ChE 471: LECTURE 4 Fall 2003

Save this PDF as:
Size: px
Start display at page:

Download "ChE 471: LECTURE 4 Fall 2003"

Transcription

1 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. This requires a mathematical mdel f the system, which in turn rests n applicatin f cnservatin laws t a well-defined cntrl vlume f the reactin system and n use f apprpriate cnstitutive expressins fr the reactin rates. The cncepts f ideal reactrs allw us t quantify reactr perfrmance as a functin f its size and selected perating cnditins. T illustrate this useful cncept we deal here with a single, hmgeneus phase, single reactin at cnstant temperature. We intrduce then the ideal batch reactr, and tw ideal cntinuus flw reactrs. In each case we apply the cnservatin f species mass principle which states (Rate f ccumulatin (Rate f Input (Rate f Output + (Rate f Generatin (- Equatin (- is applied t an apprpriately selected cntrl vlume, the largest arbitrarily selected vlume f the system in which there are n gradients in cmpsitin.. Batch Reactr The ideal batch reactr is assumed t be perfectly mixed. This implies that at a given mment in time the cncentratin is unifrm thrughut the vessel. The vlume, in the develpment belw is assumed equal t the vlume f the reactin mixture. This is then equal t the reactr vlume R in case f gas phase reactin but nt in case f liquids (< R, then. The batch reactr can be an autclave f cnst (Figure.-a and a cnstant pressure, P cnst (Figure.-b vessel. The frmer is almst always encuntered in practice. Our gal is: a T find a relatinship between species cncentratin (reactant cnversin and time n stream. b T relate reactr size and prductin rate.

2 Let us cnsider a single irreversible reactin P with an n-th rder irreversible rate f reactin n kc (- t t 0 a batch f vlume is filled with fluid f cncentratin C. Reactin is started (n C. Find hw reactant cnversin depends n reactin time? ls determine the prductin rate as a functin f reactin time. We apply (eq - t reactant : (R dn dt d(c dt (-3 a cnst b P cnst FIGURE -: Schematic f Batch Reactrs In ur case due t the fact that υ j 0, cnst irrespective f the batch reactr type, s that eq (-3 becmes j dc dt R (-4 dc dt ( kc n ; t 0 C C (-5 Separatin f variables and integratin yields: t dt dc n C dc n C 0 kc k (-6 C C C

3 t t k C n C n C t 0 k( n C t n n [ C ] (-7 C n [ k( n ( ] n (-8a r t k(n C n [( n ] (-8b Once rder f reactin, n, is specified (as shwn belw fr n0,,,.5, the relatin between t and is readily fund n 0 t C k n t k ln n.5; t 0.5k C ( 0.5 n t kc (-9 Prductin Rate f Prduct P can be related by stichimetry t he cnsumptin rate f as ml F P S F The prductin rate f P is given by: (mles f P prcessed per batch (reactin time + shut dwn time per batch (-0 C t + t s n k(n C C (- [( n ]+t s NOT BENE: Equatin (- is valid nly fr systems f cnstant density. Thus, it is valid fr all systems, gas r liquid, cnducted in an autclave at cnst (see Figure -a. It is als valid fr gaseus systems with n change in the 3

4 number f mles ( ν j 0 cnducted in P cnst. system at T cnst (Figure -b. The first equality in equatin (- gives the general result, the secnd equality presents the result fr an n-th rder irreversible reactin with resect t reactant. T use this equatin the shut dwn time, i.e. the time needed between batches, t s, must be knwn. Cnsider nw the fllwing secnd rder reactin with stichimetry P. ml 0.C Lmin a Find the batch reactr vlume needed t prduce 38 kml/min if reactr shut dwn time is 60 minutes and the desired cnversin is Initial reactant cncentratin is C (ml L. Using the right frm f equatin (-9 fr n we get the reactin time. t (min Then, slving equatin (- fr the vlume we get (t + t s.38( ,000L 0m 3 C x0.95 b What is the maximum prductin rate,, achievable in the abve batch reactr f vlume 0m 3 if t s, T, C all are fixed at previus values. Cnsider eq (- fr prductin rate as a functin f cnversin kc C +t s x 0 3 ( x (

