Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium
|
|
- Harvey Green
- 6 years ago
- Views:
Transcription
1 Lecture 17: Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS The cmmn tangent cnstructin and the lever rule...3 Practical surces f free energy data...8 INTRODUCTION TO BINARY PHASE DIAGRAMS...9 Phase diagram f an ideal slutin...9 Tie lines and the lever rule n a binary phase diagram...10 BINARY SOLUTIONS WITH LIMITED MISCIBILITY: MISCIBILITY GAPS...11 The Regular Slutin Mdel, part I...11 REFERENCES...14 Reading: Lupis, Chemical Thermdynamics f Materials, Ch 8 Binary Phase Diagrams, pp Supplementary Reading: - Lecture 18 Multi-phase Equilibria 1 f 14 11/6/05
2 Last time Lecture 18 Multi-phase Equilibria 2 f 14 11/6/05
3 Free energy diagrams f multi-phase slutins 1 Last lecture we examined the structure and interpretatin f free energy vs. cmpsitin diagrams fr ideal binary (tw-cmpnent) slutins. The free energy diagrams we intrduced last time can cnveniently be als used t analyze multiphase equilibria that allw us t graphically depict the requirements fr equilibrium. The cmmn tangent cnstructin and the lever rule KEY CONCEPTS: Free energy vs. cmpsitin diagrams are useful tls fr graphically analyzing phase equilibria in binary systems at cnstant pressure. Cmmn tangents between the free energy curves f different phases ccur in regins where 2 phases are in equilibrium. The pints where cmmn tangents tuch the free energy curves identify the cmpsitins f the tw phases in equilibrium. The lever rule is used t determine hw much f each phase is present in tw phase equilibrium regins. Suppse we have a binary ideal slutin f A and B. We shwed last time the shape f the free energy curve fr such a slutin. The mlar free energy fr the slutin can be diagrammed fr different phases f the slutin- fr example the liquid state and the slid state- as a functin f cmpsitin: Suppse we lwered the temperature frm the abve situatin. Hw wuld the tw free energy curves change? Which curve will mve mre, cnsidering that: G = H " TS Lecture 18 Multi-phase Equilibria 3 f 14 11/6/05
4 What is happening in the secnd figure? We have reduced the temperature t the pint where the stable state f pure B is a slid. Remember that the chemical ptential is given by the end- Lecture 18 Multi-phase Equilibria 4 f 14 11/6/05
5 pints f the tangent t the free energy curve at a given cmpsitin. But we find that at T 1, a line can be drawn tangent t bth free energy curves- a line that is tangent t the liquid curve at cmpsitin X L, and the slid curve at X S. Lwering the temperature slightly mre: We find that in the cmpsitin range frm X L t X S, the chemical ptentials f cmpnent A in the slid and liquid states are equal, and the chemical ptentials f B in the slid and liquid states are equal but this is the cnditin fr tw-phase equilibrium! Thus fr cmpsitins between the cmmn tangent pints, tw phases are present in the material, slid and liquid. Why d tw phases c-exist between X S and X L? Let s analyze the blwn-up diagram belw: Lecture 18 Multi-phase Equilibria 5 f 14 11/6/05
6 At cmpsitin X 1, cmparisn f the slid state free energy with that f the liquid shws that the liquid wuld be the frm with lwest free energy- thus the liquid slutin wuld be mre stable than the slid. Hwever, the free energy f the liquid is nt the lwest pssible free energy state. If the A and B atms in the hmgenus liquid slutin re-arrange, a prtin transfrming t a slid with cmpsitin X S and a prtin remaining in a liquid slutin with cmpsitin altered t X L, the hetergeneus slid/liquid mixture takes n the free energy G sep, which is lwer than that f the hmgeneus liquid slutin at X 1. f L and f S are the phase fractins f liquid and slid phases, respectively. Nte that because a hetergeneus (2- phase) mixture is being frmed, the free energy is determined in a manner similar t that discussed earlier fr hetergeneus mixtures (e.g. ur blck f Si in cntact with a blck f Ge)- simply a weighted average f the mlar free energies f the liquid phase (cmpsitin X L ) and the slid phase (cmpsitin X S ). Lecture 18 Multi-phase Equilibria 6 f 14 11/6/05
