Lecture 3: Diffusion: Fick s first law


 Jonathan Goodwin
 2 years ago
 Views:
Transcription
1 Lctur 3: Diffusion: Fick s first law Today s topics What is diffusion? What drivs diffusion to occur? Undrstand why diffusion can surprisingly occur against th concntration gradint? Larn how to dduc th Fick s first law, and undrstand th maning of diffusion cofficint and diffusion lngth. In last two lcturs, w larnd th thrmodynamics, concrnd mainly with stabl or quilibrium systms. Th study of matrials Kintics, lik phas transformation, concrns thos mchanism by which a systm attmpts to rach th quilibrium stat and how long it taks. On of th most fundamntal procsss that control th rat at which many transformation occur is th diffusion, as w will larn in th following svral lcturs and us throughout th whol smstr. Gnral rviw of diffusion: Diffusion dscribs th sprad of particls (which can also b atoms, molculs) through random motion usually (but not always) from rgions of highr concntration to rgions of lowr concntration. Th tim dpndnc of th statistical distribution in spac is givn by th diffusion quation. Th concpt of diffusion is tid to that of mass transfr drivn by a concntration gradint, but diffusion can still occur whn thr is no concntration gradint (but thr will b no nt flux). History: Th concpt of diffusion mrgd from physical scincs. Th paradigmatic xampls wr hat diffusion, molcular diffusion and rownian motion. Thir mathmatical dscription was laboratd by Josph Fourir in 8, dolf Fick in 855 and by lbrt Einstin in 905. Spcifically, atomic diffusion is a diffusion procss whrby th random thrmallyactivatd movmnt of atoms in a solid rsults in th nt transport of atoms. For xampl, hlium atoms insid a balloon can diffus through th wall of th balloon and scap, rsulting in th balloon slowly dflating. Othr air molculs (.g. oxygn, nitrogn) hav lowr mobilitis and thus diffus mor slowly through th balloon wall. Thr is a concntration gradint in th balloon wall, bcaus th balloon was initially filld with hlium, and thus thr is plnty of hlium on th insid, but thr is rlativly littl hlium on th outsid (hlium is not a major componnt of air). Th rat of transport is govrnd by th diffusivity and th concntration gradint. Diffusion in solid: In th crystal solid stat, diffusion within th crystal lattic occurs by ithr intrstitial or substitutional mchanisms and is rfrrd to as lattic diffusion. In intrstitial lattic diffusion, a diffusant (such as C in an iron alloy), will diffus in btwn th lattic structur of anothr crystallin lmnt. In substitutional lattic diffusion (slfdiffusion for xampl), th
2 atom can only mov by substituting plac with anothr atom. Substitutional lattic diffusion is oftn contingnt upon th availability of point vacancis throughout th crystal lattic. Diffusing particls migrat from point vacancy to point vacancy by th rapid, ssntially random jumping about (jump diffusion). S blow in this Lctur for dtails about intrstitial or substitutional. Diffusion is drivn by dcras in Gibbs fr nrgy or chmical potntial diffrnc. s a simpl illustration of this, considr th figur blow, whr two blocks of th sam  solid solution, but with diffrnt compositions (concntrations), ar wldd togthr and hld at a tmpratur high nough for long rang diffusion to occur. Cas : along concntration gradint  rich  rich μ G G a G μ G m For cas : μ > μ > => gos from to => gos from to Th molar fr nrgy diagram of th  alloy is shown at right: th molar fr nrgy of ach part is givn by G and G, and th initial total fr nrgy of th wldd block is G a, upon th diffusion as illustratd on th lft (so as to liminat th concntration diffrnc), th total fr nrgy dcrass towards G m, th fr nrgy charactristic of a homognous systm. In this cas, th dcras in fr nrgy is producd by and diffusion along th concntration gradint. Howvr, diffusion nds not always b along th concntration gradint. For xampl, in th alloy systms that contain a miscibility gap, th fr nrgy curv can hav a ngativ curvatur at low tmpratur, as shown blow in Cas. In such a cas, and atoms would diffus against th concntration gradint (i.., toward th rgions of high concntration as shown at lft blow), though this diffusion is still a natural (spontanous) procss as it rducs th total fr nrgy from G a to G m as shown. For cas : μ > μ > => gos from to => gos from to