5 This expressin has a maximum which we can lcate by differentiatin d 0 ( ( ( x 0 d x 0, 6 ± Clearly, the psitive sign is nt permissible as cnversin cannt exceed unity. We need t check whether the answer is a maximum r a minimum. d > 0 fr < 0.70 d d < 0 fr x > 0.70 Maximum at max x ml min n increase in prductivity f unreacted t be recycled x00 % can be achieved at the expense f mre 38 One must include the cst f separatin int the real ecnmic ptimizatin.. Cntinuus Flw Reactrs (Steady State.. Cntinuus Flw Stirred Tank Reactr (CFSTR r CSTR r STR The CSTR is assumed perfectly mixed, which implies that there are n spatial gradients f cmpsitin thrughut the reactr. Since the reactr perates at steady state, this implies that a single value f species cncentratin is fund in each pint f the reactr at all times and this is 5

6 equal t the value in the utflw. The utflw stream is a true representative f the reactin mixture in the reactr. F O F F ( C C O FIGURE -: Schematic f a Cntinuus Flw Stirred Tank Reactr (CSTR What des the abve idealizatin f the mixing pattern in a CSTR imply? It pstulates that the rate f mixing is instantaneus s that the feed lses its identify instantly and all the reactin mixture is at the cmpsitin f the utlet. Practically this implies that the rate f mixing frm macrscpic level dwn t a mlecular scale is rders f magnitude faster than the reactin rate and is s fast in every pint f the vessel. Then the mass balance f eq (- can be applied t the whle vlume f the reactr recgnizing that at steady state the accumulatin term is identically zer. gain, taking a simple example f an irreversible reactin P applicatin f eq (- t reactant yields: F F + ((R 0 (- Mlar flw rate f unreacted in the utflw by definitin is given by F F (- Q C (-. The prductin rate f P is given by ( (R P (-3 Reactr vlume is given by eq (- F ( Q C x ( (-4 6

7 Reactr space time is defined by τ Q C ( (-5 Using stichimetry we readily develp the relatin between prductin rate,, and reactr vlume,. Let us cnsider again the example f ur nd rder reactin, P, with the rate belw: kc n ml 0.C L min Find CSTR vlume needed t prcess 38 ml/min. Suppse we chse again 0.95 fr ur exit cnversin. Frm eq (-3 we get 0. C (- nd slving fr vlume F P 38 5,000L 5m 3 0.C ( 0.x( 0.95 If we cnsider eq (-3 it is clear that nw the maximum prductin rate is btained when the reactin rate is the highest. That fr n-th rder reactins is at zer cnversin. S the maximum frm CSTR,000 L is btainable at 0. max 0. x x 5,000 5,00 ml/min. The penalty r this enrmus prductin rate is that the prduct is at zer purity. Hence, the separatin csts wuld be enrmus. The average rate in a CSTR is equal t the rate at exit cnditins. ( ( exit 0.C ( exit 0.x( x0 4 (ml / Lmin 7

8 .. Plug Flw Reactr (PFR The main assumptins f the plug flw reactr are: i perfect instantaneus mixing perpendicular t flw, ii n mixing in directin f flw This implies pistn like flw with the reactin rate and cncentratin that vary alng reactr C O C O F O F d ( d F F ( FIGURE -3: Schematic f a Plug Flw Reactr (PFR Since there are nw cmpsitin gradients in the directin f flw, the cntrl vlume is a differential vlume t which eq (- is applied. Let us again use the mass balance n reactant F F + +R 0 (-6 F + R 0 F lim 0 ( lim( R 0 df d ( (-7 Since F F ( then df F d s that F d d ( (-8 With initial cnditins: 0 0 (-9 8

9 Upn separatin f variables in (eq -8 and integratin: d F (-0 ( Fr an n-th rder reactin (with ε 0 we get F n kc d Q ( n n kc [( n ] (n (- The expressin fr the PFR space time τ Q kc n (n ( n [ ] (- is nw identical t the expressin fr reactin time t in the batch reactr. Fr the example f the secnd rder reactin used earlier we get F F kc d kc ( F kc F kc F Q C τ Q kc (Same as the expressin fr reactin time t in the batch reactr Let us cnsider ur example f the secnd rder reactin and find the PFR vlume needed t prduce 38 ml/min ml ( 0.C Lmin when C ml L and desired cnversin Frm stichimetry it fllws that F F 9