7 Hw much slid phase frms? Hw much liquid is present? The cmpsitin f the liquid phase is X L, and the cmpsitin f the slid phase is X S. Therefre, the amunt f each phase present can be determined simply by requiring that the average cmpsitin f the system remains X 1 : Similarly, if we write X 1 in terms f f S we btain: These tw equatins fr the fractin f slid and liquid frmed have a graphical equivalent: The mathematical and graphical cnstructin t identify the fractin f each phase is knwn as the lever rule. Lecture 18 Multi-phase Equilibria 7 f 14 11/6/05
8 Practical surces f free energy data Where d we get the infrmatin fr these diagrams? Natinal Institute f Standards and Technlgy Chemistry WebBk heat capacity, enthalpy, and entrpy data JANAF Tables Jint Army Navy Air Frce database f thermchemical data Exhaustive Cp, entrpy, enthalpy, free energy data QD511.J Selected Values f Thermdynamic Prperties f Metals and Allys R. Hultgren, R.L. Orr, P.D. Andersn, and K.K. Kelley Jhn Wiley, NY 1963 QD171.S44 Therm-Calc Sftware available n Athena fr perfrming many thermdynamic calculatins, building phase diagrams, etc. Lecture 18 Multi-phase Equilibria 8 f 14 11/6/05
9 Intrductin t binary phase diagrams KEY CONCEPTS: The phase equilibria as a functin f cmpsitin fr a fixed temperature (and fixed pressure) predicted by Free energy vs. cmpsitin diagrams can be cllated t create a binary phase diagram, which maps ut stable phases in T vs. cmpsitin space (pressure assume fixed) the binary system analg f single cmpnent phase diagrams. The Gibbs phase rule can be applied t these diagrams, accunting fr the fixed pressure (D + P = C + 1). Tie lines allw the lever rule t be directly applied t phase diagrams in rder t calculate the amunt f each phase present in multiphase equilibria. Phase diagram f an ideal slutin Frm an examinatin f free energy vs. cmpsitin diagrams, we fund that phase separatin (induced fr example by reducing the temperature and freezing a liquid slutin) prceeds by the fllwing prgressin acrss the cmpsitin windw f an ideal binary slutin (Fr a system where T m,b > T m,a ): T > T m,b > T m,a T = T m,b > T m,a T m,b > T 1 > T m,a T m,b > T 1 > T 2 > T m,a T m,b > T 2 > T 3 > T m,a T m,b > T = T m,a It wuld make sense t btain a cntinuus map f the phases present as a functin f X B and temperature fr a binary system: such a map is a key tl in materials science & engineering and is knwn as a binary phase diagram. Fr the ideal binary slutin we have been analyzing, the phase diagram lks like this: Lecture 18 Multi-phase Equilibria 9 f 14 11/6/05
10 P = cnstant T m (pure B) T = T 1 T Hmgeneus liquid mixture tw-phase regin T = T 2 T m (pure A) Hmgeneus slid mixture K B Figure by MIT OCW. This is the simplest frm a binary phase diagram can take. Tie lines and the lever rule n a binary phase diagram The lever rule that we develped using free energy vs. cmpsitin diagrams can be directly applied t a binary phase diagram (T vs. cmpsitin). This is dne using tie lines hrizntal istherms cnnecting the bundaries f a tw-phase regin: Lecture 18 Multi-phase Equilibria 10 f 14 11/6/05
11 Binary slutins with limited miscibility: Miscibility gaps The Regular Slutin Mdel, part I What happens if the mlecules in the slutin interact with a finite energy? The enthalpy f mixing will nw have a finite value, either favring ( "H mix < 0) r disfavring ( "H mix > 0) mixing f the tw cmpnents. The simplest mdel f a slutin with finite interactins is called the regular slutin mdel: Let the enthalpy f mixing take n a finite value given by: We take the entrpy f mixing t be the same as in the ideal slutin. This gives a ttal free energy f mixing which is: The regular slutin mdel describes the liquid phase f many real systems such as Pb-Sn, Ga- Sb, and Tl-Sn, and sme slid slutins. Tday we will analyze the behavir f a system with this free energy functin; in a few lectures we will shw hw the given frms f the enthalpy and entrpy f mixing arise frm cnsideratin f mlecular states (using statistical mechanics). Lecture 18 Multi-phase Equilibria 11 f 14 11/6/05
12 T=100 K " = 20,000 J/mle!H mix,rs " = 10,000 J/mle " = -10,000 J/mle XB X B The verall free energy f mixing arises frm the balance between favrable mixing entrpy and unfavrable enthalpy cntributins: Lecture 18 Multi-phase Equilibria 12 f 14 11/6/05