3 Cas : against concntration gradint  rich  rich μ G G a G μ G m Diffusion is always along chmical potntial gradint! Diffusion stops whn chmical potntial of all spcis vrywhr ar sam. In most cass, chmical potntial incrass with incrasing concntration, so it is convnint to xprss diffusion in trm of concntration. Now lts considr Intrstitial diffusion vs. Substitutional diffusion: Intrstitial Substitutional (by vacancy) Considrd at low concntration Now Lt s dduc th Diffusion Equation for intrstitial diffusion basd on th following illustration, moving from position to. 3
4 x x+a c (x) ~ concntration at x, dc c (x+a) = c(x) + a ~ concntration at x+a μ(x) ~ chmical potntial at x, ΔG ~ activation barrir d µ( x) μ(x+a) =μ(x) + a ~ chmical potntial at x+a Th forward rat  G G ; RT  s last Lctur for how to dduc this quation with an assumption that ΔG << RT, and this is usually tru for diffusion, whr th fr nrgy chang within short distanc is small. ΔG = G (x+a)  G (x) = μ(x+a)  μ(x) (hr ΔG is only contributd by th chang in chmical potntial ) Now G RT = µ ( x + a) µ ( x) a dµ = RT RT RT d µ( x) (as dfind abov, μ(x+a) =μ(x) + a ) Lt ν b vibrational frquncy, thn an atom will hav nough nrgy in unit tim (pr scond) to ovrcom th barrir ν can dfin as Γ.  G tims, i.., th numbr of jump of stp a pr scond, which w Γ = ν  G In a thrdimnsional spac (lattic), an atom can jump in six quivalnt dirctions (±x, ±y, ±z), ν so th numbr of jumps toward right (along x ) in on scond is. So, th nt forward rat for an atom to jump from x to x+a is 4
5 Rat = ν a dµ dµ ( ) (whr <0) RT Lt n(x) b th numbr of atoms (solut) pr unit ara at x, thn th nt flux along x. (i.., numbr of atom passing through unit ara in unit tim along x ) is ν J = n(x) a dµ ( ) () RT Sinc n(x) = a c(x), Eq. () can b writtn as J =  c ( x) dµ RT () Now lt s considr th xprssion of chmical potntial as w larnd in th cours of Thrmodynamics: μ(x) = μ 0 + RTlna(x) = μ 0 + RT ln γ cx ( ) whr a(x) is th activity of solut (atom) at x, γ is th activity cofficint, a constant. Thn, w hav dµ RT dc ( x) = c(x) (3) Substituting Eq. (3) into Eq. (), w hav J =  dc ( x) (4) Lt s dfin D = Thn w hav dc ( x) J = D as th intrinsic diffusion cofficint (Unit: D: cm /sc; J: numbr/cm /sc) This is th Fick s first law of diffusion. 5
6 Now, lt s considr diffusion in a thrdimnsional spac, i.., random walk of an atom: s dfind on pag 4, Γ = ν  G Combining with D = W hav D = Γ a = Thn w hav  G Γ= ν = D / a (Γ: numbr of jump an atom mak pr scond) For a random walk in thrdimnsions, an atom travls an avrag distanc of stps (i.., n tims of jump) with a stp lngth of a. n a aftr n Thus, aftr tim t, th atom jumps Γ t tims (stps). So it movs a distanc of r = a Dt Γ t = a a = D t.4 D t This is usually dfind as th diffusion lngth.
Principles of Humidity Dalton s law
Principls of Humidity Dalton s law Air is a mixtur of diffrnt gass. Th main gas componnts ar: Gas componnt volum [%] wight [%] Nitrogn N 2 78,03 75,47 Oxygn O 2 20,99 23,20 Argon Ar 0,93 1,28 Carbon dioxid
More informationhttp://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force
ctivation nrgis http://www.wwnorton.com/chmistry/tutorials/ch14.htm (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd
More informationGas Radiation. MEL 725 PowerPlant Steam Generators (300) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi
Gas Radiation ME 725 PowrPlant Stam Gnrators (300) Dr. Prabal Talukdar Assistant Profssor Dpartmnt of Mchanical Enginring T Dlhi Radiation in absorbingmitting mdia Whn a mdium is transparnt to radiation,
More information14.3 Area Between Curves
14. Ara Btwn Curvs Qustion 1: How is th ara btwn two functions calculatd? Qustion : What ar consumrs and producrs surplus? Earlir in this chaptr, w usd dfinit intgrals to find th ara undr a function and
More informationExponential Growth and Decay; Modeling Data
Exponntial Growth and Dcay; Modling Data In this sction, w will study som of th applications of xponntial and logarithmic functions. Logarithms wr invntd by John Napir. Originally, thy wr usd to liminat
More information10/06/08 1. Aside: The following is an online analytical system that portrays the thermodynamic properties of water vapor and many other gases.
