Repulsive Force

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "http://www.wwnorton.com/chemistry/tutorials/ch14.htm Repulsive Force"

Transcription

1 ctivation nrgis (back to collision thory...) Potntial and Kintic nrgy during a collision + + ngativly chargd lctron cloud Rpulsiv Forc ngativly chargd lctron cloud - as colliding molculs approach th rpulsion slows thm down so kintic nrgy dcrass. - as thy push against th rpulsiv forc potntial nrgy incrass (lik comprssing a spring) is convrtd to - so: Kintic Enrgy Potntial Enrgy KE + PE = Total E (stays constant) if on gos down, th othr gos up. Potntial nrgy diagrams s molculs approach ach othr, KE is convrtd to PE Molculs form a tmporary, unstabl spcis calld th ctivatd Complx rarrangs to form th PRODUCT molculs Potntial Enrgy (kj) (High KE, Low PE) Product Molculs mov apart and spd up. PE is convrtd to KE. (High KE, Low PE) Progrss of Raction

2 Think of this as a barrir which must b ovrcom bfor th raction can tak plac Potntial Enrgy (kj) THE CTIVTION ENERGY BRRIER Raction Procds If colliding molculs don t hav nough KE to convrt to PE to mak it ovr th ctivation Enrgy Barrir, it is an UNSUCCESSFUL collision and thr is NO raction. Th molculs will just bounc off of ach othr unchangd. Potntial Enrgy (kj) THE CTIVTION ENERGY BRRIER Raction Procds CTIVTION ENERGY (Ea) - Th minimum nrgy rquird for a succssfull collision. (or) Th minimum nrgy racting molculs must hav in ordr to form th ctivatd Complx. Th ctivatd Complx can b dfind as a vry short-livd, unstabl combination of ractant atoms that xists bfor products ar formd.

3 NOTE: Th ctivation Enrgy (Ea) is fixd by th natur of th ractants (# s and strngths of bonds in ractants.) Ea is NOT affctd by Δtmpratur or Δ concntration.! Ea = 85 - = 35 kj Progrss of Raction Tmpratur s rol - th tmpratur dtrmins how many (or what fraction of th) molculs will hav nrgy > Ea (to mak it ovr th barrir & hav a succssful collision) Rcall KE distributions: g.) t a LOW tmpratur: Numbr of Molculs Curv at Lowr Tmp. (T 1 ) ctivation Enrgy (E a ) Kintic Enrgy t Tmpratur T 1 (lowr tmp), th molculs rprsntd by this ara do NOT hav sufficint KE for a succssful collision t Tmpratur T 1 (lowr tmp.), only ths molculs hav sufficint nrgy for a succssful collision

4 Most of us don t hav th nrgy to mak it ovr th barrir! Yaaay! fw of us mad it!!! Potntial Enrgy Progrss of Raction Notic in th diagrams on th prvious pag and abov, that only a small fraction of th molculs had nough nrgy to ovrcom th ctivation Enrgy barrir. Now, at a Highr Tmpratur: ctivation Enrgy (E a ) Numbr of Molculs Curv at Highr Tmp. (T 2 ) t a highr Tmpratur (T 2 ), thr ar lss molculs which don t hav nough KE for a succssful collision. Kintic Enrgy t Tmpratur T 2 (highr tmp.), thr ar mor molculs which hav sufficint nrgy for a succssful collision t th highr tmpratur, a gratr fraction of th molculs hav sufficint nrgy to mak it ovr th ctivation Enrgy barrir. (i. a gratr fraction of th molculs posss nough nrgy to form th ctivatd Complx):

5 fw of us don t hav th nrgy to mak it ovr th barrir! Yaaay! gratr fraction of us mad it this tim! Potntial Enrgy Progrss of Raction Looking at th diagram abov, you can s that at a highr tmpratur, a gratr fraction of th molculs hav sufficint nrgy to mak it ovr th barrir. Thrfor th raction is fastr. So if you study th graphs on th prvious pags, you will s that: Incrasing th tmpratur incrass th fraction of molculs which hav sufficint nrgy to form th ctivatd Complx (i. sufficint nrgy to mak it ovr th activation nrgy barrir.) This is on rason that incrasing th tmpratur will INCRESE th rat of raction. lso, NOTICE that a chang in tmpratur dos NOT chang th Potntial Enrgy diagram at all. Tmpratur dos NOT affct th ctivation nrgy or th ΔΗ!! Considr two ractions T THE SME TEMPERTURE: Ea E a Progrss of Raction Raction Progrss of Raction Raction B Which raction is fastr? Explain why.