10 Substitutin in the expressin fr reactr vlume (eq (- we get: F P kc kc ( 38 7,600L 7.6m3 0.x( 0.95 The maximum prductin rate frm that vlume can be btained at zer cnversin kc ( 0.xx ml / min max verage rate in PFR F ( entrance 0.C 0. 0 ml Lmin ( exit 0.C ( x0 4 ml L min 38 7, x0 3 ml min Clearly there is a big variatin in the reactin rate between the entrance and exit f the plug flw reactr (PFR..3 STY Space Time Yield lumetric Reactr Prductivity - RP Reactr vlumetric prductivity (RP is defined by: R P (-3 Fr ur nd rder reactin example f stichimetry P, RP fr the tw cntinuus flw reactrs is: CSTR R P (R P exit ( exit kc ( (-4a PFR R P kc ( (-4b 0

11 Fr the same exit cnversin (R P PFR kc ( (R P CSTR kc ( t 0.95 (R P PFR (R P CSTR 0 Indeed 0 x 7,600 L 5,000 L This is why higher CSTR vlume is needed. t 0 (R P PFR R P ( CSTR There is n difference! Let us cnsider anther example t illustrate sme imprtant pints. Ex: + 3B P + S stichimetry ml r 0.C C B - rate f reactin L min C ml L and 0 ml/min is the desired prductin rate are the feed reactant cncentratin and desired cnversin ssume first that we will perate at stichimetric rati s that C B 3 (ml/l. The reactin ccurs in the liquid phase s that ε 0. Find the needed reactr vlume. a Batch (t s 60 min 0.C ( (C B b a C 0.C 3 ( 3 ( 3 0.C 3 ( 3

12 Reactin time is: t 3 0.C t g 0.x a ( 3 ( x 3.8 ( x t 3.6 ( 36 ( t 0.83 min C t + t s 0.95x x0,798 L.8m b CSTR F - frm stichimetry - basic design equatin (-4 F F ( 0.C C B 0.C 3 ( C B 3 C x C ( ( ( ( exit 0.xC 3 ( exit 0.xx9( x0-4 (ml/l min 3 3 4,444(L 44.4m 0.05

13 c PFR F - frm stichimetry Basic design equatin (- F d F P C F 0.C 3 ( x 3 ( x ( x x0.95 ( 00 8x 0.95 ( x ( 0.95,67(L.7 m Nw the rate, at stichimetric feed rati, alng the PFR as a functin f cnversin is C ( x 3 3.6( 3 PFR reactr vlume as functin f cnversin at stichimetric feed rati is F P 3.6 F P ( x 3.8x ( x 3 Hence, the prductin rate frm a given PFR vlume as a functin f cnversin (at stichimetric feed rate is stich.8 ( x ( Hw much can we increase the prductin rate by dubling C B t C B 6 (ml/l, i.e. by using B in excess? 3

14 Nw the rate as a functin f cnversin is: 3 0.C ( C B C 3.6( ( 3 0.x 3 x 3 ( x ( x a Batch t C ( 3.6 ( x( x T integrate use partial fractins: x + B +Cx ( x ( x + (B +Cx( x ( x( x 4 4 x + x + B Bx + Cx Cx 4+B B+C0-3-B-0 B-3 B-3 -C0 C ( x( x + x 3 x ( x x x ( x ( x ln( x + ln( x x ln( ln( ln + ln ( + ln x ( ( t.8 ln x ( ( 0.95 t.05 ln.8 x x ln t.055 min Batch ill advised at these cnditins since t s >> t! 4

15 new C t +t s 0.95x,798 ml min % ld 0 By perating at duble the stichimetric requirement f B we increase, at same, the prductin rate f the batch reactr by 80%. b CSTR 3.6( ( 3.6( 0.95( x0.05x ml L min new ld R P ,494 4,40 ml min 00 4, x00 44,000% In a CSTR we increase the prductin rate by 44,000%! c PFR F new ( x( x ( x( x 3.8 ( x( x 3.8x new x ln x ( (.8x0.95x,67 new ln x0.95x,67 ( ln.05 ( new,05 ml / min 5