10/06/08 1 5. Th watrair htrognous systm Asid: Th following is an onlin analytical systm that portrays th thrmodynamic proprtis of watr vapor and many othr gass. http://wbbook.nist.gov/chmistry/fluid/
More informationQuestion 3: How do you find the relative extrema of a function?
ustion 3: How do you find th rlativ trma of a function? Th stratgy for tracking th sign of th drivativ is usful for mor than dtrmining whr a function is incrasing or dcrasing. It is also usful for locating
More informationFundamentals: NATURE OF HEAT, TEMPERATURE, AND ENERGY
Fundamntals: NATURE OF HEAT, TEMPERATURE, AND ENERGY DEFINITIONS: Quantum Mchanics study of individual intractions within atoms and molculs of particl associatd with occupid quantum stat of a singl particl
More informationGenetic Drift and Gene Flow Illustration
Gntic Drift and Gn Flow Illustration This is a mor dtaild dscription of Activity Ida 4, Chaptr 3, If Not Rac, How do W Explain Biological Diffrncs? in: How Ral is Rac? A Sourcbook on Rac, Cultur, and Biology.
More informationNonHomogeneous Systems, Euler s Method, and Exponential Matrix
NonHomognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous firstordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach
More informationNew Basis Functions. Section 8. Complex Fourier Series
Nw Basis Functions Sction 8 Complx Fourir Sris Th complx Fourir sris is prsntd first with priod 2, thn with gnral priod. Th connction with th ralvalud Fourir sris is xplaind and formula ar givn for convrting
More informatione = C / electron Q = Ne
Physics 0 Modul 01 Homwork 1. A glass rod that has bn chargd to +15.0 nc touchs a mtal sphr. Aftrword, th rod's charg is +8.00 nc. What kind of chargd particl was transfrrd btwn th rod and th sphr, and
More informationThe example is taken from Sect. 1.2 of Vol. 1 of the CPN book.
Rsourc Allocation Abstract This is a small toy xampl which is wllsuitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of Cnts. Hnc, it can b rad by popl
More informationEcon 371: Answer Key for Problem Set 1 (Chapter 1213)
con 37: Answr Ky for Problm St (Chaptr 23) Instructor: Kanda Naknoi Sptmbr 4, 2005. (2 points) Is it possibl for a country to hav a currnt account dficit at th sam tim and has a surplus in its balanc
More informationCPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions
CPS 22 Thory of Computation REGULAR LANGUAGES Rgular xprssions Lik mathmatical xprssion (5+3) * 4. Rgular xprssion ar built using rgular oprations. (By th way, rgular xprssions show up in various languags:
More informationQUANTITATIVE METHODS CLASSES WEEK SEVEN
QUANTITATIVE METHODS CLASSES WEEK SEVEN Th rgrssion modls studid in prvious classs assum that th rspons variabl is quantitativ. Oftn, howvr, w wish to study social procsss that lad to two diffrnt outcoms.
More informationTraffic Flow Analysis (2)
Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. GangLn Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,
More informationVibrational Spectroscopy
Vibrational Spctroscopy armonic scillator Potntial Enrgy Slction Ruls V( ) = k = R R whr R quilibrium bond lngth Th dipol momnt of a molcul can b pandd as a function of = R R. µ ( ) =µ ( ) + + + + 6 3
More informationThe Matrix Exponential
Th Matrix Exponntial (with xrciss) 92.222  Linar Algbra II  Spring 2006 by D. Klain prliminary vrsion Corrctions and commnts ar wlcom! Th Matrix Exponntial For ach n n complx matrix A, dfin th xponntial
More informationAP Calculus AB 2008 Scoring Guidelines
AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a notforprofit mmbrship association whos mission is to connct studnts to collg succss and opportunity.
More informationNoble gas configuration. Atoms of other elements seek to attain a noble gas electron configuration. Electron configuration of ions
Valnc lctron configuration dtrmins th charactristics of lmnts in a group Nobl gas configuration Th nobl gass (last column in th priodic tabl) ar charactrizd by compltly filld s and p orbitals this is a
More informationby John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia
Studnt Nots Cost Volum Profit Analysis by John Donald, Lcturr, School of Accounting, Economics and Financ, Dakin Univrsity, Australia As mntiond in th last st of Studnt Nots, th ability to catgoris costs
More informationDeer: Predation or Starvation
: Prdation or Starvation National Scinc Contnt Standards: Lif Scinc: s and cosystms Rgulation and Bhavior Scinc in Prsonal and Social Prspctiv s, rsourcs and nvironmnts Unifying Concpts and Procsss Systms,
More informationME 612 Metal Forming and Theory of Plasticity. 6. Strain
Mtal Forming and Thory of Plasticity mail: azsnalp@gyt.du.tr Makin Mühndisliği Bölümü Gbz Yüksk Tknoloji Enstitüsü 6.1. Uniaxial Strain Figur 6.1 Dfinition of th uniaxial strain (a) Tnsil and (b) Comprssiv.
