Example
|
|
- Donna Hubbard
- 6 years ago
- Views:
Transcription
1 Chapte.4 iffusion with Chemical eaction Example fluiize coal eacto opeates at 45 K an atm. The pocess will be limite by the iffusion of oxygen countecuent to the cabon ioxie, CO, fome at the paticle suface. ssume that the coal is pue soli cabon with a ensity of 80 g/m 3 an that the paticle is spheical with an initial iamete of m. i (% O an 79% N ) exists seveal iametes away fom the sphee. The iffusivity of oxygen in the gas mixtue at 45 K is m /s. If a quasi-steay state pocess is assume, calculate the time necessay to euce the iamete of the cabon paticle to m. (ef. Funamentals of Momentum, Heat, an Mass Tansfe by Welty, Wics, an Wilson, 4 th Eition, 00, pg. 496.) Solution The eaction at the cabon suface is C(s) + O (g) CO (g) We have iffusion of oxygen () towa the suface an iffusion of cabon ioxie (B) away fom the suface. The mola flux of oxygen is given by N, c mix y + y (N, + N B, ) In this equation, is the aial istance fom the cente of the cabon paticle. Since N, N B,, we have N, c mix y The system is not at steay state, the mola flux is not inepenent of since the aea of mass tansfe 4π is not a constant. Using quasi steay state assumption, the mass (mole) tansfe ate, 4π N,, is assume to be inepenent of at any instant of time. W 4π N, 4π c mix y constant y, y,inf -3
2 t the suface of the coal paticle, the eaction ate is much faste than the iffusion ate to the suface so that the oxygen concentation can be consiee to be zeo: y, 0. Sepaating the vaiables an integating gives y, 4π c mix y 0 W W 4π c mix y, > W 4πc mix y, Since one mole of cabon will isappea fo each mole of oxygen consume at the suface W C W 4πc mix y, Maing a cabon balance gives ρc 4 3 π M C t 3 ρc M C 4π t 4πc mix y, Sepaating the vaiables an integating fom t 0 to t gives t t 0 ρc M c C y mix, f i ρc t M c C y mix, ( i f ) The total gas concentation can be obtaine fom the ieal gas law c P T (0.0806)(45) mol/m3 Note: m 3 atm/mol o K The time necessay to euce the iamete of the cabon paticle fom m to m is then ( ) ( ) 5 5 (80) t 4 ()(0.006)(.3 0 )(0.) 0.9 s -4
3 Example Pulveize coal pellets, which may be appoximate as cabon sphees of aius mm, ae bune in a pue oxygen atmosphee at 450 K an atm. Oxygen is tansfee to the paticle suface by iffusion, whee it is consume in the eaction C(s) + O (g) CO (g). The eaction ate is fist oe an of the fom ɺ " C O whee 0. m/s. This is the eaction ate pe unit suface aea of the cabon pellets. Neglecting change in, etemine the steay-state O mola consumption ate in mol/s. t 450 K, the binay iffusion coefficient fo O an CO is m /s. (ef. Funamentals of Heat Tansfe by Incopea an ewitt.) Solution We have iffusion of oxygen () towa the suface an iffusion of cabon ioxie (B) away fom the suface. The mola flux of oxygen is given by N, c y + y (N, + N B, ) In this equation, is the aial istance fom the cente of the cabon paticle. Since N, N B,, we have N, c y The system is not at steay state, the mola flux is not inepenent of since the aea of mass tansfe 4π is not a constant. Using quasi steay state assumption, the mass (mole) tansfe ate, 4π N,, is assume to be inepenent of at any instant of time. W 4π N, 4π c y constant y, y,inf The oxygen concentation at the suface of the coal paticle, y,, will be etemine fom the eaction at the suface. The mole faction of oxygen at a location fa fom the pellet is. Sepaating the vaiables an integating gives y, 4π c y y, W W 4π c (y, y, ) > W 4πc ( y, ) -5
4 The mole of oxygen aive at the cabon suface is equal to the mole of oxygen consume by the chemical eaction W 4π ɺ " 4π C O 4π c y, 4πc ( y, ) 4π c y, ( y, ) y, > y, + " y, The total gas concentation can be obtaine fom the ieal gas law. (Note: m 3 atm/mol K) c P T (0.0806)(450) mol/m3 The steay-state O mola consumption ate is W 4πc ( y, ) 4π( )( )( 0.63)(0-3 ) W mol/s Example biofilm consists of living cells immobilize in a gelatinous matix. toxic oganic solute (species ) iffuses into the biofilm an is egae to hamless poucts by the cells within the biofilm. We want to teat 0. m 3 pe hou of wastewate containing 0. mole/m 3 of the toxic substance phenol using a system consisting of biofilms on otating is as shown below. Waste wate fee steam biofilm C 0 C (z) Inet soli suface Well-mixe contacto C 0 Teate waste wate biofilm z0 etemine the equie suface aea of the biofilm with mm thicness to euce the phenol concentation in the outlet steam to 0.0 mole/m 3. The ate of isappeaance of phenol (species ) within the biofilm is escibe by the following equation -6