16 x00,05 0 x00 0,49% ld 0 In a PFR ver 0,000% increase in is btained. We present belw these ratis f prductin rate btainable at nnstichimetric rati f C B C ( C B C stich and at stichimetric rati f C B /C 3/ fr ur example reactin. This rati is: Fr a PFR:.8 ln x (nn stich ( ( F 3.6x P( stich ( ( ln x ( ( Specifically fr 0.95 we get (nn stich (stich 0.05 x x.05 ln0.5.0 ln ln Fr a CSTR (nn stich 3.6( ( ( (stich 3.6( 3 ( ( nn stich.05 ( stich Let us examine the situatin when the reactin just cnsidered ccurs at P cnst, T cnst in the gaseus phase. Then due t stichimetry we have B + 3B P + S υ j

17 Cnsider stichimetric feed f reactants at C B /C 3/. y ( υ ε y υ j ( υ 0.4 ( x C C 0.6 C B C C B 3 C xC 3 3 ( 3 ( ( 3 ( CSTR ( R x0( 0.6x ( ( ,444x ,534(L Tremendus reductin in required vlume cmpared t the ε 0 case ccurs! PFR F d 0.95 F p ( 0.6x 3 3.6( x 3 ( 0.6x ( x 3.8x (L x x 3 gain a significant reductin in PFR reactr vlume requirement is bserved. Why? 7

18 .4 Graphic Cmparisn f PFR and CSTR F F CSTR PFR ( exit d The graphic representatin f the abve tw design equatins is represented belw fr an n-th rder reactin. Clearly, fr fixed feed cnditins and feed rate and fr chsen desired cnversin the vlume f the CSTR will always be larger than r equal t the PFR vlume. F CSTR area f bx F PFR area under the curve FIGURE -4: Graphical Cmparisn f CSTR and PFR 8

(2) Even if such a value of k was possible, the neutrons multiply

(2) Even if such a value of k was possible, the neutrons multiply CHANGE OF REACTOR Nuclear Thery - Curse 227 POWER WTH REACTVTY CHANGE n this lessn, we will cnsider hw neutrn density, neutrn flux and reactr pwer change when the multiplicatin factr, k, r the reactivity,

More information

Computational modeling techniques

Computational modeling techniques Cmputatinal mdeling techniques Lecture 4: Mdel checing fr ODE mdels In Petre Department f IT, Åb Aademi http://www.users.ab.fi/ipetre/cmpmd/ Cntent Stichimetric matrix Calculating the mass cnservatin relatins

More information

Thermodynamics and Equilibrium

Thermodynamics 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 information

February 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 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

Materials Engineering 272-C Fall 2001, Lecture 7 & 8 Fundamentals of Diffusion

Materials 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 information

Thermodynamics Partial Outline of Topics

Thermodynamics 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 information

General Chemistry II, Unit II: Study Guide (part 1)

General 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 information

Math 105: Review for Exam I - Solutions

Math 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 information

Compressibility Effects

Compressibility Effects Definitin f Cmpressibility All real substances are cmpressible t sme greater r lesser extent; that is, when yu squeeze r press n them, their density will change The amunt by which a substance can be cmpressed

More information

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium

Lecture 17: Free Energy of Multi-phase Solutions at Equilibrium Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical

More information

University Chemistry Quiz /04/21 1. (10%) Consider the oxidation of ammonia:

University 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 information

Lecture 12: Chemical reaction equilibria

Lecture 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 information

CHAPTER PRACTICE PROBLEMS CHEMISTRY

CHAPTER 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 information

Examiner: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data

Examiner: Dr. Mohamed Elsharnoby Time: 180 min. Attempt all the following questions Solve the following five questions, and assume any missing data Benha University Cllege f Engineering at Banha Department f Mechanical Eng. First Year Mechanical Subject : Fluid Mechanics M111 Date:4/5/016 Questins Fr Final Crrective Examinatin Examiner: Dr. Mhamed

More information

Part One: Heat Changes and Thermochemistry. This aspect of Thermodynamics was dealt with in Chapter 6. (Review)

Part 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 information

More Tutorial at

More 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 information

Process Engineering Thermodynamics E (4 sp) Exam

Process 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

Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1

Physics 212. Lecture 12. Today's Concept: Magnetic Force on moving charges. Physics 212 Lecture 12, Slide 1 Physics 1 Lecture 1 Tday's Cncept: Magnetic Frce n mving charges F qv Physics 1 Lecture 1, Slide 1 Music Wh is the Artist? A) The Meters ) The Neville rthers C) Trmbne Shrty D) Michael Franti E) Radiatrs

More information

Chapter 17 Free Energy and Thermodynamics

Chapter 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

ALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?