More informationBasis risk. When speaking about forward or futures contracts, basis risk is the market
Basis risk Whn spaking about forward or futurs contracts, basis risk is th markt risk mismatch btwn a position in th spot asst and th corrsponding futurs contract. Mor broadly spaking, basis risk (also
More informationMathematics. Mathematics 3. hsn.uk.net. Higher HSN23000
hsn uknt Highr Mathmatics UNIT Mathmatics HSN000 This documnt was producd spcially for th HSNuknt wbsit, and w rquir that any copis or drivativ works attribut th work to Highr Still Nots For mor dtails
More informationForeign Exchange Markets and Exchange Rates
Microconomics Topic 1: Explain why xchang rats indicat th pric of intrnational currncis and how xchang rats ar dtrmind by supply and dmand for currncis in intrnational markts. Rfrnc: Grgory Mankiw s Principls
More informationThe Normal Distribution: A derivation from basic principles
Th Normal Distribution: A drivation from basic principls Introduction Dan Tagu Th North Carolina School of Scinc and Mathmatics Studnts in lmntary calculus, statistics, and finit mathmatics classs oftn
More informationIntroduction to Finite Element Modeling
Introduction to Finit Elmnt Modling Enginring analysis of mchanical systms hav bn addrssd by driving diffrntial quations rlating th variabls of through basic physical principls such as quilibrium, consrvation
More informationSPECIFIC HEAT AND HEAT OF FUSION
PURPOSE This laboratory consists of to sparat xprimnts. Th purpos of th first xprimnt is to masur th spcific hat of to solids, coppr and rock, ith a tchniqu knon as th mthod of mixturs. Th purpos of th
More informationChapter 3: Capacitors, Inductors, and Complex Impedance
haptr 3: apacitors, Inductors, and omplx Impdanc In this chaptr w introduc th concpt of complx rsistanc, or impdanc, by studying two ractiv circuit lmnts, th capacitor and th inductor. W will study capacitors
More informationSolutions to Homework 8 chem 344 Sp 2014
1. Solutions to Homwork 8 chm 44 Sp 14 .. 4. All diffrnt orbitals mans thy could all b paralll spins 5. Sinc lctrons ar in diffrnt orbitals any combination is possibl paird or unpaird spins 6. Equivalnt
More informationModule 7: Discrete State Space Models Lecture Note 3
Modul 7: Discrt Stat Spac Modls Lctur Not 3 1 Charactristic Equation, ignvalus and ign vctors For a discrt stat spac modl, th charactristic quation is dfind as zi A 0 Th roots of th charactristic quation
More informationGateway 125,126,130 Fall 2006 Exam 1 KEY p1
Gatway 125,126,130 Fall 2006 Exam 1 KEY p1 Q16 (1 point ach) Plas plac th corrct lttr/s in th box. 1) How many lctrons can th third principal quantum lvl (n = 3) hold? a. 2 b. 8 c. 16 d. 18. 32 2) Arrang
More informationAdverse Selection and Moral Hazard in a Model With 2 States of the World
Advrs Slction and Moral Hazard in a Modl With 2 Stats of th World A modl of a risky situation with two discrt stats of th world has th advantag that it can b natly rprsntd using indiffrnc curv diagrams,
More information14.02 Principles of Macroeconomics Problem Set 4 Solutions Fall 2004
art I. Tru/Fals/Uncrtain Justify your answr with a short argumnt. 4.02 rincipls of Macroconomics roblm St 4 Solutions Fall 2004. High unmploymnt implis that th labor markt is sclrotic. Uncrtain. Th unmploymnt
More informationLecture 20: Emitter Follower and Differential Amplifiers
Whits, EE 3 Lctur 0 Pag of 8 Lctur 0: Emittr Followr and Diffrntial Amplifirs Th nxt two amplifir circuits w will discuss ar ry important to lctrical nginring in gnral, and to th NorCal 40A spcifically.
More informationModelling and Solving TwoStep Equations: ax + b = c
Modlling and Solving ToStp Equations: a + b c Focus on Aftr this lsson, you ill b abl to φ modl problms φ ith tostp linar quations solv tostp linar quations and sho ho you ord out th ansr Cali borrod
More information3. Yes. You can put 20 of the 6V lights in series, or you can put several of the 6V lights in series with a large resistance.