5 c whee 0.09 s - The iffusivity of phenol in the biofilm at the pocess tempeatue of 5 o C is m /s. Phenol is equally soluble in both wate an the biofilm. (ef. Funamentals of Momentum, Heat, an Mass Tansfe by Welty, Wics, an Wilson, 4 th Eition, 00, pg. 496.) Solution The ate of phenol pocesse by the biofilms, W, is etemine fom the mateial balance on the pocess unit W 0. m 3 /h(0. 0.0) mol/m mol/h W is then equal to the ate of phenol iffuse into the biofilms an can be calculate fom c W S N,z S z 0 In this equation, S is the equie suface aea of the biofilm an N,z is the mola flux of phenol at the suface of the biofilm. The mola flux of (phenol) is given by N,z c y + y (N,z + N B,z ) Since the biofilm is stagnant (o noniffusing), N B,z 0. Solving fo N,z give N,z ( y ) c y The mole faction of phenol in the biofilm, y, is much less than one so that c can be consiee to be constant. Theefoe N,z c y c Biofilm Soli suface N,z Maing a mole balance aoun the contol volume S z gives z -7
6 S N,z z S N,z z+ z + S z 0 iviing the equation by S z an letting z 0 yiels N, z Substituting N,z c (E-) c into equation (E-) we obtain c c > c c (E-) The solution to the homogeneous equation (E-) has two foms ) c C exp ) c B sinh z z + C exp + B cosh z z The fist exponential fom () is moe convenient if the omain of z is infinite: 0 z while the secon fom using hypebolic functions () is moe convenient if the omain of z is finite: 0 z δ. The constants of integation C, C, B, an B ae to be etemine fom the two bounay conitions. We use the hypebolic functions as the solution to Eq. (E-). c B sinh z + B cosh z (E-3) t z 0, c c s c 0 B t z δ, Theefoe c 0 B cosh δ + B sinh δ sinh B B cosh δ δ sinh c 0 cosh δ δ Equation (E-3) becomes -8
7 sinh c c 0 cosh δ δ sinh z + c 0 cosh z cosh δcosh z sinh δsinh z c c 0 cosh δ Using the ientity cosh( B) cosh()cosh(b) sinh()sinh(b) we have c c 0 δ cosh δ cosh ( z) c z 0 c 0 sinh ( δ z) cosh δ z 0 c 0 tanh δ The mola flux of phenol at the biofilm suface is given by N,z c c0 δ z 0 tanh δ δ The imensionless paamete δ Fo this poblem we have epesents the atio of eaction ate to iffusion ate m s 0 m 0 s δ 9.49 This value inicates that the ate of eaction is vey api elative to the ate of iffusion. The flux of phenol into the biofilm is then -9
8 N,z 0 (0.0)( 0 ) 0.00 (9.49) tanh(9.49) mol/(m s) The equie suface aea of the biofilm is finally S W N, z (3.9 0 )(3600) 57.0 m Example Consie a spheical oganism of aius within which espiation occus at a unifom volumetic ate of C. That is, oxygen (species ) consumption is govene by a fist-oe, homogeneous chemical eaction. (a) If a mola concentation of C () C,0 is maintaine at the suface of the oganism, obtain an expession fo the aial istibution of oxygen, C (), within the oganism. (b) Obtain an expession fo the ate of oxygen consumption within the oganism. (c) Consie an oganism of aius 0.0 mm an a iffusion coefficient fo oxygen tansfe of 0-8 m /s. If C, mol/m 3 an 0 s -, what is the mola concentation of O at the cente of the oganism? What is the ate of oxygen consumption by the oganism? Solution (a) If a mola concentation of C () C,0 is maintaine at the suface of the oganism, obtain an expession fo the aial istibution of oxygen, C (), within the oganism. + Figue E- Illustation of a spheical shell 4π The one-imensional mola flux of is given by the equation " N C (E-) pplying a mole balance on the spheical shell shown in Figue E- yiels fo steay state 4π N " 4π " N + 4π
9 iviing the equation by the contol volume (4π ) an taing the limit as 0, we obtain ( " N ) + 0 (E-) Fo a fist oe eaction, C an substituting the mola flux fom equation (E-) into the above equation, we have C C 0 C C 0 (E-3) In this equation, an ae constants inepenent of. We want to tansfom this equation into the fom y α y 0 (E-4) Let α, we can tansfom equation (4.6-3) into the fom of equation (E-4) by the following algebaic manipulations C α C 0 C C + α C 0 C C + α C 0 Since becomes ( C ) C C + C + C C +, the above equation ( C ) α C 0 Let y C, the equation has the same fom as equation (E-4) with the solution y B sinh(α) + B cosh(α) o C B sinh(α) + B cosh(α), whee α -3
10 The two constants of integation B an B can be obtaine fom the bounay conitions t 0, C finite o C 0 t, C C 0 (a nown value) pplying the bounay at 0 yiels 0 B pplying the bounay at yiels C 0 C B sinh(α) B sinh( α) Theefoe the concentation pofile fo species within the oganism is C C 0 sinh( α) sinh( α) (E-5) α t the cente of the oganism, the concentation is given by C ( 0) C 0 sinh( α) (b) Obtain an expession fo the ate of oxygen consumption within the oganism. ate of oxygen consumption within the oganism. 4π ( C ) The oxygen concentation within the oganism is given by equation (E-5) C C 0 sinh( α) sinh( α) (E-5) C C sinh( α) 0 α sinh( α ) + cosh( α) C C sinh( α) 0 α cosh( α) sinh( α) C C 0 [ ] ( α ) coth( α) ) -3