6 Collision Gomtry (corrct alignmnt) g. for th rx. 2 + B 2 2B: + B B th abov collision has unfavourabl alignmnt (nd highr nrgy for collision to b ffctiv) B B B + + B B B Ractant Molculs ( 2 & B 2 ) PPROCH ECH OTHER Thy collid and form an ( 2 B 2 ) Th C braks apart to form th (2B) In th abov collision, th ractants hav favourabl alignmnt (lss nrgy ndd for an ffctiv collision) Potntial nrgy diagram Rout with UNFVOURBLE Collision Gomtry (lignmnt) POTENTIL ENERGY Ractants Rout with FVOURBLE Collision Gomtry (lignmnt) Products RECTION PROCEEDS

7 To Summariz Collision Thory so far: For any succssful collision (on rsulting in a raction): 3 Rquirmnts: 1.) - particls must collid 2.) - thy must collid with sufficint nrgy > Ea 3.) - thy nd to hav corrct alignmnt (collision gomtry) (to kp Ea as low as possibl) Ea, ΔΗ and bond strngths for forward and rvrs ractions POTENTIL ENERGY Ea Enrgy ndd for Ractants to form th ctivatd Complx ΔΗ- Enrgy Diffrnc btwn Ractants and Products. (In this cas ΔΗ is ngativ so Rx. is Exothrmic Progrss of Raction Try this qustion: Forward Raction Progrss of Raction

8 Using th graph abov, find: Ea (forward rx.) = kj ΔΗ (forward rx. ) = kj -Considring rvrs rx. This forward raction is thrmic 2 00 POTENTIL ENERGY Ea (rvrs rx.) ΔΗ (rvrs rx.) Rvrs Raction Ea (rvrs rx.) = kj Progrss of Raction ΔΗ (rvrs rx. ) = kj This rvrs raction is thrmic Givn th following Potntial Enrgy Diagram for th Raction: 2 + B2 2B POTENTIL ENERGY B B B Progrss of Raction

9 a) Ea (forward) = KJ b) Enrgy ndd to brak bonds in 2 & B 2 - B-B KJ c) Ea (rvrs) = KJ d) Enrgy ndd to brak bonds in B (-B) KJ ) Which has th strongr bonds 2 & B 2 or 2B? f) On a PE diagram, spcis with strongr bonds (mor stabl) ar (low/high) r on th graph g) Which st of spcis ( 2 & B 2, 2 B 2, or 2B) hav th wakst bonds?. This spcis is th most stabl. It is calld th h) Which st of spcis has th highst PE? i) Which st of spcis has th highst KE? j) Draw a graph of KE vs. raction procds for th sam forward rx. KINETIC E N E R G Y Progrss of Raction

Noble gas configuration. Atoms of other elements seek to attain a noble gas electron configuration. Electron configuration of ions

Noble 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 information

Lecture 3: Diffusion: Fick s first law

Lecture 3: Diffusion: Fick s first law 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

More information

Principles of Humidity Dalton s law

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 information

Solutions to Homework 8 chem 344 Sp 2014

Solutions 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 information

Question 3: How do you find the relative extrema of a function?

Question 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 information

e = C / electron Q = Ne

e = 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 information

Gateway 125,126,130 Fall 2006 Exam 1 KEY p1

Gateway 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 information

Page 1 of 16 Fall 2011: 5.112 PRINCIPLES OF CHEMICAL SCIENCE Problem Set #4 solutions This problem set was graded out of 99 points

Page 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 information

by John Donald, Lecturer, School of Accounting, Economics and Finance, Deakin University, Australia

by 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 information

14.3 Area Between Curves

14.3 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 information

Renewable Energy Sources. Solar Cells SJSU-E10 S John Athanasiou

Renewable Energy Sources. Solar Cells SJSU-E10 S John Athanasiou Rnwabl Enrgy Sourcs. Solar Clls SJSU-E10 S-2008 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 information

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13)

Econ 371: Answer Key for Problem Set 1 (Chapter 12-13) con 37: Answr Ky for Problm St (Chaptr 2-3) 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 information