CHAPTE 6: DC Circuits sponss to Qustions. Evn though th bird s ft ar at high potntial with rspct to th ground, thr is vry littl potntial diffrnc btwn thm, bcaus thy ar clos togthr on th wir. Th rsistanc
More informationInstallation Saving Spaceefficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison
Contnts Tchnology Nwly Dvlopd Cllo Tchnology Cllo Tchnology : Improvd Absorption of Light Doublsidd Cll Structur Cllo Tchnology : Lss Powr Gnration Loss Extrmly Low LID Clls 3 3 4 4 4 Advantag Installation
More informationEFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS
25 Vol. 3 () JanuaryMarch, pp.375/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut
More informationSimulated Radioactive Decay Using Dice Nuclei
Purpos: In a radioactiv sourc containing a vry larg numbr of radioactiv nucli, it is not possibl to prdict whn any on of th nucli will dcay. Although th dcay tim for any on particular nuclus cannot b prdictd,
More informationC H A P T E R 1 Writing Reports with SAS
C H A P T E R 1 Writing Rports with SAS Prsnting information in a way that s undrstood by th audinc is fundamntally important to anyon s job. Onc you collct your data and undrstand its structur, you nd
More informationInternational Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research)
Intrnational Association of Scintific Innovation and Rsarch (IASIR) (An Association Unifing th Scincs, Enginring, and Applid Rsarch) ISSN (Print): 79000 ISSN (Onlin): 79009 Intrnational Journal of Enginring,
More informationFactorials! Stirling s formula
Author s not: This articl may us idas you havn t larnd yt, and might sm ovrly complicatd. It is not. Undrstanding Stirling s formula is not for th faint of hart, and rquirs concntrating on a sustaind mathmatical
More informationCurrent and Resistance
Chaptr 6 Currnt and Rsistanc 6.1 Elctric Currnt...66.1.1 Currnt Dnsity...66. Ohm s Law...64 6.3 Elctrical Enrgy and Powr...67 6.4 Summary...68 6.5 Solvd Problms...69 6.5.1 Rsistivity of a Cabl...69
More informationSPECIAL VOWEL SOUNDS
SPECIAL VOWEL SOUNDS Plas consult th appropriat supplmnt for th corrsponding computr softwar lsson. Rfr to th 42 Sounds Postr for ach of th Spcial Vowl Sounds. TEACHER INFORMATION: Spcial Vowl Sounds (SVS)
More informationStatistical Machine Translation
Statistical Machin Translation Sophi Arnoult, Gidon Mailltt d Buy Wnnigr and Andra Schuch Dcmbr 7, 2010 1 Introduction All th IBM modls, and Statistical Machin Translation (SMT) in gnral, modl th problm
More informationSUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT. Eduard N. Klenov* RostovonDon. Russia
SUBATOMIC PARTICLES AND ANTIPARTICLES AS DIFFERENT STATES OF THE SAME MICROCOSM OBJECT Eduard N. Klnov* RostovonDon. Russia Th distribution law for th valus of pairs of th consrvd additiv quantum numbrs
More informationSection 7.4: Exponential Growth and Decay
1 Sction 7.4: Exponntial Growth and Dcay Practic HW from Stwart Txtbook (not to hand in) p. 532 # 117 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart
More information7 Timetable test 1 The Combing Chart
7 Timtabl tst 1 Th Combing Chart 7.1 Introduction 7.2 Tachr tams two workd xampls 7.3 Th Principl of Compatibility 7.4 Choosing tachr tams workd xampl 7.5 Ruls for drawing a Combing Chart 7.6 Th Combing
More information5.4 Exponential Functions: Differentiation and Integration TOOTLIFTST:
.4 Eponntial Functions: Diffrntiation an Intgration TOOTLIFTST: Eponntial functions ar of th form f ( ) Ab. W will, in this sction, look at a spcific typ of ponntial function whr th bas, b, is.78.... This
More informationDept. of Materials Science and Engineering. Problem Set 8 Solutions
MSE 30/ECE 30 Elctrical Prortis Of Matrials Dt. of Matrials Scinc and Enginring Fall 0/Bill Knowlton Problm St 8 Solutions. Using th rlationshi of n i n i i that is a function of E g, rcrat th lot shown
More information811ISD Economic Considerations of Heat Transfer on Sheet Metal Duct
Air Handling Systms Enginring & chnical Bulltin 811ISD Economic Considrations of Hat ransfr on Sht Mtal Duct Othr bulltins hav dmonstratd th nd to add insulation to cooling/hating ducts in ordr to achiv
More informationOptical Modulation Amplitude (OMA) and Extinction Ratio
Application Not: HFAN.. Rv; 4/8 Optical Modulation Amplitud (OMA) and Extinction Ratio AVAILABLE Optical Modulation Amplitud (OMA) and Extinction Ratio Introduction Th optical modulation amplitud (OMA)
More informationRenewable Energy Sources. Solar Cells SJSUE10 S John Athanasiou
Rnwabl Enrgy Sourcs. Solar Clls SJSUE10 S2008 John Athanasiou 1 Rnwabl Enrgy Sourcs Rnwabl: Thy can last indfinitly 1. Wind Turbin: Convrting th wind nrgy into lctricity Wind, Propllr, Elctric Gnrator,
More informationPage 1 of 16 Fall 2011: 5.112 PRINCIPLES OF CHEMICAL SCIENCE Problem Set #4 solutions This problem set was graded out of 99 points
Pag of 6 Fall 0: 5. PRINCIPLES OF CHEMICAL SCIENCE Problm St #4 solutions This problm st was gradd out of 99 points Qustion (out of 7 points) (i) For ach pair, dtrmin which compound has bonds with gratr
More informationTopic: Introduction to Brayton Cycle
MAE41Enrgy Systm Prsntation Topic: Introduction to Brayton Cycl Prpard by: L Lng Fng 1. Gas Turb powr Plant.. History of Brayton Cycl.. Air standard Brayton Cycl 4. Work and Hat Transfr Brayton cycl.