11 / Let φ α Thiele moulus fo a fist oe eaction. Ignoing the minus sign, the ate of oxygen consumption within the oganism is then ate of oxygen consumption 4π C 0 (φ cothφ - ) ate of oxygen consumption 4π C 0 (φ cothφ - ) (c) Consie an oganism of aius 0.0 mm an a iffusion coefficient fo oxygen tansfe of 0-8 m /s. If C, mol/m 3 an 0 s -, what is the mola concentation of O at the cente of the oganism? What is the ate of oxygen consumption by the oganism? α t the cente of the oganism, the concentation is given by C ( 0) C 0 sinh( α) α / / m α / 4 ( ) / 4.47 α C ( 0) C 0 sinh( α) sinh(4.47) mol/m 3 ate of oxygen consumption 4π C 0 (φ cothφ - ) ate 4π(0-4 )(0-8 )( ) [4.47 coth(4.47) - ] mol/s The following Matlab pogam plots the concentation of oxygen within the oganism as a function of position. % Example.4-4 % alfa4.47e4; % m e-4; % m alfa4.47; C05e-5; % mol/m3 o(:50)/50; *o; -33
12 CC0*sinh(alfa*)./(o*sinh(alfa)); plot(o,c) gi on xlabel('/');ylabel('c_(mol/m^3)') Figue E.4-4 Oxygen concentation pofile in a spheical oganism. We now consie the iffusion of species into a spheical catalyst paticle whee homogeneous fist oe chemical eaction occus. The concentation pofile fo species within the spheical catalyst paticle is then C C sinh( α) sinh( α) (.4-) In this equation C is the concentation of species at the suface of the catalyst paticle an α is efine by the expession α, whee is the fist oe ate constant an is the iffusivity of in the paticle. t the cente of the bea, the concentation is given by α C ( 0) C sinh( α) (.4-) -34
GRAVITATION. Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., New Delhi -18 PG 1
Einstein Classes, Unit No. 0, 0, Vahman Ring Roa Plaza, Vikas Pui Extn., New Delhi -8 Ph. : 96905, 857, E-mail einsteinclasses00@gmail.com, PG GRAVITATION Einstein Classes, Unit No. 0, 0, Vahman Ring Roa
More informationPhysics 107 HOMEWORK ASSIGNMENT #15
Physics 7 HOMEWORK SSIGNMENT #5 Cutnell & Johnson, 7 th eition Chapte 8: Poblem 4 Chapte 9: Poblems,, 5, 54 **4 small plastic with a mass of 6.5 x - kg an with a chage of.5 µc is suspene fom an insulating
More informationPH126 Exam I Solutions
PH6 Exam I Solutions q Q Q q. Fou positively chage boies, two with chage Q an two with chage q, ae connecte by fou unstetchable stings of equal length. In the absence of extenal foces they assume the equilibium
More informationElectric Potential and Gauss s Law, Configuration Energy Challenge Problem Solutions
Poblem 1: Electic Potential an Gauss s Law, Configuation Enegy Challenge Poblem Solutions Consie a vey long o, aius an chage to a unifom linea chage ensity λ a) Calculate the electic fiel eveywhee outsie
More informationMAE 210B. Homework Solution #6 Winter Quarter, U 2 =r U=r 2 << 1; ) r << U : (1) The boundary conditions written in polar coordinates,
MAE B Homewok Solution #6 Winte Quate, 7 Poblem a Expecting a elocity change of oe oe a aial istance, the conition necessay fo the ow to be ominate by iscous foces oe inetial foces is O( y ) O( ) = =
More informationEquilibria of a cylindrical plasma
// Miscellaneous Execises Cylinical equilibia Equilibia of a cylinical plasma Consie a infinitely long cyline of plasma with a stong axial magnetic fiel (a geat fusion evice) Plasma pessue will cause the
More information15. SIMPLE MHD EQUILIBRIA
15. SIMPLE MHD EQUILIBRIA In this Section we will examine some simple examples of MHD equilibium configuations. These will all be in cylinical geomety. They fom the basis fo moe the complicate equilibium
More informationGeneral Relativity Homework 5
Geneal Relativity Homewok 5. In the pesence of a cosmological constant, Einstein s Equation is (a) Calculate the gavitational potential point souce with = M 3 (). R µ Rg µ + g µ =GT µ. in the Newtonian
More informationConservation of Linear Momentum using RTT
07/03/2017 Lectue 21 Consevation of Linea Momentum using RTT Befoe mi-semeste exam, we have seen the 1. Deivation of Reynols Tanspot Theoem (RTT), 2. Application of RTT in the Consevation of Mass pinciple
More informationCHAPTER 25 ELECTRIC POTENTIAL
CHPTE 5 ELECTIC POTENTIL Potential Diffeence and Electic Potential Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic foce on the paticle given by F=E. When
More informationBasic oces an Keple s Laws 1. Two ientical sphees of gol ae in contact with each othe. The gavitational foce of attaction between them is Diectly popotional to the squae of thei aius ) Diectly popotional
More informationHidden Two-Step Phase Transition and Competing
Suppoting Infomation fo Hien Two-Step Phase Tansition an Competing Reaction Pathways in LiFePO 4 Yukinoi Koyama, Takeshi Uyama, Yuki Oikasa, Takahio Naka, Hieyuki Komatsu, Keiji Shimoa, Hauno Muayama,
More informationSolutions to Problems : Chapter 19 Problems appeared on the end of chapter 19 of the Textbook
Solutions to Poblems Chapte 9 Poblems appeae on the en of chapte 9 of the Textbook 8. Pictue the Poblem Two point chages exet an electostatic foce on each othe. Stategy Solve Coulomb s law (equation 9-5)
More informationNumerical solution of diffusion mass transfer model in adsorption systems. Prof. Nina Paula Gonçalves Salau, D.Sc.