Fundamentals: NATURE OF HEAT, TEMPERATURE, AND ENERGY

Fundamentals: 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 information

Exponential Growth and Decay; Modeling Data

Exponential 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 information

Foreign Exchange Markets and Exchange Rates

Foreign 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 information

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix

Non-Homogeneous Systems, Euler s Method, and Exponential Matrix Non-Homognous Systms, Eulr s Mthod, and Exponntial Matrix W carry on nonhomognous first-ordr linar systm of diffrntial quations. W will show how Eulr s mthod gnralizs to systms, giving us a numrical approach

More information

3. Yes. You can put 20 of the 6-V lights in series, or you can put several of the 6-V lights in series with a large resistance.

3. Yes. You can put 20 of the 6-V lights in series, or you can put several of the 6-V 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 information

Financial Mathematics

Financial Mathematics Financial Mathatics A ractical Guid for Actuaris and othr Businss rofssionals B Chris Ruckan, FSA & Jo Francis, FSA, CFA ublishd b B rofssional Education Solutions to practic qustions Chaptr 7 Solution

More information

Modelling and Solving Two-Step Equations: ax + b = c

Modelling and Solving Two-Step Equations: ax + b = c Modlling and Solving To-Stp Equations: a + b c Focus on Aftr this lsson, you ill b abl to φ modl problms φ ith to-stp linar quations solv to-stp linar quations and sho ho you ord out th ansr Cali borrod

More information

7 Timetable test 1 The Combing Chart

7 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 information

The photoelectric effect (~1900) Waves have another property: Interference. Waves have another property: Interference.

The 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 information

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison

Installation Saving Space-efficient Panel Enhanced Physical Durability Enhanced Performance Warranty The IRR Comparison Contnts Tchnology Nwly Dvlopd Cllo Tchnology Cllo Tchnology : Improvd Absorption of Light Doubl-sidd Cll Structur Cllo Tchnology : Lss Powr Gnration Loss Extrmly Low LID Clls 3 3 4 4 4 Advantag Installation

More information

Genetic Drift and Gene Flow Illustration

Genetic 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 information

Statistical Machine Translation

Statistical 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 information

10/06/08 1. Aside: The following is an on-line analytical system that portrays the thermodynamic properties of water vapor and many other gases.

10/06/08 1. Aside: The following is an on-line analytical system that portrays the thermodynamic properties of water vapor and many other gases. 10/06/08 1 5. Th watr-air htrognous systm Asid: Th following is an on-lin analytical systm that portrays th thrmodynamic proprtis of watr vapor and many othr gass. http://wbbook.nist.gov/chmistry/fluid/

More information

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers)

Intermediate Macroeconomic Theory / Macroeconomic Analysis (ECON 3560/5040) Final Exam (Answers) Intrmdiat Macroconomic Thory / Macroconomic Analysis (ECON 3560/5040) Final Exam (Answrs) Part A (5 points) Stat whthr you think ach of th following qustions is tru (T), fals (F), or uncrtain (U) and brifly

More information

AP Chemistry. CHAPTER 21- Nuclear Chemistry Radioactivity

AP Chemistry. CHAPTER 21- Nuclear Chemistry Radioactivity AP Chmistry CHAPTER - Nuclar Chmistry. Radioactivity Whn nucli chang spontanously, mitting nrgy, thy ar said to b radioactiv. Nuclar chmistry is th study of nuclar ractions and thir uss. Nuclons ar particls

More information

QUANTITATIVE METHODS CLASSES WEEK SEVEN

QUANTITATIVE 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 information

Basis risk. When speaking about forward or futures contracts, basis risk is the market

Basis 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 information

A Derivation of Bill James Pythagorean Won-Loss Formula

A Derivation of Bill James Pythagorean Won-Loss Formula A Drivation of Bill Jams Pythagoran Won-Loss 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 information

CPS 220 Theory of Computation REGULAR LANGUAGES. Regular expressions

CPS 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 information

14.02 Principles of Macroeconomics Problem Set 4 Solutions Fall 2004

14.02 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 information

Section 7.4: Exponential Growth and Decay

Section 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 # 1-17 odd In th nxt two ction, w xamin how population growth can b modld uing diffrntial quation. W tart

More information

AP Calculus AB 2008 Scoring Guidelines

AP Calculus AB 2008 Scoring Guidelines AP Calculus AB 8 Scoring Guidlins Th Collg Board: Conncting Studnts to Collg Succss Th Collg Board is a not-for-profit mmbrship association whos mission is to connct studnts to collg succss and opportunity.