More informationSigmoid Functions and Their Usage in Artificial Neural Networks
Sigmoid Functions and Thir Usag in Artificial Nural Ntworks Taskin Kocak School of Elctrical Enginring and Computr Scinc Applications of Calculus II: Invrs Functions Eampl problm Calculus Topic: Invrs
More information(Analytic Formula for the European Normal Black Scholes Formula)
(Analytic Formula for th Europan Normal Black Schols Formula) by Kazuhiro Iwasawa Dcmbr 2, 2001 In this short summary papr, a brif summary of Black Schols typ formula for Normal modl will b givn. Usually
More informationSPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM
RESEARCH PAPERS IN MANAGEMENT STUDIES SPREAD OPTION VALUATION AND THE FAST FOURIER TRANSFORM M.A.H. Dmpstr & S.S.G. Hong WP 26/2000 Th Judg Institut of Managmnt Trumpington Strt Cambridg CB2 1AG Ths paprs
More informationCapacitance and Dielectrics
Chaptr 5 Capacitanc and Dilctrics 5.1 Introduction...53 5. Calculation of Capacitanc...54 Exampl 5.1: ParalllPlat Capacitor...54 Intractiv Simulation 5.1: ParalllPlat Capacitor...56 Exampl 5.: Cylindrical
More informationESCI 241 Meteorology Lesson 6 Humidity
ESCI 41 Mtorology Lsson 6 Humiity Raing: MT Chatr 5 PARTIAL PRESSURE In a mixtur of gass, ach gas scis contributs to th total rssur. ο Th rssur xrt by a singl gas scis is known as th artial rssur for that
More informationFinite Element Vibration Analysis
Finit Elmnt Vibration Analysis Introduction In prvious topics w larnd how to modl th dynamic bhavior of multidof systms, as wll as systms possssing infinit numbrs of DOF. As th radr may raliz, our discussion
More informationChapter 5 Capacitance and Dielectrics
5 5 5 Chaptr 5 Capacitanc and Dilctrics 5.1 Introduction... 53 5. Calculation of Capacitanc... 54 Exampl 5.1: ParalllPlat Capacitor... 54 Exampl 5.: Cylindrical Capacitor... 56 Exampl 5.3: Sphrical
More informationESCI 341 Atmospheric Thermodynamics Lesson 14 Humidity Dr. DeCaria
PARIAL PRESSURE ESCI 341 Atmoshric hrmoynamics Lsson 14 Humiity Dr. DCaria In a mixtur of gass, ach gas scis contributs to th total rssur. ο h rssur xrt by a singl gas scis is known as th artial rssur
More informationOXYGEN TRANSFER MEASUREMENTS AT SURFACE AERATORS IN WASTE WATER AS BASIS FOR ENERGY SAVING IN AERATION
OXYGEN TRANSFER MEASUREMENTS AT SURFACE AERATORS IN WASTE WATER AS BASIS FOR ENERGY SAVING IN AERATION Ditr Lomp Hochschu Brmrhavn Grmany Ahmt NuruBruns Achim, Grmany ABSTRACT Oxygn transfr masurmnts
More informationEAS44600 Groundwater Hydrology Lecture 8: Storage Properties of Aquifers Dr. Pengfei Zhang
EAS44600 Groundatr Hydrology Lctur 8: Storag Proprtis of Aquifrs Dr. Pngfi Zhang Moistur Contnt Rcall that th porosity (n) of arth matrials is th ratio of th volum of th voids (V v ) to th total volum
More informationTN Calculating Radiated Power and Field Strength for Conducted Power Measurements
Calculating adiatd owr and Fild Strngth for Conductd owr Masurmnts TN100.04 Calculating adiatd owr and Fild Strngth for Conductd owr Masurmnts Copyright Smtch 007 1 of 9 www.smtch.com Calculating adiatd
More informationA Derivation of Bill James Pythagorean WonLoss Formula
A Drivation of Bill Jams Pythagoran WonLoss Formula Ths nots wr compild by John Paul Cook from a papr by Dr. Stphn J. Millr, an Assistant Profssor of Mathmatics at Williams Collg, for a talk givn to th
More informationSimulation of the electric field generated by a brown ghost knife fish
C H A P T R 2 7 Simulation of th lctric fild gnratd by a brown ghost knif fish lctric fild CONCPTS 27.1 Th fild modl 27.2 lctric fild diagrams 27.3 Suprposition of lctric filds 27.4 lctric filds and forcs
More informationThe Fourier Transform
Th Fourir Transfor Larning outcos Us th Discrt Fourir Transfor to prfor frquncy analysis on a discrt (digital) signal Eplain th significanc of th Fast Fourir Transfor algorith; Eplain why windowing is
More informationImproving Managerial Accounting and Calculation of Labor Costs in the Context of Using Standard Cost
Economy Transdisciplinarity Cognition www.ugb.ro/tc Vol. 16, Issu 1/2013 5054 Improving Managrial Accounting and Calculation of Labor Costs in th Contxt of Using Standard Cost Lucian OCNEANU, Constantin
More informationThe photoelectric effect (~1900) Waves have another property: Interference. Waves have another property: Interference.