Numeical solution of diffusion mass tansfe model in adsoption systems Pof., D.Sc. Agenda Mass Tansfe Mechanisms Diffusion Mass Tansfe Models Solving Diffusion Mass Tansfe Models Paamete Estimation 2 Mass
More informationSolute Transport In Biological Systems Design of An Artificial Kidney Utilizing Urease in Polymeric Beads. Dialysate. Flow out C(z) U Q,C b UB
hapte Solute Tanspot In Biological Systems.14 Design of n tificial Kidney Utilizg Uease Polymeic Beads Fo the teatment of uemia discussed section.11, fesh dialysate is used kidney dialysis to mata a concentation
More information( )( )( ) ( ) + ( ) ( ) ( )
3.7. Moel: The magnetic fiel is that of a moving chage paticle. Please efe to Figue Ex3.7. Solve: Using the iot-savat law, 7 19 7 ( ) + ( ) qvsinθ 1 T m/a 1.6 1 C. 1 m/s sin135 1. 1 m 1. 1 m 15 = = = 1.13
More informationYoun-Woo Lee School of Chemical and Biological Engineering Seoul National University , 599 Gwanangro, Gwanak-gu, Seoul, Korea
hemical Reacto esign Y W L Youn-Woo Lee School of hemical and iological Engineeing 55-74, 599 Gwanango, Gwana-gu, Seoul, Koea ywlee@snu.ac. http://sfpl.snu.ac. hapte 6 Multiple Reactions hemical Reaction
More information2. Radiation Field Basics I. Specific Intensity
. Raiation Fiel Basics Rutten:. Basic efinitions of intensity, flux Enegy ensity, aiation pessue E Specific ntensity t Pencil beam of aiation at position, iection n, caying enegy E, pasg though aea, between
More informationCHAPTER 2 DERIVATION OF STATE EQUATIONS AND PARAMETER DETERMINATION OF AN IPM MACHINE. 2.1 Derivation of Machine Equations
1 CHAPTER DERIVATION OF STATE EQUATIONS AND PARAMETER DETERMINATION OF AN IPM MACHINE 1 Deivation of Machine Equations A moel of a phase PM machine is shown in Figue 1 Both the abc an the q axes ae shown
More informationCSTR - PFR - PBR
1. Mole Balances o The Rate of Reaction, - o The Geneal Mole Balance Equation o Continuous low Reactos - CSTR (Continuous-Stied Tank Reacto) - PR (Tubula Reacto) - PBR (Packed-Bed Reacto) o Industial Reactos
More informationA Crash Course in (2 2) Matrices
A Cash Couse in ( ) Matices Seveal weeks woth of matix algeba in an hou (Relax, we will only stuy the simplest case, that of matices) Review topics: What is a matix (pl matices)? A matix is a ectangula
More information2.25 Advanced Fluid Mechanics
MIT Depatment of Mechanical Engineeing 2.25 Advanced Fluid Mechanics Poblem 4.27 This poblem is fom Advanced Fluid Mechanics Poblems by A.H. Shapio and A.A. Sonin u(,t) pg Gas Liquid, density Conside a
More informationLecture 2 - Thermodynamics Overview
2.625 - Electochemical Systems Fall 2013 Lectue 2 - Themodynamics Oveview D.Yang Shao-Hon Reading: Chapte 1 & 2 of Newman, Chapte 1 & 2 of Bad & Faulkne, Chaptes 9 & 10 of Physical Chemisty I. Lectue Topics:
More informationOne-Dimensional, Steady-State. State Conduction with Thermal Energy Generation
One-Dimensional, Steady-State State Conduction with Themal Enegy Geneation Implications of Enegy Geneation Involves a local (volumetic) souce of themal enegy due to convesion fom anothe fom of enegy in
More informationCurrent, Resistance and
Cuent, Resistance and Electomotive Foce Chapte 25 Octobe 2, 2012 Octobe 2, 2012 Physics 208 1 Leaning Goals The meaning of electic cuent, and how chages move in a conducto. What is meant by esistivity
More informationCBE Transport Phenomena I Final Exam. December 19, 2013
CBE 30355 Tanspot Phenomena I Final Exam Decembe 9, 203 Closed Books and Notes Poblem. (20 points) Scaling analysis of bounday laye flows. A popula method fo measuing instantaneous wall shea stesses in
More informationCHAPTER 10 ELECTRIC POTENTIAL AND CAPACITANCE
CHAPTER 0 ELECTRIC POTENTIAL AND CAPACITANCE ELECTRIC POTENTIAL AND CAPACITANCE 7 0. ELECTRIC POTENTIAL ENERGY Conside a chaged paticle of chage in a egion of an electic field E. This filed exets an electic
More informationEKT 356 MICROWAVE COMMUNICATIONS CHAPTER 2: PLANAR TRANSMISSION LINES
EKT 356 MICROWAVE COMMUNICATIONS CHAPTER : PLANAR TRANSMISSION LINES 1 Tansmission Lines A device used to tansfe enegy fom one point to anothe point efficiently Efficiently minimum loss, eflection and
More informationA 1. EN2210: Continuum Mechanics. Homework 7: Fluid Mechanics Solutions
EN10: Continuum Mechanics Homewok 7: Fluid Mechanics Solutions School of Engineeing Bown Univesity 1. An ideal fluid with mass density ρ flows with velocity v 0 though a cylindical tube with cosssectional
More informationN igerian Journal of M athematics and Applications V olume 24, (2015),
N igeian Jounal of M athematics an Applications V olume 24, 205), 228 236 c N ig. J. M ath. Appl. http : //www.kwsman.com Flow of an Incompessible MHD Thi Gae Flui Though a Cylinical Pipe with Isothemal
More informationQuantum Mechanics I - Session 5
Quantum Mechanics I - Session 5 Apil 7, 015 1 Commuting opeatos - an example Remine: You saw in class that Â, ˆB ae commuting opeatos iff they have a complete set of commuting obsevables. In aition you
More informationIf there are multiple rxns, use concentrations not conversions. These might occur in combination or by themselves.