13 80000 T=100 K " = 20,000 J/mle #!S mix,rs !H mix,rs !G mix,rs X B The free energy f the system varies with the value f Ω and with temperature: As a functin f temperature at a fixed psitive value f Ω: Lecture 18 Multi-phase Equilibria 13 f 14 11/6/05
14 References 1. Carter, W. C Thermdynamics f Materials Lecture Ntes (2002). Lecture 18 Multi-phase Equilibria 14 f 14 11/6/05
Lecture 13: Electrochemical Equilibria
3.012 Fundamentals f Materials Science Fall 2005 Lecture 13: 10.21.05 Electrchemical Equilibria Tday: LAST TIME...2 An example calculatin...3 THE ELECTROCHEMICAL POTENTIAL...4 Electrstatic energy cntributins
More informationThermodynamics and Equilibrium
Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,
More informationAP CHEMISTRY CHAPTER 6 NOTES THERMOCHEMISTRY
AP CHEMISTRY CHAPTER 6 NOTES THERMOCHEMISTRY Energy- the capacity t d wrk r t prduce heat 1 st Law f Thermdynamics: Law f Cnservatin f Energy- energy can be cnverted frm ne frm t anther but it can be neither
More informationChapters 29 and 35 Thermochemistry and Chemical Thermodynamics
Chapters 9 and 35 Thermchemistry and Chemical Thermdynamics 1 Cpyright (c) 011 by Michael A. Janusa, PhD. All rights reserved. Thermchemistry Thermchemistry is the study f the energy effects that accmpany
More informationSpontaneous Processes, Entropy and the Second Law of Thermodynamics
Chemical Thermdynamics Spntaneus Prcesses, Entrpy and the Secnd Law f Thermdynamics Review Reactin Rates, Energies, and Equilibrium Althugh a reactin may be energetically favrable (i.e. prducts have lwer
More informationLecture 23: Lattice Models of Materials; Modeling Polymer Solutions
Lecture 23: 12.05.05 Lattice Mdels f Materials; Mdeling Plymer Slutins Tday: LAST TIME...2 The Bltzmann Factr and Partitin Functin: systems at cnstant temperature...2 A better mdel: The Debye slid...3
More informationAppendix I: Derivation of the Toy Model
SPEA ET AL.: DYNAMICS AND THEMODYNAMICS OF MAGMA HYBIDIZATION Thermdynamic Parameters Appendix I: Derivatin f the Ty Mdel The ty mdel is based upn the thermdynamics f an isbaric twcmpnent (A and B) phase
More informationALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?
Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S
More informationLecture 12: Chemical reaction equilibria
3.012 Fundamentals f Materials Science Fall 2005 Lecture 12: 10.19.05 Chemical reactin equilibria Tday: LAST TIME...2 EQUATING CHEMICAL POTENTIALS DURING REACTIONS...3 The extent f reactin...3 The simplest
More informationMore Tutorial at
Answer each questin in the space prvided; use back f page if extra space is needed. Answer questins s the grader can READILY understand yur wrk; nly wrk n the exam sheet will be cnsidered. Write answers,
More informationLecture 24: Flory-Huggins Theory
Lecture 24: 12.07.05 Flry-Huggins Thery Tday: LAST TIME...2 Lattice Mdels f Slutins...2 ENTROPY OF MIXING IN THE FLORY-HUGGINS MODEL...3 CONFIGURATIONS OF A SINGLE CHAIN...3 COUNTING CONFIGURATIONS FOR
More informationPart One: Heat Changes and Thermochemistry. This aspect of Thermodynamics was dealt with in Chapter 6. (Review)
CHAPTER 18: THERMODYNAMICS AND EQUILIBRIUM Part One: Heat Changes and Thermchemistry This aspect f Thermdynamics was dealt with in Chapter 6. (Review) A. Statement f First Law. (Sectin 18.1) 1. U ttal
More informationChapter 4 Thermodynamics and Equilibrium
Chapter Thermdynamics and Equilibrium Refer t the fllwing figures fr Exercises 1-6. Each represents the energies f fur mlecules at a given instant, and the dtted lines represent the allwed energies. Assume
More informationUnit 14 Thermochemistry Notes
Name KEY Perid CRHS Academic Chemistry Unit 14 Thermchemistry Ntes Quiz Date Exam Date Lab Dates Ntes, Hmewrk, Exam Reviews and Their KEYS lcated n CRHS Academic Chemistry Website: https://cincchem.pbwrks.cm
More information" 1 = # $H vap. Chapter 3 Problems
Chapter 3 rblems rblem At 1 atmsphere pure Ge melts at 1232 K and bils at 298 K. he triple pint ccurs at =8.4x1-8 atm. Estimate the heat f vaprizatin f Ge. he heat f vaprizatin is estimated frm the Clausius
More informationSupporting information