ALE 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 information

Pattern Recognition 2014 Support Vector Machines

Pattern 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 information

( ) kt. Solution. From kinetic theory (visualized in Figure 1Q9-1), 1 2 rms = 2. = 1368 m/s

( ) 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 information

Chem 75 February 16, 2017 Exam 2 Solutions

Chem 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 information

22.54 Neutron Interactions and Applications (Spring 2004) Chapter 11 (3/11/04) Neutron Diffusion

22.54 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 information

Chem 115 POGIL Worksheet - Week 8 Thermochemistry (Continued), Electromagnetic Radiation, and Line Spectra

Chem 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 information

ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS

ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS ENGINEERING COUNCIL CERTIFICATE LEVEL THERMODYNAMIC, FLUID AND PROCESS ENGINEERING C106 TUTORIAL 5 THE VISCOUS NATURE OF FLUIDS On cmpletin f this tutrial yu shuld be able t d the fllwing. Define viscsity

More information

Electrochemistry. Reduction: the gaining of electrons. Reducing agent (reductant): species that donates electrons to reduce another reagent.

Electrochemistry. 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 information

AP CHEMISTRY CHAPTER 6 NOTES THERMOCHEMISTRY

AP 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 information

Module 4: General Formulation of Electric Circuit Theory

Module 4: General Formulation of Electric Circuit Theory Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated

More information

11. DUAL NATURE OF RADIATION AND MATTER

11. DUAL NATURE OF RADIATION AND MATTER 11. DUAL NATURE OF RADIATION AND MATTER Very shrt answer and shrt answer questins 1. Define wrk functin f a metal? The minimum energy required fr an electrn t escape frm the metal surface is called the

More information

4F-5 : Performance of an Ideal Gas Cycle 10 pts

4F-5 : Performance of an Ideal Gas Cycle 10 pts 4F-5 : Perfrmance f an Cycle 0 pts An ideal gas, initially at 0 C and 00 kpa, underges an internally reversible, cyclic prcess in a clsed system. The gas is first cmpressed adiabatically t 500 kpa, then

More information

Chapters 29 and 35 Thermochemistry and Chemical Thermodynamics

Chapters 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 information

Revision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax

Revision: 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 information

(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f

(1.1) V which contains charges. If a charge density ρ, is defined as the limit of the ratio of the charge contained. 0, and if a force density f 1.0 Review f Electrmagnetic Field Thery Selected aspects f electrmagnetic thery are reviewed in this sectin, with emphasis n cncepts which are useful in understanding magnet design. Detailed, rigrus treatments

More information

CHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review

CHEM 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 information

Semester 2 AP Chemistry Unit 12

Semester 2 AP Chemistry Unit 12 Cmmn In Effect and Buffers PwerPint The cmmn in effect The shift in equilibrium caused by the additin f a cmpund having an in in cmmn with the disslved substance The presence f the excess ins frm the disslved

More information

lecture 5: Nucleophilic Substitution Reactions

lecture 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 information

Interference is when two (or more) sets of waves meet and combine to produce a new pattern.

Interference 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 information

Surface and Contact Stress

Surface 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 information

Entropy, Free Energy, and Equilibrium

Entropy, 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 information

General Chemistry II, Unit I: Study Guide (part I)

General 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 information

Electric Current and Resistance

Electric 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 information

ELECTRON CYCLOTRON HEATING OF AN ANISOTROPIC PLASMA. December 4, PLP No. 322

ELECTRON CYCLOTRON HEATING OF AN ANISOTROPIC PLASMA. December 4, PLP No. 322 ELECTRON CYCLOTRON HEATING OF AN ANISOTROPIC PLASMA by J. C. SPROTT December 4, 1969 PLP N. 3 These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated. They are fr private

More information

Find 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? 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 eep this site up and bring yu even mre cntent cnsider dnating via the lin n ur site. Still having truble understanding the material? Chec ut ur Tutring

More information

A Few Basic Facts About Isothermal Mass Transfer in a Binary Mixture

A 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 information

Differentiation Applications 1: Related Rates

Differentiation 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 information

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems.