More information

Chapter 5 Capacitance and Dielectrics

Chapter 5 Capacitance and Dielectrics 5 5 5- Chaptr 5 Capacitanc and Dilctrics 5.1 Introduction... 5-3 5. Calculation of Capacitanc... 5-4 Exampl 5.1: Paralll-Plat Capacitor... 5-4 Exampl 5.: Cylindrical Capacitor... 5-6 Exampl 5.3: Sphrical

More information

Adverse Selection and Moral Hazard in a Model With 2 States of the World

Adverse 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 information

Long run: Law of one price Purchasing Power Parity. Short run: Market for foreign exchange Factors affecting the market for foreign exchange

Long 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 information

Step 1: Checking the shaft

Step 1: Checking the shaft Stp 1: Chcking th shaft Th shaft diamtr at th baring sat should b within tolranc as shown in our Product Catalog. As a gnral guid, +0.000", 0.002" is adquat. Any tapr or out of roundnss in th shaft at

More information

New Basis Functions. Section 8. Complex Fourier Series

New 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 ral-valud Fourir sris is xplaind and formula ar givn for convrting

More information

Simulated Radioactive Decay Using Dice Nuclei

Simulated 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 information

Parallel and Distributed Programming. Performance Metrics

Parallel 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 information

5 2 index. e e. Prime numbers. Prime factors and factor trees. Powers. worked example 10. base. power

5 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 information

The Normal Distribution: A derivation from basic principles

The 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 information

Capacitance and Dielectrics

Capacitance and Dielectrics Chaptr 5 Capacitanc and Dilctrics 5.1 Introduction...5-3 5. Calculation of Capacitanc...5-4 Exampl 5.1: Paralll-Plat Capacitor...5-4 Intractiv Simulation 5.1: Paralll-Plat Capacitor...5-6 Exampl 5.: Cylindrical

More information

Current and Resistance

Current and Resistance Chaptr 6 Currnt and Rsistanc 6.1 Elctric Currnt...6-6.1.1 Currnt Dnsity...6-6. Ohm s Law...6-4 6.3 Elctrical Enrgy and Powr...6-7 6.4 Summary...6-8 6.5 Solvd Problms...6-9 6.5.1 Rsistivity of a Cabl...6-9

More information

Deer: Predation or Starvation

Deer: 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 information

Vibrational Spectroscopy

Vibrational 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 information

Simulation of the electric field generated by a brown ghost knife fish

Simulation 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 information

intro Imagine that someone asked you to describe church using only the bible. What would you say to them?

intro 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 r-imagining what

More information

SPECIFIC HEAT AND HEAT OF FUSION

SPECIFIC 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 information

OXYGEN 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 OXYGEN TRANSFER MEASUREMENTS AT SURFACE AERATORS IN WASTE WATER AS BASIS FOR ENERGY SAVING IN AERATION Ditr Lomp Hochschu Brmrhavn Grmany Ahmt Nuru-Bruns Achim, Grmany ABSTRACT Oxygn transfr masurmnts

More information

PES 3950/PHYS 6950: Homework Assignment 5

PES 3950/PHYS 6950: Homework Assignment 5 PES 3950/PHYS 6950: Homwork ssignmnt 5 Handd out: Wdnsday pril 8 Du in: Wdnsday pril, at t start of class at 3:05 pm sarp Sow all working and rasoning to rciv full points. Qustion [5 points] a)[0 points]

More information

The example is taken from Sect. 1.2 of Vol. 1 of the CPN book.