Electrnic Supplementary Material (ESI) fr Physical Chemistry Chemical Physics This jurnal is The wner Scieties 01 ydrgen perxide electrchemistry n platinum: twards understanding the xygen reductin reactin
More informationChapter 17: Thermodynamics: Spontaneous and Nonspontaneous Reactions and Processes
Chapter 17: hermdynamics: Spntaneus and Nnspntaneus Reactins and Prcesses Learning Objectives 17.1: Spntaneus Prcesses Cmparing and Cntrasting the hree Laws f hermdynamics (1 st Law: Chap. 5; 2 nd & 3
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationEntropy, Free Energy, and Equilibrium
Nv. 26 Chapter 19 Chemical Thermdynamics Entrpy, Free Energy, and Equilibrium Nv. 26 Spntaneus Physical and Chemical Prcesses Thermdynamics: cncerned with the questin: can a reactin ccur? A waterfall runs
More informationChapter 17 Free Energy and Thermodynamics
Chemistry: A Mlecular Apprach, 1 st Ed. Nivald Tr Chapter 17 Free Energy and Thermdynamics Ry Kennedy Massachusetts Bay Cmmunity Cllege Wellesley Hills, MA 2008, Prentice Hall First Law f Thermdynamics
More information( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s
.9 Kinetic Mlecular Thery Calculate the effective (rms) speeds f the He and Ne atms in the He-Ne gas laser tube at rm temperature (300 K). Slutin T find the rt mean square velcity (v rms ) f He atms at
More informationUniversity Chemistry Quiz /04/21 1. (10%) Consider the oxidation of ammonia:
University Chemistry Quiz 3 2015/04/21 1. (10%) Cnsider the xidatin f ammnia: 4NH 3 (g) + 3O 2 (g) 2N 2 (g) + 6H 2 O(l) (a) Calculate the ΔG fr the reactin. (b) If this reactin were used in a fuel cell,
More informationChE 471: LECTURE 4 Fall 2003
ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.
More informationCHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review
Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system
More informationGeneral Chemistry II, Unit II: Study Guide (part 1)
General Chemistry II, Unit II: Study Guide (part 1) CDS Chapter 21: Reactin Equilibrium in the Gas Phase General Chemistry II Unit II Part 1 1 Intrductin Sme chemical reactins have a significant amunt
More informationCHEM 116 Electrochemistry at Non-Standard Conditions, and Intro to Thermodynamics
CHEM 116 Electrchemistry at Nn-Standard Cnditins, and Intr t Thermdynamics Imprtant annuncement: If yu brrwed a clicker frm me this semester, return it t me at the end f next lecture r at the final exam
More informationChem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra
Chem 115 POGIL Wrksheet - Week 8 Thermchemistry (Cntinued), Electrmagnetic Radiatin, and Line Spectra Why? As we saw last week, enthalpy and internal energy are state functins, which means that the sum
More informationlecture 5: Nucleophilic Substitution Reactions
lecture 5: Nuclephilic Substitutin Reactins Substitutin unimlecular (SN1): substitutin nuclephilic, unimlecular. It is first rder. The rate is dependent upn ne mlecule, that is the substrate, t frm the
More informationChem 75 February 16, 2017 Exam 2 Solutions
1. (6 + 6 pints) Tw quick questins: (a) The Handbk f Chemistry and Physics tells us, crrectly, that CCl 4 bils nrmally at 76.7 C, but its mlar enthalpy f vaprizatin is listed in ne place as 34.6 kj ml
More informationRevision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax
.7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical
More informationFebruary 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA
February 28, 2013 COMMENTS ON DIFFUSION, DIFFUSIVITY AND DERIVATION OF HYPERBOLIC EQUATIONS DESCRIBING THE DIFFUSION PHENOMENA Mental Experiment regarding 1D randm walk Cnsider a cntainer f gas in thermal
More information**DO NOT ONLY RELY ON THIS STUDY GUIDE!!!**
Tpics lists: UV-Vis Absrbance Spectrscpy Lab & ChemActivity 3-6 (nly thrugh 4) I. UV-Vis Absrbance Spectrscpy Lab Beer s law Relates cncentratin f a chemical species in a slutin and the absrbance f that
More informationA.P. CHEMISTRY. SOLUTIONS AND ACID BASE CHEMISTRY. p 1
A.P. CHEMISTRY. SOLUTIONS AND ACID BASE CHEMISTRY. p 1 (Nte: questins 1 t 14 are meant t be dne WITHOUT calculatrs!) 1.Which f the fllwing is prbably true fr a slid slute with a highly endthermic heat
More informationCHAPTER PRACTICE PROBLEMS CHEMISTRY