hapte 6 MLTIPLE RETIONS If thee ae multiple xns, use concentations not convesions. intemediate. Seies Reactions onsecutive xns. Paallel Reactions. omplex Reactions: Seies and Paallel 4. Independent None
More informationRigid Body Dynamics 2. CSE169: Computer Animation Instructor: Steve Rotenberg UCSD, Winter 2018
Rigid Body Dynamics 2 CSE169: Compute Animation nstucto: Steve Rotenbeg UCSD, Winte 2018 Coss Poduct & Hat Opeato Deivative of a Rotating Vecto Let s say that vecto is otating aound the oigin, maintaining
More informationEKT 345 MICROWAVE ENGINEERING CHAPTER 2: PLANAR TRANSMISSION LINES
EKT 345 MICROWAVE ENGINEERING CHAPTER : PLANAR TRANSMISSION LINES 1 Tansmission Lines A device used to tansfe enegy fom one point to anothe point efficiently Efficiently minimum loss, eflection and close
More informationPhysics 122, Fall December 2012
Physics 1, Fall 01 6 Decembe 01 Toay in Physics 1: Examples in eview By class vote: Poblem -40: offcente chage cylines Poblem 8-39: B along axis of spinning, chage isk Poblem 30-74: selfinuctance of a
More informationSPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm
8//11 Electicity has Enegy SPH4I Electic Potential M. Buns To sepaate negative an positive chages fom each othe, wok must be one against the foce of attaction. Theefoe sepeate chages ae in a higheenegy
More informationof Technology: MIT OpenCourseWare). (accessed MM DD, YYYY). License: Creative Commons Attribution- Noncommercial-Share Alike.
MIT OpenCouseWae http://ocw.mit.eu 6.013/ESD.013J Electomagnetics an Applications, Fall 005 Please use the following citation fomat: Makus Zahn, Eich Ippen, an Davi Staelin, 6.013/ESD.013J Electomagnetics
More information2 E. on each of these two surfaces. r r r r. Q E E ε. 2 2 Qencl encl right left 0
Ch : 4, 9,, 9,,, 4, 9,, 4, 8 4 (a) Fom the diagam in the textbook, we see that the flux outwad though the hemispheical suface is the same as the flux inwad though the cicula suface base of the hemisphee
More informationChemical Reaction Engineering
Lectue hemical Reaction Engineeing (RE) is the field that studies the ates and mechanisms of chemical eactions and the design of the eactos in which they take place. Web Lectue lass Lectue 8-husday Multiple
More informationPhysics 107 TUTORIAL ASSIGNMENT #8
Physics 07 TUTORIAL ASSIGNMENT #8 Cutnell & Johnson, 7 th edition Chapte 8: Poblems 5,, 3, 39, 76 Chapte 9: Poblems 9, 0, 4, 5, 6 Chapte 8 5 Inteactive Solution 8.5 povides a model fo solving this type
More informationThat is, the acceleration of the electron is larger than the acceleration of the proton by the same factor the electron is lighter than the proton.
PHY 8 Test Pactice Solutions Sping Q: [] A poton an an electon attact each othe electically so, when elease fom est, they will acceleate towa each othe. Which paticle will have a lage acceleation? (Neglect
More informationStellar Structure and Evolution
Stella Stuctue and Evolution Theoetical Stella odels Conside each spheically symmetic shell of adius and thickness d. Basic equations of stella stuctue ae: 1 Hydostatic equilibium π dp dp d G π = G =.