The 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 wll-suitd as a first introduction to Cnts. Th CN modl is dscribd in grat dtail, xplaining th basic concpts of C-nts. Hnc, it can b rad by popl

More information

Gas Radiation. MEL 725 Power-Plant Steam Generators (3-0-0) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi

Gas Radiation. MEL 725 Power-Plant Steam Generators (3-0-0) Dr. Prabal Talukdar Assistant Professor Department of Mechanical Engineering IIT Delhi Gas Radiation ME 725 Powr-Plant Stam Gnrators (3-0-0) Dr. Prabal Talukdar Assistant Profssor Dpartmnt of Mchanical Enginring T Dlhi Radiation in absorbing-mitting mdia Whn a mdium is transparnt to radiation,

More information

5.4 Exponential Functions: Differentiation and Integration TOOTLIFTST:

5.4 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 information

Remember 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

Remember 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 information

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13

Lecture notes: 160B revised 9/28/06 Lecture 1: Exchange Rates and the Foreign Exchange Market FT chapter 13 Lctur nots: 160B rvisd 9/28/06 Lctur 1: xchang Rats and th Forign xchang Markt FT chaptr 13 Topics: xchang Rats Forign xchang markt Asst approach to xchang rats Intrst Rat Parity Conditions 1) Dfinitions

More information

A Note on Approximating. the Normal Distribution Function

A Note on Approximating. the Normal Distribution Function Applid Mathmatical Scincs, Vol, 00, no 9, 45-49 A Not on Approimating th Normal Distribution Function K M Aludaat and M T Alodat Dpartmnt of Statistics Yarmouk Univrsity, Jordan Aludaatkm@hotmailcom and

More information

Some Useful Integrals of Exponential Functions

Some Useful Integrals of Exponential Functions prvious indx nxt Som Usful Intgrls of Exponntil Functions Michl Fowlr W v shown tht diffrntiting th xponntil function just multiplis it by th constnt in th xponnt, tht is to sy, d x x Intgrting th xponntil

More information

Module 7: Discrete State Space Models Lecture Note 3

Module 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 information

TIME MANAGEMENT. 1 The Process for Effective Time Management 2 Barriers to Time Management 3 SMART Goals 4 The POWER Model e. Section 1.

TIME 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 information

Simulation of a Solar Cell considering Single-Diode Equivalent Circuit Model

Simulation of a Solar Cell considering Single-Diode Equivalent Circuit Model Simulation of a Solar Cll considring Singl-Diod Equivalnt Circuit Modl E.M.G. Rodrigus, R. Mlício,, V.M.F. Mnds and J.P.S. Catalão, Univrsity of Bira Intrior R. Font do Lamiro, - Covilhã (Portugal) Phon:

More information

The Matrix Exponential

The 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 information

Topic: Introduction to Brayton Cycle

Topic: Introduction to Brayton Cycle MAE41-Enrgy 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 information

Making and Using the Hertzsprung - Russell Diagram

Making and Using the Hertzsprung - Russell Diagram Making and Using th Hrtzsprung - Russll Diagram Nam In astronomy th Hrtzsprung-Russll Diagram is on of th main ways that w organiz data dscribing how stars volv, ags of star clustrs, masss of stars tc.

More information

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman

Cloud and Big Data Summer School, Stockholm, Aug., 2015 Jeffrey D. Ullman Cloud and Big Data Summr Scool, Stockolm, Aug., 2015 Jffry D. Ullman Givn a st of points, wit a notion of distanc btwn points, group t points into som numbr of clustrs, so tat mmbrs of a clustr ar clos

More information

Chapter 4. Atomic structure

Chapter 4. Atomic structure Thomson modl of th atom Chaptr 4. Atomic structur Gigr and Marsdn s xprimnt: According to Thomson modl, it was xpctd that th alpha particl (hlium atoms lost two ', laving charg of +) would go right through

More information

Chapter 4: Biochemical redox reactions

Chapter 4: Biochemical redox reactions Chaptr 4: Biochmical ractions 4.1 Introduction 4.2 Biochmical half-ractions, 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 information

The Fourier Transform

The 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 information

Lecture 20: Emitter Follower and Differential Amplifiers

Lecture 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 information

LABORATORY 1 IDENTIFICATION OF CIRCUIT IN A BLACK-BOX

LABORATORY 1 IDENTIFICATION OF CIRCUIT IN A BLACK-BOX LABOATOY IDENTIFICATION OF CICUIT IN A BLACK-BOX OBJECTIES. To idntify th configuration of an lctrical circuit nclosd in a two-trminal black box.. To dtrmin th valus of ach componnt in th black box circuit.