Building to Transformations on Coordinate Axis Grade 5: Geometry Graph points on the coordinate plane to solve real-world and mathematical problems. Building t Transfrmatins n Crdinate Axis Grade 5: Gemetry Graph pints n the crdinate plane t slve real-wrld and mathematical prblems. 5.G.1. Use a pair f perpendicular number lines, called axes, t define

More information

Ecology 302 Lecture III. Exponential Growth (Gotelli, Chapter 1; Ricklefs, Chapter 11, pp )

Ecology 302 Lecture III. Exponential Growth (Gotelli, Chapter 1; Ricklefs, Chapter 11, pp ) Eclgy 302 Lecture III. Expnential Grwth (Gtelli, Chapter 1; Ricklefs, Chapter 11, pp. 222-227) Apcalypse nw. The Santa Ana Watershed Prject Authrity pulls n punches in prtraying its missin in apcalyptic

More information

CHAPTER Read Chapter 17, sections 1,2,3. End of Chapter problems: 25

CHAPTER 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 information

Accelerated Chemistry POGIL: Half-life

Accelerated Chemistry POGIL: Half-life Name: Date: Perid: Accelerated Chemistry POGIL: Half-life Why? Every radiistpe has a characteristic rate f decay measured by its half-life. Half-lives can be as shrt as a fractin f a secnd r as lng as

More information

Lim f (x) e. Find the largest possible domain and its discontinuity points. Why is it discontinuous at those points (if any)?

Lim 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 information

Bicycle Generator Dump Load Control Circuit: An Op Amp Comparator with Hysteresis

Bicycle Generator Dump Load Control Circuit: An Op Amp Comparator with Hysteresis Bicycle Generatr Dump Lad Cntrl Circuit: An Op Amp Cmparatr with Hysteresis Sustainable Technlgy Educatin Prject University f Waterl http://www.step.uwaterl.ca December 1, 2009 1 Summary This dcument describes

More information

Appendix I: Derivation of the Toy Model

Appendix 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 information

Lecture 5: Equilibrium and Oscillations

Lecture 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 information

Session #22: Homework Solutions

Session #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 information

Introduction: A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem

Introduction: A Generalized approach for computing the trajectories associated with the Newtonian N Body Problem A Generalized apprach fr cmputing the trajectries assciated with the Newtnian N Bdy Prblem AbuBar Mehmd, Syed Umer Abbas Shah and Ghulam Shabbir Faculty f Engineering Sciences, GIK Institute f Engineering

More information

OF SIMPLY SUPPORTED PLYWOOD PLATES UNDER COMBINED EDGEWISE BENDING AND COMPRESSION

OF 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 information

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS

2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes.

More information

Find 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? 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 information

N 2 (g) + 3H 2 (g) 2NH 3 (g) o Three mole ratios can be derived from the balanced equation above: Example: Li(s) + O 2 (g) Li 2 O(s)

N 2 (g) + 3H 2 (g) 2NH 3 (g) o Three mole ratios can be derived from the balanced equation above: Example: Li(s) + O 2 (g) Li 2 O(s) Chapter 9 - Stichimetry Sectin 9.1 Intrductin t Stichimetry Types f Stichimetry Prblems Given is in mles and unknwn is in mles. Given is in mles and unknwn is in mass (grams). Given is in mass and unknwn

More information

CHEM 116 Electrochemistry at Non-Standard Conditions, and Intro to Thermodynamics

CHEM 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 information

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards:

MODULE FOUR. This module addresses functions. SC Academic Elementary Algebra Standards: MODULE FOUR This mdule addresses functins SC Academic Standards: EA-3.1 Classify a relatinship as being either a functin r nt a functin when given data as a table, set f rdered pairs, r graph. EA-3.2 Use

More information

Making and Experimenting with Voltaic Cells. I. Basic Concepts and Definitions (some ideas discussed in class are omitted here)

Making and Experimenting with Voltaic Cells. I. Basic Concepts and Definitions (some ideas discussed in class are omitted here) Making xperimenting with Vltaic Cells I. Basic Cncepts Definitins (sme ideas discussed in class are mitted here) A. Directin f electrn flw psitiveness f electrdes. If ne electrde is mre psitive than anther,