More informationLECTURER: DR. MAZLAN ABDUL WAHID HEAT TRANSFER
SM 4463 LU: D. MZLN BDUL WID http://www.fm.utm.my/~mazlan FULY OF MNIL NGINING UNIVSII KNOLOGI MLYSI SKUDI, JOO, MLYSI Mazlan 006 NSF D MZLN hapte Fundamental oncepts of onduction ssoc. of. D. Mazlan bdul
More informationChemical Reaction Engineering
Lectue 3 hemical Reaction Engineeing (RE) is the field that studies the ates and mechanisms of chemical eactions and the design of the eactos in which they take place. Web Lectue 3 lass Lectue 9-Thusday
More informationPhysics 2212 GH Quiz #2 Solutions Spring 2016
Physics 2212 GH Quiz #2 Solutions Sping 216 I. 17 points) Thee point chages, each caying a chage Q = +6. nc, ae placed on an equilateal tiangle of side length = 3. mm. An additional point chage, caying
More informationBlack Body Radiation and Radiometric Parameters:
Black Body Radiation and Radiometic Paametes: All mateials absob and emit adiation to some extent. A blackbody is an idealization of how mateials emit and absob adiation. It can be used as a efeence fo
More informationASTR415: Problem Set #6
ASTR45: Poblem Set #6 Cuan D. Muhlbege Univesity of Mayland (Dated: May 7, 27) Using existing implementations of the leapfog and Runge-Kutta methods fo solving coupled odinay diffeential equations, seveal
More informationFlux. Area Vector. Flux of Electric Field. Gauss s Law
Gauss s Law Flux Flux in Physics is used to two distinct ways. The fist meaning is the ate of flow, such as the amount of wate flowing in a ive, i.e. volume pe unit aea pe unit time. O, fo light, it is
More informationSubstances that are liquids or solids under ordinary conditions may also exist as gases. These are often referred to as vapors.
Chapte 0. Gases Chaacteistics of Gases All substances have thee phases: solid, liquid, and gas. Substances that ae liquids o solids unde odinay conditions may also exist as gases. These ae often efeed
More informationEntropy and Free Energy: Predicting the direction of spontaneous change The approach to Chemical equilibrium
Lectue 8-9 Entopy and Fee Enegy: Pedicting the diection of spontaneous change The appoach to Chemical equilibium Absolute entopy and the thid law of themodynamics To define the entopy of a compound in
More information= 4 3 π( m) 3 (5480 kg m 3 ) = kg.
CHAPTER 11 THE GRAVITATIONAL FIELD Newton s Law of Gavitation m 1 m A foce of attaction occus between two masses given by Newton s Law of Gavitation Inetial mass and gavitational mass Gavitational potential
More informationUniversity Physics (PHY 2326)
Chapte Univesity Physics (PHY 6) Lectue lectostatics lectic field (cont.) Conductos in electostatic euilibium The oscilloscope lectic flux and Gauss s law /6/5 Discuss a techniue intoduced by Kal F. Gauss
More informationApplied Aerodynamics
Applied Aeodynamics Def: Mach Numbe (M), M a atio of flow velocity to the speed of sound Compessibility Effects Def: eynolds Numbe (e), e ρ c µ atio of inetial foces to viscous foces iscous Effects If
More informationChapter 22 The Electric Field II: Continuous Charge Distributions
Chapte The lectic Field II: Continuous Chage Distibutions A ing of adius a has a chage distibution on it that vaies as l(q) l sin q, as shown in Figue -9. (a) What is the diection of the electic field
More information3.6 Applied Optimization
.6 Applied Optimization Section.6 Notes Page In this section we will be looking at wod poblems whee it asks us to maimize o minimize something. Fo all the poblems in this section you will be taking the
More informationworking pages for Paul Richards class notes; do not copy or circulate without permission from PGR 2004/11/3 10:50
woking pages fo Paul Richads class notes; do not copy o ciculate without pemission fom PGR 2004/11/3 10:50 CHAPTER7 Solid angle, 3D integals, Gauss s Theoem, and a Delta Function We define the solid angle,
More informationPhysics 2A Chapter 10 - Moment of Inertia Fall 2018
Physics Chapte 0 - oment of netia Fall 08 The moment of inetia of a otating object is a measue of its otational inetia in the same way that the mass of an object is a measue of its inetia fo linea motion.