More information

HOMEWORK FOR UNIT 5-1: FORCE AND MOTION

HOMEWORK FOR UNIT 5-1: 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 information

Mathematics. Mathematics 3. hsn.uk.net. Higher HSN23000

Mathematics. 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 information

Applications of the compound interest formula

Applications of the compound interest formula Applications of th compound intrst formula Quit oftn, thr of th variabls usd in th compound intrst formula ar known and th fourth nds to b found. Finding P workd xampl 6 Aunt Frda lavs Thlma a lgacy som

More information

Economic Analysis of Floating Exchange Rate Systems

Economic Analysis of Floating Exchange Rate Systems Economic Analysis of Floating Rat Systms Th businss sction of any nwspapr will hav a tabl of spot s. Ths ar th s at which a prson could hav bought othr currncis or forign, such as th English Pound, Frnch

More information

Increasing Net Debt as a percentage of Average Equalized ValuaOon

Increasing Net Debt as a percentage of Average Equalized ValuaOon City of Orang Township Warning Trnd: Incrasing Nt Dbt as a prcntag of avrag qualizd valuation Nt Dbt 3 yr. Avg. qualizd Valuation Incrasing Nt Dbt as a prcntag of Avrag Equalizd ValuaOon rc 1.20% 1.00%

More information

C H A P T E R 1 Writing Reports with SAS

C 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 information

Defining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind

Defining Retirement Success for Defined Contribution Plan Sponsors: Begin with the End in Mind Dfining Rtirmnt Succss for Dfind Contribution Plan Sponsors: Bgin with th End in Mind David Blanchtt, CFA, CFP, AIFA Had of Rtirmnt Rsarch Morningstar Invstmnt Managmnt david.blanchtt@morningstar.com Nathan

More information

Lab 8: Sputtering Magnetrons

Lab 8: Sputtering Magnetrons Lab 8: puttring Magntrons To undrstand sputtring magntrons w must first look at simpl dc glows. puttring magntrons ar charactrizd by a rgion with a strong lctric fild and a crossd (at right angl) magntic

More information

Factorials! Stirling s formula

Factorials! 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 information

Theoretical aspects of investment demand for gold

Theoretical aspects of investment demand for gold Victor Sazonov (Russia), Dmitry Nikolav (Russia) Thortical aspcts of invstmnt dmand for gold Abstract Th main objctiv of this articl is construction of a thortical modl of invstmnt in gold. Our modl is

More information

Rural and Remote Broadband Access: Issues and Solutions in Australia

Rural and Remote Broadband Access: Issues and Solutions in Australia Rural and Rmot Broadband Accss: Issus and Solutions in Australia Dr Tony Warrn Group Managr Rgulatory Stratgy Tlstra Corp Pag 1 Tlstra in confidnc Ovrviw Australia s gographical siz and population dnsity

More information

Differential Equations (MTH401) Lecture That a non-homogeneous linear differential equation of order n is an equation of the form n

Differential Equations (MTH401) Lecture That a non-homogeneous linear differential equation of order n is an equation of the form n Diffrntial Equations (MTH40) Ltur 7 Mthod of Undtrmind Coffiints-Surosition Aroah Rall. That a non-homognous linar diffrntial quation of ordr n is an quation of th form n n d d d an + a a a0 g( ) n n +

More information

SPECIAL VOWEL SOUNDS

SPECIAL 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 information

Lift Selection Guide

Lift Selection Guide Lift Slction Guid Hlping you choos th right lifts to kp your staff and rsidnts saf Th Dirct Supply diffrnc Kp your community saf DIRECT SUPPLY MAKES EQUIPMENT SELECTION EASY BENEFITS OF SAFE LIFTING PRACTICES

More information

LG has introduced the NeON 2, with newly developed Cello Technology which improves performance and reliability. Up to 320W 300W

LG has introduced the NeON 2, with newly developed Cello Technology which improves performance and reliability. Up to 320W 300W Cllo Tchnology LG has introducd th NON 2, with nwly dvlopd Cllo Tchnology which improvs prformanc and rliability. Up to 320W 300W Cllo Tchnology Cll Connction Elctrically Low Loss Low Strss Optical Absorption

More information

Outside Cut 1 of fabric Cut 1 of interfacing

Outside Cut 1 of fabric Cut 1 of interfacing a a Outsi Cut o abric Cut o intracing a a b b Outsi Cut o abric Cut o intracing Placmnt lin or Mony Pockts Dix Not: F. Cut Fol b. Pin t /8 in 5. Nx bottom pics sw th 6. For t Prss, 7. Lay togth on th 8.