Chemical Kinetics Name: Batch: Date: Rate f reactin. 4NH 3 (g) + 5O (g) à 4NO (g) + 6 H O (g) If the rate f frmatin f NO is 3.6 0 3 ml L s, calculate (i) the rate f disappearance f NH 3 (ii) rate f frmatin
More informationLecture 6: Phase Space and Damped Oscillations
Lecture 6: Phase Space and Damped Oscillatins Oscillatins in Multiple Dimensins The preius discussin was fine fr scillatin in a single dimensin In general, thugh, we want t deal with the situatin where:
More informationRecitation 06. n total = P total V/RT = (0.425 atm * 10.5 L) / ( L atm mol -1 K -1 * 338 K) = mol
Recitatin 06 Mixture f Ideal Gases 1. Chapter 5: Exercise: 69 The partial pressure f CH 4 (g) is 0.175 atm and that f O 2 (g) is 0.250 atm in a mixture f the tw gases. a. What is the mle fractin f each
More informationGeneral Chemistry II, Unit I: Study Guide (part I)
1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the
More informationBootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >
Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);
More informationCHEM 116 Concentrations and Colligative Properties
UMass stn, Chem 116 CHEM 116 Cncentratins and Clligative Prperties FSG is Mndays 11:00 am Lecture 10 Prf. Sevian and Tuesdays 3:30 pm bth in S-1-89 Tday s agenda Ways f expressing cncentratin Clligative
More informationCHAPTER Read Chapter 17, sections 1,2,3. End of Chapter problems: 25
CHAPTER 17 1. Read Chapter 17, sectins 1,2,3. End f Chapter prblems: 25 2. Suppse yu are playing a game that uses tw dice. If yu cunt the dts n the dice, yu culd have anywhere frm 2 t 12. The ways f prducing
More informationChapter 8 Reduction and oxidation
Chapter 8 Reductin and xidatin Redx reactins and xidatin states Reductin ptentials and Gibbs energy Nernst equatin Disprprtinatin Ptential diagrams Frst-Ebswrth diagrams Ellingham diagrams Oxidatin refers
More informationDepartment of Economics, University of California, Davis Ecn 200C Micro Theory Professor Giacomo Bonanno. Insurance Markets
Department f Ecnmics, University f alifrnia, Davis Ecn 200 Micr Thery Prfessr Giacm Bnann Insurance Markets nsider an individual wh has an initial wealth f. ith sme prbability p he faces a lss f x (0
More informationDetermining the Accuracy of Modal Parameter Estimation Methods
Determining the Accuracy f Mdal Parameter Estimatin Methds by Michael Lee Ph.D., P.E. & Mar Richardsn Ph.D. Structural Measurement Systems Milpitas, CA Abstract The mst cmmn type f mdal testing system
More informationFind this material useful? You can help our team to keep this site up and bring you even more content consider donating via the link on our site.
Find this material useful? Yu can help ur team t keep this site up and bring yu even mre cntent cnsider dnating via the link n ur site. Still having truble understanding the material? Check ut ur Tutring
More informationIntelligent Pharma- Chemical and Oil & Gas Division Page 1 of 7. Global Business Centre Ave SE, Calgary, AB T2G 0K6, AB.
Intelligent Pharma- Chemical and Oil & Gas Divisin Page 1 f 7 Intelligent Pharma Chemical and Oil & Gas Divisin Glbal Business Centre. 120 8 Ave SE, Calgary, AB T2G 0K6, AB. Canada Dr. Edelsys Cdrniu-Business
More informationUnit 11 Solutions- Guided Notes. What are alloys? What is the difference between heterogeneous and homogeneous mixtures?
Name: Perid: Unit 11 Slutins- Guided Ntes Mixtures: What is a mixture and give examples? What is a pure substance? What are allys? What is the difference between hetergeneus and hmgeneus mixtures? Slutins:
More informationChemistry 20 Lesson 11 Electronegativity, Polarity and Shapes
Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin
More informationTypes of Energy COMMON MISCONCEPTIONS CHEMICAL REACTIONS INVOLVE ENERGY
CHEMICAL REACTIONS INVOLVE ENERGY The study energy and its transrmatins is knwn as thermdynamics. The discussin thermdynamics invlve the cncepts energy, wrk, and heat. Types Energy Ptential energy is stred
More informationDispersion Ref Feynman Vol-I, Ch-31
Dispersin Ref Feynman Vl-I, Ch-31 n () = 1 + q N q /m 2 2 2 0 i ( b/m) We have learned that the index f refractin is nt just a simple number, but a quantity that varies with the frequency f the light.