More informationChapter 1: Mole Balances
CHEMICL RECTION ENGINEERING (SK3223) Chapte : Mole Balances WN NORHRYTI WN SLLEH hayati@petoleum.utm.my RIZIN MD. KSMNI afiziana@petoleum.utm.my Rate of Reaction The eaction ate is the ate at which a species
More informationEasy. r p 2 f : r p 2i. r p 1i. r p 1 f. m blood g kg. P8.2 (a) The momentum is p = mv, so v = p/m and the kinetic energy is
Chapte 8 Homewok Solutions Easy P8. Assume the velocity of the blood is constant ove the 0.60 s. Then the patient s body and pallet will have a constant velocity of 6 0 5 m 3.75 0 4 m/ s 0.60 s in the
More information4. Some Applications of first order linear differential
August 30, 2011 4-1 4. Some Applications of fist ode linea diffeential Equations The modeling poblem Thee ae seveal steps equied fo modeling scientific phenomena 1. Data collection (expeimentation) Given
More informationINTERACTION OF HYDRODYNAMIC ENVIRONMENT ON PERFORMANCE OF HOMOGENEOUS BIOREACTORS WITH ENZYME KINETIC MODELS
Cuent Stuies of Biotechnology Volume II. - Envionment INTERACTION OF HYDRODYNAMIC ENVIRONMENT ON PERFORMANCE OF HOMOGENEOUS BIOREACTORS WITH ENZYME KINETIC MODELS ŽELIMIR KURTANJEK * Faculty of Foo Technology
More information556: MATHEMATICAL STATISTICS I
556: MATHEMATICAL STATISTICS I CHAPTER 5: STOCHASTIC CONVERGENCE The following efinitions ae state in tems of scala anom vaiables, but exten natually to vecto anom vaiables efine on the same obability
More informationSynthesis of Epichlorohydrin from Glycerol. Hydrochlorination of Glycerol
Synthesis of Epichloohydin fom yceol. Hydochloination of yceol Geogy Dmitiev S.*, Leonid Zanaveskin N. Fedeation State Unitay Oganization "Kapov Institute of Physical hemisty" Russia, Moscow, Minusinskaya
More informationPhysics 4A Chapter 8: Dynamics II Motion in a Plane
Physics 4A Chapte 8: Dynamics II Motion in a Plane Conceptual Questions and Example Poblems fom Chapte 8 Conceptual Question 8.5 The figue below shows two balls of equal mass moving in vetical cicles.
More informationChapter 2: Basic Physics and Math Supplements
Chapte 2: Basic Physics and Math Supplements Decembe 1, 215 1 Supplement 2.1: Centipetal Acceleation This supplement expands on a topic addessed on page 19 of the textbook. Ou task hee is to calculate
More informationSection 5: Magnetostatics
ection 5: Magnetostatics In electostatics, electic fiels constant in time ae pouce by stationay chages. In magnetostatics magnetic fiels constant in time ae pouces by steay cuents. Electic cuents The electic
More informationReview: Electrostatics and Magnetostatics
Review: Electostatics and Magnetostatics In the static egime, electomagnetic quantities do not vay as a function of time. We have two main cases: ELECTROSTATICS The electic chages do not change postion
More informationChapter 13 Gravitation
Chapte 13 Gavitation In this chapte we will exploe the following topics: -Newton s law of gavitation, which descibes the attactive foce between two point masses and its application to extended objects
More informationABSTRACT SIMULATION OF DYNAMIC PRESSURE- Professor Timothy A. Barbari Department of Chemical Engineering
ABSTRACT Title: SIMULATION OF DYNAMIC PRESSURE- SWING GAS SORPTION IN POLYMERS Heathe Jane St. Piee, Maste of Science, 2005 Diected By: Pofesso Timothy A. Babai Depatment of Chemical Engineeing A tanspot
More informationIn the previous section we considered problems where the
5.4 Hydodynamically Fully Developed and Themally Developing Lamina Flow In the pevious section we consideed poblems whee the velocity and tempeatue pofile wee fully developed, so that the heat tansfe coefficient
More informationChapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic Field and Magnetic Force. Chapter 28: Magnetic fields. Chapter 28: Magnetic fields
Chapte 8: Magnetic fiels Histoically, people iscoe a stone (e 3 O 4 ) that attact pieces of ion these stone was calle magnets. two ba magnets can attact o epel epening on thei oientation this is ue to
More informationModule Summary Sheets. Mechanics 3 (Version B: Reference to new book) Topic 4: Volumes of revolution and centres of mass by integration
MEI Mathematics in Eucation an Inusty MEI Stuctue Mathematics Moule Summay Sheets (Vesion B: Refeence to new book) Topic : Cicula motion Topic : Elastic spings an stings Topic 3: Moelling oscillations
More informationELECTROSTATICS::BHSEC MCQ 1. A. B. C. D.
ELETROSTATIS::BHSE 9-4 MQ. A moving electic chage poduces A. electic field only. B. magnetic field only.. both electic field and magnetic field. D. neithe of these two fields.. both electic field and magnetic
More informationThis full text version, available on TeesRep, is the post-print (final version prior to publication) of:
This full text vesion, available on TeesRep, is the post-pint (final vesion pio to publication) of: Zhang, J., Coultha, J., Cheng, R. an Amstong Bian, (003) 'Theoetical an expeimental stuies of the spatial
More informationMuch that has already been said about changes of variable relates to transformations between different coordinate systems.
MULTIPLE INTEGRLS I P Calculus Cooinate Sstems Much that has alea been sai about changes of vaiable elates to tansfomations between iffeent cooinate sstems. The main cooinate sstems use in the solution
More informationAstrophysical Fluid Dynamics Solution Set 5 By Eric Bellm, Jeff Silverman, and Eugene Chiang
Astophysical Fluid Dynamics Solution Set 5 By Eic Bellm, Jeff Silveman, and Eugene Chiang Readings: Shu pages 73 8; pages 4 3 of Couse Reade, photocopied fom Fank, King, and Raine Poblem. Thee Can Be Only
More informationChapter 16 Electrochemical Processes
Electo_chapte16.doc 3-31-5 Chapte 16 Electochemical Pocesses This chapte consides some applications of electochemical tanspot and eactions in envionmental engineeing. Fist we eview some application examples.