More information

SMART 2020 Germany Addendum. The ICT sector as the driving force on the way to sustained climate protection.

SMART 2020 Germany Addendum. The ICT sector as the driving force on the way to sustained climate protection. . Th ICT sctor as th driving forc on th way to sustaind climat protction. Situation. Climat chang is happning fastr than was prdictd just a fw yars ago. Climat chang is a thrat to businss and socity. Information

More information

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS

EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS 25 Vol. 3 () January-March, pp.37-5/tripathi EFFECT OF GEOMETRICAL PARAMETERS ON HEAT TRANSFER PERFORMACE OF RECTANGULAR CIRCUMFERENTIAL FINS *Shilpa Tripathi Dpartmnt of Chmical Enginring, Indor Institut

More information

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives.

Keywords Cloud Computing, Service level agreement, cloud provider, business level policies, performance objectives. Volum 3, Issu 6, Jun 2013 ISSN: 2277 128X Intrnational Journal of Advancd Rsarch in Computr Scinc and Softwar Enginring Rsarch Papr Availabl onlin at: wwwijarcsscom Dynamic Ranking and Slction of Cloud

More information

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List.

CPU. Rasterization. Per Vertex Operations & Primitive Assembly. Polynomial Evaluator. Frame Buffer. Per Fragment. Display List. Elmntary Rndring Elmntary rastr algorithms for fast rndring Gomtric Primitivs Lin procssing Polygon procssing Managing OpnGL Stat OpnGL uffrs OpnGL Gomtric Primitivs ll gomtric primitivs ar spcifid by

More information

STATEMENT OF INSOLVENCY PRACTICE 3.2

STATEMENT OF INSOLVENCY PRACTICE 3.2 STATEMENT OF INSOLVENCY PRACTICE 3.2 COMPANY VOLUNTARY ARRANGEMENTS INTRODUCTION 1 A Company Voluntary Arrangmnt (CVA) is a statutory contract twn a company and its crditors undr which an insolvncy practitionr

More information

Projections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective

Projections - 3D Viewing. Overview Lecture 4. Projection - 3D viewing. Projections. Projections Parallel Perspective Ovrviw Lctur 4 Projctions - 3D Viwing Projctions Paralll Prspctiv 3D Viw Volum 3D Viwing Transformation Camra Modl - Assignmnt 2 OFF fils 3D mor compl than 2D On mor dimnsion Displa dvic still 2D Analog

More information

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769

WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 08-16-85 WORKERS' COMPENSATION ANALYST, 1774 SENIOR WORKERS' COMPENSATION ANALYST, 1769 Summary of Dutis : Dtrmins City accptanc of workrs' compnsation cass for injurd mploys; authorizs appropriat tratmnt

More information

Traffic Flow Analysis (2)

Traffic Flow Analysis (2) Traffic Flow Analysis () Statistical Proprtis. Flow rat distributions. Hadway distributions. Spd distributions by Dr. Gang-Ln Chang, Profssor Dirctor of Traffic safty and Oprations Lab. Univrsity of Maryland,

More information

Dept. of Materials Science and Engineering. Problem Set 8 Solutions

Dept. 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 information

Today: Electron waves?!

Today: 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 information

AQA. Physical Education. Questions and Answers

AQA. Physical Education. Questions and Answers AQA AS Physical Education Qustions and Answrs Qustions and answrs This CD compriss a worksht with som xam-styl qustions, a summary of som frquntly askd qustions and, finally, a sampl unit tst. Mark schms,

More information

ADSORPTION OF METALS ONTO TEA FACTORY WASTE: A REVIEW

ADSORPTION OF METALS ONTO TEA FACTORY WASTE: A REVIEW ADSORPTION OF METALS ONTO TEA FACTORY WASTE: A REVIEW Kailas L. Waswar Dpartmnt of Chmical Enginring, Visvsvaraya National Institut of Tchnology (VNIT) Nagpur - 440011, Maharashtra, INDIA Email: k_waswar@rdiffmail.com

More information

Optical Modulation Amplitude (OMA) and Extinction Ratio

Optical 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 information