More informationChem 116 POGIL Worksheet - Week 3 - Solutions Intermolecular Forces, Liquids, Solids, and Solutions
Chem 116 POGIL Wrksheet - Week 3 - Slutins Intermlecular Frces, Liquids, Slids, and Slutins Key Questins 1. Is the average kinetic energy f mlecules greater r lesser than the energy f intermlecular frces
More informationEdexcel IGCSE Chemistry. Topic 1: Principles of chemistry. Chemical formulae, equations and calculations. Notes.
Edexcel IGCSE Chemistry Tpic 1: Principles f chemistry Chemical frmulae, equatins and calculatins Ntes 1.25 write wrd equatins and balanced chemical equatins (including state symbls): fr reactins studied
More informationPhys102 Final-061 Zero Version Coordinator: Nasser Wednesday, January 24, 2007 Page: 1
Crdinatr: Nasser Wednesday, January 4, 007 Page: 1 Q1. Tw transmitters, S 1 and S shwn in the figure, emit identical sund waves f wavelength λ. The transmitters are separated by a distance λ /. Cnsider
More informationPressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects
Pressure And Entrpy Variatins Acrss The Weak Shck Wave Due T Viscsity Effects OSTAFA A. A. AHOUD Department f athematics Faculty f Science Benha University 13518 Benha EGYPT Abstract:-The nnlinear differential
More informationCHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India
CHAPTER 3 INEQUALITIES Cpyright -The Institute f Chartered Accuntants f India INEQUALITIES LEARNING OBJECTIVES One f the widely used decisin making prblems, nwadays, is t decide n the ptimal mix f scarce
More informationAP Statistics Notes Unit Two: The Normal Distributions
AP Statistics Ntes Unit Tw: The Nrmal Distributins Syllabus Objectives: 1.5 The student will summarize distributins f data measuring the psitin using quartiles, percentiles, and standardized scres (z-scres).
More informationExamples: 1. How much heat is given off by a 50.0 g sample of copper when it cools from 80.0 to 50.0 C?
NOTES: Thermchemistry Part 1 - Heat HEAT- TEMPERATURE - Thermchemistry: the study f energy (in the frm f heat) changes that accmpany physical & chemical changes heat flws frm high t lw (ht cl) endthermic
More informationChem 116 POGIL Worksheet - Week 4 Properties of Solutions
Chem 116 POGIL Wrksheet - Week 4 Prperties f Slutins Key Questins 1. Identify the principal type f slute-slvent interactin that is respnsible fr frming the fllwing slutins: (a) KNO 3 in water; (b) Br 2
More informationCHAPTER 13 Temperature and Kinetic Theory. Units
CHAPTER 13 Temperature and Kinetic Thery Units Atmic Thery f Matter Temperature and Thermmeters Thermal Equilibrium and the Zerth Law f Thermdynamics Thermal Expansin Thermal Stress The Gas Laws and Abslute
More informationPattern Recognition 2014 Support Vector Machines
Pattern Recgnitin 2014 Supprt Vectr Machines Ad Feelders Universiteit Utrecht Ad Feelders ( Universiteit Utrecht ) Pattern Recgnitin 1 / 55 Overview 1 Separable Case 2 Kernel Functins 3 Allwing Errrs (Sft
More informationMaterials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion
Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals f Diffusin Diffusin: Transprt in a slid, liquid, r gas driven by a cncentratin gradient (r, in the case f mass transprt, a chemical ptential
More informationDr M. BROUARD. 5. Thermodynamic formulation of Transition State Theory Entropy of activation. Thermochemical kinetics. CHEMICAL REACTION RATES
CHEMICAL REACTION RATES Dr M. BROUARD Trinity Term 2003 A. Bimlecular Reactins 5 Lectures 1. Intrductin Simple cllisin thery. Ptential energy curves and surfaces. The reactin crdinate and barriers t reactin.
More information5.60 Thermodynamics & Kinetics Spring 2008
MIT OpenCurseWare http://cw.mit.edu 5.60 Thermdynamics & Kinetics Spring 2008 Fr infrmatin abut citing these materials r ur Terms f Use, visit: http://cw.mit.edu/terms. 5.60 Spring 2008 Lecture #17 page
More informationA Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture
Few asic Facts but Isthermal Mass Transfer in a inary Miture David Keffer Department f Chemical Engineering University f Tennessee first begun: pril 22, 2004 last updated: January 13, 2006 dkeffer@utk.edu
More informationIn the spaces provided, explain the meanings of the following terms. You may use an equation or diagram where appropriate.