More information

Unit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY

Unit code: H/ QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY Unit 43: Plant and Prcess Principles Unit cde: H/601 44 QCF level: 5 Credit value: 15 OUTCOME 3 - STATIC AND DYNAMIC FLUID SYSTEMS TUTORIAL 3 - VISCOSITY 3 Understand static and namic fluid systems with

More information

Chapter 17: Thermodynamics: Spontaneous and Nonspontaneous Reactions and Processes

Chapter 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 information

37 Maxwell s Equations

37 Maxwell s Equations 37 Maxwell s quatins In this chapter, the plan is t summarize much f what we knw abut electricity and magnetism in a manner similar t the way in which James Clerk Maxwell summarized what was knwn abut

More information

Chapter 3 Kinematics in Two Dimensions; Vectors

Chapter 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 information

Entropy. Chapter The Clausius Inequality and Entropy

Entropy. 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 information

GAUSS' LAW E. A. surface

GAUSS' LAW E. A. surface Prf. Dr. I. M. A. Nasser GAUSS' LAW 08.11.017 GAUSS' LAW Intrductin: The electric field f a given charge distributin can in principle be calculated using Culmb's law. The examples discussed in electric

More information

CHM 152 Practice Final

CHM 152 Practice Final CM 152 Practice Final 1. Of the fllwing, the ne that wuld have the greatest entrpy (if cmpared at the same temperature) is, [a] 2 O (s) [b] 2 O (l) [c] 2 O (g) [d] All wuld have the same entrpy at the

More information

EXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE

EXPERIMENTAL STUDY ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE EXPERIMENTAL STUD ON DISCHARGE COEFFICIENT OF OUTFLOW OPENING FOR PREDICTING CROSS-VENTILATION FLOW RATE Tmnbu Gt, Masaaki Ohba, Takashi Kurabuchi 2, Tmyuki End 3, shihik Akamine 4, and Tshihir Nnaka 2

More information

NOTE ON APPELL POLYNOMIALS

NOTE ON APPELL POLYNOMIALS NOTE ON APPELL POLYNOMIALS I. M. SHEFFER An interesting characterizatin f Appell plynmials by means f a Stieltjes integral has recently been given by Thrne. 1 We prpse t give a secnd such representatin,

More information

Spontaneous Processes, Entropy and the Second Law of Thermodynamics

Spontaneous 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 information

" 1 = # $H vap. Chapter 3 Problems

 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 information

x x

x 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 information

Lead/Lag Compensator Frequency Domain Properties and Design Methods

Lead/Lag Compensator Frequency Domain Properties and Design Methods Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin

More information

Complex Reactions and Mechanisms (continued)

Complex Reactions and Mechanisms (continued) 5.60 Spring 2005 Lecture #29 page 1 Cmplex Reactins and Mechanisms (cntinued) Sme cmments abut analyzing kinetic data A) Reactins with ne reactant: A prducts a) Plt r analyze [A vs. t ln[a vs. t 1/[A vs.

More information

Find 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? 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 information

Dispersion Ref Feynman Vol-I, Ch-31

Dispersion 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 information

CHAPTER 3 INEQUALITIES. Copyright -The Institute of Chartered Accountants of India

CHAPTER 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 information

3. Mass Transfer with Chemical Reaction

3. Mass Transfer with Chemical Reaction 8 3. Mass Transfer with Chemical Reactin 3. Mass Transfer with Chemical Reactin In the fllwing, the fundamentals f desrptin with chemical reactin, which are applied t the prblem f CO 2 desrptin in ME distillers,

More information

5 th grade Common Core Standards

5 th grade Common Core Standards 5 th grade Cmmn Cre Standards In Grade 5, instructinal time shuld fcus n three critical areas: (1) develping fluency with additin and subtractin f fractins, and develping understanding f the multiplicatin

More information

Lecture 4. The First Law of Thermodynamics

Lecture 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 information

, which yields. where z1. and z2

, which yields. where z1. and z2 The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin

More information

Edexcel IGCSE Chemistry. Topic 1: Principles of chemistry. Chemical formulae, equations and calculations. Notes.