Atomic spctra So light is a wav! Class 27: Atomic spctra And why atoms ar violins Rmindrs/Updats: rading 14.3, 16.3 Solutions and grad updats today? (fixd D2L) 1 mor homwork #11 du nxt Thursday. Unsubmittd
More informationConstraintBased Analysis of Gene Deletion in a Metabolic Network
ConstraintBasd Analysis of Gn Dltion in a Mtabolic Ntwork Abdlhalim Larhlimi and Alxandr Bockmayr DFGRsarch Cntr Mathon, FB Mathmatik und Informatik, Fri Univrsität Brlin, Arnimall, 3, 14195 Brlin, Grmany
More information5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power
Prim numbrs W giv spcial nams to numbrs dpnding on how many factors thy hav. A prim numbr has xactly two factors: itslf and 1. A composit numbr has mor than two factors. 1 is a spcial numbr nithr prim
More informationGround Fault Current Distribution on Overhead Transmission Lines
FACTA UNIVERSITATIS (NIŠ) SER.: ELEC. ENERG. vol. 19, April 2006, 7184 Ground Fault Currnt Distribution on Ovrhad Transmission Lins Maria Vintan and Adrian Buta Abstract: Whn a ground fault occurs on
More informationA Theoretical Model of Public Response to the Homeland Security Advisory System
A Thortical Modl of Public Rspons to th Homland Scurity Advisory Systm Amy (Wnxuan) Ding Dpartmnt of Information and Dcision Scincs Univrsity of Illinois Chicago, IL 60607 wxding@uicdu Using a diffrntial
More informationLong run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange
Lctur 6: Th Forign xchang Markt xchang Rats in th long run CON 34 Mony and Banking Profssor Yamin Ahmad xchang Rats in th Short Run Intrst Parity Big Concpts Long run: Law of on pric Purchasing Powr Parity
More informationCIRCUITS AND ELECTRONICS. Basic Circuit Analysis Method (KVL and KCL method)
6. CIRCUITS AND ELECTRONICS Basic Circuit Analysis Mthod (KVL and KCL mthod) Cit as: Anant Agarwal and Jffry Lang, cours matrials for 6. Circuits and Elctronics, Spring 7. MIT 6. Fall Lctur Rviw Lumpd
More informationTIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.
Prsonal Dvlopmnt Track Sction 1 TIME MANAGEMENT Ky Points 1 Th Procss for Effctiv Tim Managmnt 2 Barrirs to Tim Managmnt 3 SMART Goals 4 Th POWER Modl In th Army, w spak of rsourcs in trms of th thr M
More informationChapter 4: Biochemical redox reactions
Chaptr 4: Biochmical ractions 4.1 Introduction 4.2 Biochmical halfractions, th Faraday conststant and th uction potntial 4.2.1 Dfining th uction potntial: 4.2.2 Th standard uction potntial is also th
More informationIntroduction to the Concept of Exergy  Masanori Shukuya & Abdelaziz Hammache
ESPOO V RESEARCH NOES 58 asanori Shukuya & Abdlaziz Hammach Introduction to th Concpt of Exrgy  for a ttr Undrstanding of LowmpraturHating and HighmpraturCooling Systms V IEOEIA RESEARCH NOES 58 Introduction
More informationVersion 1.0. General Certificate of Education (Alevel) January 2012. Mathematics MPC3. (Specification 6360) Pure Core 3. Final.