CEM1405 2007-J-2 June 2007 In the spaces prvided, explain the meanings f the fllwing terms. Yu may use an equatin r diagram where apprpriate. 5 (a) hydrgen bnding An unusually strng diple-diple interactin
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More informationEntropy. Chapter The Clausius Inequality and Entropy
Chapter 7 Entrpy In the preceding chapter we btained a number f imprtant results by applying the secnd law t cyclic prcesses assciated with heat engines and reversed heat engines perating with ne and tw
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationVerification of Quality Parameters of a Solar Panel and Modification in Formulae of its Series Resistance
Verificatin f Quality Parameters f a Slar Panel and Mdificatin in Frmulae f its Series Resistance Sanika Gawhane Pune-411037-India Onkar Hule Pune-411037- India Chinmy Kulkarni Pune-411037-India Ojas Pandav
More informationLim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?
THESE ARE SAMPLE QUESTIONS FOR EACH OF THE STUDENT LEARNING OUTCOMES (SLO) SET FOR THIS COURSE. SLO 1: Understand and use the cncept f the limit f a functin i. Use prperties f limits and ther techniques,
More informationx x
Mdeling the Dynamics f Life: Calculus and Prbability fr Life Scientists Frederick R. Adler cfrederick R. Adler, Department f Mathematics and Department f Bilgy, University f Utah, Salt Lake City, Utah
More informationMatter Content from State Frameworks and Other State Documents
Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with
More informationElectrochemistry. Reduction: the gaining of electrons. Reducing agent (reductant): species that donates electrons to reduce another reagent.
Electrchemistry Review: Reductin: the gaining f electrns Oxidatin: the lss f electrns Reducing agent (reductant): species that dnates electrns t reduce anther reagent. Oxidizing agent (xidant): species
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs
More informationPhys. 344 Ch 7 Lecture 8 Fri., April. 10 th,
Phys. 344 Ch 7 Lecture 8 Fri., April. 0 th, 009 Fri. 4/0 8. Ising Mdel f Ferrmagnets HW30 66, 74 Mn. 4/3 Review Sat. 4/8 3pm Exam 3 HW Mnday: Review fr est 3. See n-line practice test lecture-prep is t
More informationProcess Engineering Thermodynamics E (4 sp) Exam
Prcess Engineering Thermdynamics 42434 E (4 sp) Exam 9-3-29 ll supprt material is allwed except fr telecmmunicatin devices. 4 questins give max. 3 pints = 7½ + 7½ + 7½ + 7½ pints Belw 6 questins are given,
More information(Communicated at the meeting of January )
Physics. - Establishment f an Abslute Scale fr the herm-electric Frce. By G. BOR ELlUS. W. H. KEESOM. C. H. JOHANSSON and J. O. LND E. Supplement N0. 69b t the Cmmunicatins frm the Physical Labratry at
More informationSurface and Contact Stress
Surface and Cntact Stress The cncept f the frce is fundamental t mechanics and many imprtant prblems can be cast in terms f frces nly, fr example the prblems cnsidered in Chapter. Hwever, mre sphisticated
More informationAutumn 2012 CHEM452B Bruce H. Robinson 322 Gould Hall HW 10(A) Homework 10A KEY (there will not be a 10B) 2
Autumn 0 CHEM45B Bruce H. Rbinsn Guld Hall HW 0(A) Hmewrk 0A KEY (there will nt be a 0B) QA) Let c be the speed f sund in air. he square f the speed f sund, () f the gas with respect t the change in the
More informationMANIPAL INSTITUTE OF TECHNOLOGY
MANIPAL INSTITUTE OF TECHNOLOGY MANIPAL UNIVERSITY, MANIPAL SECOND SEMESTER B.Tech. END-SEMESTER EXAMINATION - MAY 013 SUBJECT: ENGINEERING PHYSICS (PHY101/10) Time: 3 Hrs. Max. Marks: 50 Nte: Answer any
More informationName: Period: Date: BONDING NOTES HONORS CHEMISTRY
Name: Perid: Date: BONDING NOTES HONORS CHEMISTRY Directins: This packet will serve as yur ntes fr this chapter. Fllw alng with the PwerPint presentatin and fill in the missing infrmatin. Imprtant terms
More informationOF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION
U. S. FOREST SERVICE RESEARCH PAPER FPL 50 DECEMBER U. S. DEPARTMENT OF AGRICULTURE FOREST SERVICE FOREST PRODUCTS LABORATORY OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION
More informationEdexcel GCSE Physics
Edexcel GCSE Physics Tpic 10: Electricity and circuits Ntes (Cntent in bld is fr Higher Tier nly) www.pmt.educatin The Structure f the Atm Psitively charged nucleus surrunded by negatively charged electrns
More informationPhysical Nature of the Covalent Bond Appendix H + H > H 2 ( ) ( )
Physical Nature f the Cvalent Bn Appeni his stuy f the nature f the H cvalent bn frms a mlecular rbital as a linear cmbinatin f scale hyrgenic rbitals, LCAO-MO. he quantum mechanical integrals necessary
More informationSession #22: Homework Solutions
Sessin #22: Hmewrk Slutins Prblem #1 (a) In the cntext f amrphus inrganic cmpunds, name tw netwrk frmers, tw netwrk mdifiers, and ne intermediate. (b) Sketch the variatin f mlar vlume with temperature
More informationDifferentiation Applications 1: Related Rates
Differentiatin Applicatins 1: Related Rates 151 Differentiatin Applicatins 1: Related Rates Mdel 1: Sliding Ladder 10 ladder y 10 ladder 10 ladder A 10 ft ladder is leaning against a wall when the bttm
More informationLCAO APPROXIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (cation, anion or radical).