Edexcel 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 information

GOAL... ability to predict

GOAL... ability to predict THERMODYNAMICS Chapter 18, 11.5 Study f changes in energy and transfers f energy (system < = > surrundings) that accmpany chemical and physical prcesses. GOAL............................. ability t predict

More information

Unit 11 Solutions- Guided Notes. What are alloys? What is the difference between heterogeneous and homogeneous mixtures?

Unit 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 information

PHYS 314 HOMEWORK #3

PHYS 314 HOMEWORK #3 PHYS 34 HOMEWORK #3 Due : 8 Feb. 07. A unifrm chain f mass M, lenth L and density λ (measured in k/m) hans s that its bttm link is just tuchin a scale. The chain is drpped frm rest nt the scale. What des

More information

Kinematic transformation of mechanical behavior Neville Hogan

Kinematic transformation of mechanical behavior Neville Hogan inematic transfrmatin f mechanical behavir Neville Hgan Generalized crdinates are fundamental If we assume that a linkage may accurately be described as a cllectin f linked rigid bdies, their generalized

More information

Kinetics of Particles. Chapter 3

Kinetics of Particles. Chapter 3 Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between

More information

Chapter 4. Unsteady State Conduction

Chapter 4. Unsteady State Conduction Chapter 4 Unsteady State Cnductin Chapter 5 Steady State Cnductin Chee 318 1 4-1 Intrductin ransient Cnductin Many heat transfer prblems are time dependent Changes in perating cnditins in a system cause

More information

Lecture 23: Lattice Models of Materials; Modeling Polymer Solutions

Lecture 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 information

Variable-volume operation of a stirred tank reactor

Variable-volume operation of a stirred tank reactor Retrspective Theses and Dissertatins 1970 Variable-vlume peratin f a stirred tank reactr Mnty Marvin Lund Iwa State University Fllw this and additinal wrks at: http://lib.dr.iastate.edu/rtd Part f the

More information

Pressure And Entropy Variations Across The Weak Shock Wave Due To Viscosity Effects

Pressure 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 information

Equilibrium of Stress

Equilibrium of Stress Equilibrium f Stress Cnsider tw perpendicular planes passing thrugh a pint p. The stress cmpnents acting n these planes are as shwn in ig. 3.4.1a. These stresses are usuall shwn tgether acting n a small

More information

B. Definition of an exponential

B. Definition of an exponential Expnents and Lgarithms Chapter IV - Expnents and Lgarithms A. Intrductin Starting with additin and defining the ntatins fr subtractin, multiplicatin and divisin, we discvered negative numbers and fractins.

More information

CHEM 1001 Problem Set #3: Entropy and Free Energy

CHEM 1001 Problem Set #3: Entropy and Free Energy CHEM 1001 Prblem Set #3: Entry and Free Energy 19.7 (a) Negative; A liquid (mderate entry) cmbines with a slid t frm anther slid. (b)psitive; One mle f high entry gas frms where n gas was resent befre.

More information

Heat Effects of Chemical Reactions

Heat Effects of Chemical Reactions eat Effects f hemical Reactins Enthalpy change fr reactins invlving cmpunds Enthalpy f frmatin f a cmpund at standard cnditins is btained frm the literature as standard enthalpy f frmatin Δ (O (g = -9690

More information

3D FE Modeling Simulation of Cold Rotary Forging with Double Symmetry Rolls X. H. Han 1, a, L. Hua 1, b, Y. M. Zhao 1, c

3D FE Modeling Simulation of Cold Rotary Forging with Double Symmetry Rolls X. H. Han 1, a, L. Hua 1, b, Y. M. Zhao 1, c Materials Science Frum Online: 2009-08-31 ISSN: 1662-9752, Vls. 628-629, pp 623-628 di:10.4028/www.scientific.net/msf.628-629.623 2009 Trans Tech Publicatins, Switzerland 3D FE Mdeling Simulatin f Cld

More information

Lecture 7 Further Development of Theory and Applications

Lecture 7 Further Development of Theory and Applications P4 Stress and Strain Dr. A.B. Zavatsk HT08 Lecture 7 Further Develpment f Ther and Applicatins Hke s law fr plane stress. Relatinship between the elastic cnstants. lume change and bulk mdulus. Spherical

More information