Vrsion.0 Gnral Crtificat of Education (Alvl) January 0 Mathmatics MPC (Spcification 660) Pur Cor Final Mark Schm Mark schms ar prpard by th Principal Eaminr and considrd, togthr with th rlvant qustions,
More informationLABORATORY 1 IDENTIFICATION OF CIRCUIT IN A BLACKBOX
LABOATOY IDENTIFICATION OF CICUIT IN A BLACKBOX OBJECTIES. To idntify th configuration of an lctrical circuit nclosd in a twotrminal black box.. To dtrmin th valus of ach componnt in th black box circuit.
More informationAn Broad outline of Redundant Array of Inexpensive Disks Shaifali Shrivastava 1 Department of Computer Science and Engineering AITR, Indore
Intrnational Journal of mrging Tchnology and dvancd nginring Wbsit: www.ijta.com (ISSN 22502459, Volum 2, Issu 4, pril 2012) n road outlin of Rdundant rray of Inxpnsiv isks Shaifali Shrivastava 1 partmnt
More informationChapter 19: Permanent Magnet DC Motor Characteristics
Chaptr 19: Prmannt Magnt DC Motor Charactristics 19.1: ntroduction Dirct currnt (DC) motors compris on of th most common typs of actuator dsignd into lctromchanical systms. hy ar a vry straightforward
More informationArchitecture of the proposed standard
Architctur of th proposd standard Introduction Th goal of th nw standardisation projct is th dvlopmnt of a standard dscribing building srvics (.g.hvac) product catalogus basd on th xprincs mad with th
More informationSIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY
1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically
More informationDevelopment of Financial Management Reporting in MPLS
1 Dvlopmnt of Financial Managmnt Rporting in MPLS 1. Aim Our currnt financial rports ar structurd to dlivr an ovrall financial pictur of th dpartmnt in it s ntirty, and thr is no attmpt to provid ithr
More informationHOMEWORK FOR UNIT 51: FORCE AND MOTION
Nam Dat Partnrs HOMEWORK FOR UNIT 51: FORCE AND MOTION 1. You ar givn tn idntial springs. Dsrib how you would dvlop a sal of for (i., a mans of produing rpatabl fors of a varity of sizs) using ths springs.
More informationToday: Electron waves?!
Today: Elctron wavs?! 1. Exampl of wav diffraction: Light. 2. Prdicting th diffraction of lctrons. 3. Th Davisson, Grmr xprimnt as an xampl. W can't dfin anything prcisly. If w attmpt to, w gt into that
More informationAP Calculus MultipleChoice Question Collection 1969 1998. connect to college success www.collegeboard.com
AP Calculus MultiplChoic Qustion Collction 969 998 connct to collg succss www.collgboard.com Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a notforprofit mmbrship association whos
More informationHSBC Bank International Expat Explorer Survey 08
HSBC Bank Intrnational Expat Explorr Survy 08 Rport On: Expat Existnc Th Survy Th Expat Explorr survy qustiond 2,155 xpatriats across four continnts about th opportunitis and challngs thy fac. Th survy
More informationParallel and Distributed Programming. Performance Metrics
Paralll and Distributd Programming Prformanc! wo main goals to b achivd with th dsign of aralll alications ar:! Prformanc: th caacity to rduc th tim to solv th roblm whn th comuting rsourcs incras;! Scalability:
More informationSection 55 Inverse of a Square Matrix
 Invrs of a Squar Matrix 9 (D) Rank th playrs from strongst to wakst. Explain th rasoning hind your ranking. 68. Dominan Rlation. Eah mmr of a hss tam plays on math with vry othr playr. Th rsults ar givn
More informationintro Imagine that someone asked you to describe church using only the bible. What would you say to them?
intro Imagin that somon askd you to dscrib church using only th bibl. What would you say to thm? So many of th things w'v mad church to b arn't ssntial in scriptur. W'r on a journy of rimagining what
More informationExamples. Epipoles. Epipolar geometry and the fundamental matrix
Epipoar gomtry and th fundamnta matrix Epipoar ins Lt b a point in P 3. Lt x and x b its mapping in two imags through th camra cntrs C and C. Th point, th camra cntrs C and C and th (3D points corrspon
More informationRemember you can apply online. It s quick and easy. Go to www.gov.uk/advancedlearningloans. Title. Forename(s) Surname. Sex. Male Date of birth D
24+ Advancd Larning Loan Application form Rmmbr you can apply onlin. It s quick and asy. Go to www.gov.uk/advancdlarningloans About this form Complt this form if: you r studying an ligibl cours at an approvd
More informationCategory 7: Employee Commuting
7 Catgory 7: Employ Commuting Catgory dscription This catgory includs missions from th transportation of mploys 4 btwn thir homs and thir worksits. Emissions from mploy commuting may aris from: Automobil
More information