Principles f Organic Chemistry lecture 5, page LCAO APPROIMATIONS OF ORGANIC Pi MO SYSTEMS The allyl system (catin, anin r radical).. Draw mlecule and set up determinant. 2 3 0 3 C C 2 = 0 C 2 3 0 = -
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationThermochemistry. Thermochemistry
Thermchemistry Petrucci, Harwd and Herring: Chapter 7 CHEM 1000A 3.0 Thermchemistry 1 Thermchemistry The study energy in chemical reactins A sub-discipline thermdynamics Thermdynamics studies the bulk
More information2.161 Signal Processing: Continuous and Discrete Fall 2008
MIT OpenCurseWare http://cw.mit.edu 2.161 Signal Prcessing: Cntinuus and Discrete Fall 2008 Fr infrmatin abut citing these materials r ur Terms f Use, visit: http://cw.mit.edu/terms. Massachusetts Institute
More informationBASIC DIRECT-CURRENT MEASUREMENTS
Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard
More informationTheoretical study of third virial coefficient with Kihara potential
Theretical study f third virial cefficient with Kihara ptential Jurnal: Manuscript ID cjp-017-0705.r Manuscript Type: Article Date Submitted by the Authr: 6-Dec-017 Cmplete List f Authrs: Smuncu E.; Giresun
More informationMath 105: Review for Exam I - Solutions
1. Let f(x) = 3 + x + 5. Math 105: Review fr Exam I - Slutins (a) What is the natural dmain f f? [ 5, ), which means all reals greater than r equal t 5 (b) What is the range f f? [3, ), which means all
More information22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion
.54 Neutrn Interactins and Applicatins (Spring 004) Chapter (3//04) Neutrn Diffusin References -- J. R. Lamarsh, Intrductin t Nuclear Reactr Thery (Addisn-Wesley, Reading, 966) T study neutrn diffusin
More informationElectric Current and Resistance
Electric Current and Resistance Electric Current Electric current is the rate f flw f charge thrugh sme regin f space The SI unit f current is the ampere (A) 1 A = 1 C / s The symbl fr electric current
More informationStudy Group Report: Plate-fin Heat Exchangers: AEA Technology
Study Grup Reprt: Plate-fin Heat Exchangers: AEA Technlgy The prblem under study cncerned the apparent discrepancy between a series f experiments using a plate fin heat exchanger and the classical thery
More informationCHM112 Lab Graphing with Excel Grading Rubric
Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline
More informationExperiment #3. Graphing with Excel
Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-
More informationLecture 4. The First Law of Thermodynamics
Lecture 4. The First Law f Thermdynamics THERMODYNAMICS: Basic Cncepts Thermdynamics: (frm the Greek therme, meaning "heat" and, dynamis, meaning "pwer") is the study f energy cnversin between heat and
More informationTHE LIFE OF AN OBJECT IT SYSTEMS
THE LIFE OF AN OBJECT IT SYSTEMS Persns, bjects, r cncepts frm the real wrld, which we mdel as bjects in the IT system, have "lives". Actually, they have tw lives; the riginal in the real wrld has a life,
More informationES201 - Examination 2 Winter Adams and Richards NAME BOX NUMBER
ES201 - Examinatin 2 Winter 2003-2004 Adams and Richards NAME BOX NUMBER Please Circle One : Richards (Perid 4) ES201-01 Adams (Perid 4) ES201-02 Adams (Perid 6) ES201-03 Prblem 1 ( 12 ) Prblem 2 ( 24
More information