduate students who are about to take their first class in thermodynamics. This curve is the pressure exerted by a vapor in thermodynamic equilibrium with its liquid phase at a given temperature in a closed system. This section contains the lecture notes topics of this course. It is a part of a system, uniform through out in chemical composition and physical properties, that is separated a uniform component part of the system that is separated from the other homogeneous parts e. The use of phase diagrams and thermodynamic databases for electronic materials liu, 2003. In the present lecture, we will not be concerned with vle at. Sucrosewater phase diagram sugar 0 20 40 60 80 100 c ocomposition wt% sugar l liquid solution i. Microsoft powerpoint chapter 15 chemical equilibrium.
At equilibrium, the two phases will have the same free energy. Lecture notes on classical mechanics a work in progress daniel arovas department of physics university of california, san diego may 8, 20. N 2o 4g 2no 2g the equilibrium constant with the concentrations of reactants and products expressed in terms of molarity, k c, is. Lecture 9 chemical equilibrium and solution chemistry. For a phase transition, the two phases are in equilibrium. Gy303 petrology lecture reference materials and exercises. At the point tt vapor, liquid and solid coexist in equilibrium. Pdf phase equilibria and crystallography of ceramic oxides. Lectures on mathematical modelling of biological systems. The aim of this lecture is to give an elementary introduction to mathematical models. Twocomponent phase equilibria ii ideal and nonideal solutions. A diagram of the phases as a function of pressure and temperature is called a phase diagram. The established pressure in the gas phase is referred to as the equilibrium vapor pressure, which is normally. For a pure single phase fluid, the equilibrium state of the.
Introduction phase diagrams provide fundamental information on the equilibrium relations among different. What happens when substances change their chemical structure and interchange, and youve figured out how to calculate where equilibrium lies in the case of chemical reactions. Lecture notes on classical mechanics a work in progress. In the fields of the diagram phase fields only one phase exists. An equilibrium is asymptotically stable if tracej 0. Configurational bias and methods for chain molecules. It consists of atoms of at least two different types where solute atoms. Phase equilibria the equilibrium phase is always the one with the lowest free energy g h t s the driving force for a phase change is the minimization of free energy equilibrium state with minimum free energy under some specified combination of temperature, pressure, and composition e.
Phase equilibria phase equilibria phase equilibrium describes the way phases such as solid, liquid andor gas coexist at some temperatures. Thermal insulation in materials processing reactors, melting, quenching and radiative losses at high temperature from furnaces and other reactors. Twocomponent phase equilibria ii ideal and nonideal. First law first law of thermodynamics and its applications 2 3. Download englishus transcript pdf the following content is provided under a creative commons license. In the limit, one talks about a reversible reaction where dips 0. A gas phase equilibrium consider a simple gas phase reaction, the conversion of cis. Application of the thermodynamic concepts to the analysis of phase equilibria, phase transformations, and phase. On the phase boundary two phases are in equilibrium. Physical equilibria our first foray into equilibria is to examine phenomena associated with two phases of matter achieving equilibrium in which the free energy in each phase is the same and there is no change in the overall values of system state functions. Single component phase diagrams the stability of phases can be predicted by the chemical potential, in that the most stable form of the substance will have the minimum chemical potential at the given temperature and pressure. This course, based on matsci 204 thermodynamics and phase equilibria, introduces learners to thermodynamics and and how it governs phase equilibria. To understand and predict the effect mixing substances has on properties such as vapor pressure, boiling point, freezing point, etc.
Phase equilibria in fluid mixtures is a classical problem in the theory of liquids vfiich. Phase equilibria and phase separation proceedings of the 5th. Phase equilibria one component course home syllabus. Binary liquid mixtures vapor pressure for an ideal binary mixture of two volatile liquids, a and b. The system now consists of a liquid phase and a very small amount of gas phase. We use them to find the compositions of the gas and liquid phases at coexistence. K c 2 n o no 2 4 2 gas phase expressions can also be expressed by k p. So, recently youve been looking at chemical equilibria. Pay special attention to the introductory treatment of phases. Calculation of normative mineralogy from chemical analyses of igneous rocks weight % oxides pdf document. Essentials for phase equilibria in materials nptel. Open circles represent compositions of most of the specimens prepared for the study. Criterion for phase equilibrium the thermodynamic criterion for phase equilibrium is simple. Four laws that drive the universe related presentation peter atkins, 2007.
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