More information5.4 Second Law of Thermodynamics Irreversible Flow 5
5.4 Second Law of hemodynamics Ievesile Flow 5 5.4 Second Law of hemodynamics Ievesile Flow he second law of themodynamics fomalizes the notion of loss. he second law of themodynamics affods us with a
More informationPractice. Understanding Concepts. Answers J 2. (a) J (b) 2% m/s. Gravitation and Celestial Mechanics 287
Pactice Undestanding Concepts 1. Detemine the gavitational potential enegy of the Eath Moon system, given that the aveage distance between thei centes is 3.84 10 5 km, and the mass of the Moon is 0.0123
More informationPHYSICS NOTES GRAVITATION
GRAVITATION Newton s law of gavitation The law states that evey paticle of matte in the univese attacts evey othe paticle with a foce which is diectly popotional to the poduct of thei masses and invesely
More informationPhys102 Second Major-182 Zero Version Monday, March 25, 2019 Page: 1
Monday, Mach 5, 019 Page: 1 Q1. Figue 1 shows thee pais of identical conducting sphees that ae to be touched togethe and then sepaated. The initial chages on them befoe the touch ae indicated. Rank the
More informationPhysics 2B Chapter 22 Notes - Magnetic Field Spring 2018
Physics B Chapte Notes - Magnetic Field Sping 018 Magnetic Field fom a Long Staight Cuent-Caying Wie In Chapte 11 we looked at Isaac Newton s Law of Gavitation, which established that a gavitational field
More informationExact Solution for Electro- Thermo- Mechanical Behavior of Composite Cylinder Reinforced by BNNTs under Non- Axisymmetric Thermo- Mechanical Loads
mikabi Univesity of Technology (Tehan Polytechnic) Vol, No, Sping 3, pp - mikabi Intenational Jounal of Science & Reseach (Moeling, Ientification, Simulation & Contol) (IJ - MISC) Exact Solution fo Electo-
More informationDo not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Mathematics Main Seies UG Examination 2015 16 FLUID DYNAMICS WITH ADVANCED TOPICS MTH-MD59 Time allowed: 3 Hous Attempt QUESTIONS 1 and 2, and THREE othe questions.
More informationElectrostatics (Electric Charges and Field) #2 2010
Electic Field: The concept of electic field explains the action at a distance foce between two chaged paticles. Evey chage poduces a field aound it so that any othe chaged paticle expeiences a foce when
More informationPhysics Courseware Physics II Electric Field and Force
Physics Cousewae Physics II lectic iel an oce Coulomb s law, whee k Nm /C test Definition of electic fiel. This is a vecto. test Q lectic fiel fo a point chage. This is a vecto. Poblem.- chage of µc is
More informationSupporting information
Electonic Supplementay Mateial (ESI) fo Physical Chemisty Chemical Physics. This jounal is the Owne Societies 18 Suppoting infomation Nonstoichiometic oxides as a continuous homologous seies: linea fee-enegy
More informationHomework 3 MAE 118C Problems 2, 5, 7, 10, 14, 15, 18, 23, 30, 31 from Chapter 5, Lamarsh & Baratta. The flux for a point source is:
. Homewok 3 MAE 8C Poblems, 5, 7, 0, 4, 5, 8, 3, 30, 3 fom Chpte 5, msh & Btt Point souces emit nuetons/sec t points,,, n 3 fin the flux cuent hlf wy between one sie of the tingle (blck ot). The flux fo
More informationThe Millikan Experiment: Determining the Elementary Charge
LAB EXERCISE 7.5.1 7.5 The Elementay Chage (p. 374) Can you think of a method that could be used to suggest that an elementay chage exists? Figue 1 Robet Millikan (1868 1953) m + q V b The Millikan Expeiment:
More informationTHERMODYNAMICS OF SURFACES AND INTERFACES
THERMODYNAMIC OF URFACE AND INTERFACE 1. Intoduction Eveything has to end somewhee. Fo solids, o liquids that "somewhee" is a suface, o an inteface between phases. Fo liquids, the inteface is between the
More information, and the curve BC is symmetrical. Find also the horizontal force in x-direction on one side of the body. h C
Umeå Univesitet, Fysik 1 Vitaly Bychkov Pov i teknisk fysik, Fluid Dynamics (Stömningsläa), 2013-05-31, kl 9.00-15.00 jälpmedel: Students may use any book including the textbook Lectues on Fluid Dynamics.
More informationGeometry of the homogeneous and isotropic spaces
Geomety of the homogeneous and isotopic spaces H. Sonoda Septembe 2000; last evised Octobe 2009 Abstact We summaize the aspects of the geomety of the homogeneous and isotopic spaces which ae most elevant
More informationHeat transfer has direction as well as magnitude. The rate of heat conduction
cen58933_ch2.qd 9/1/22 8:46 AM Page 61 HEAT CONDUCTION EQUATION CHAPTER 2 Heat tansfe has diection as well as magnitude. The ate of heat conduction in a specified diection is popotional to the tempeatue
More informationChapter 2: Conversion and Reactor Sizing
CHEMICL RECTIO EGIEERIG (SK3223) Chapte 2: Convesion and Reacto Sizing W ORHRYTI W SLLEH hayati@petoleum.utm.my RIZI MD. KSMI afiziana@petoleum.utm.my Convesion, To quantify how fa a eaction has pogessed
More information4. Compare the electric force holding the electron in orbit ( r = 0.53
Electostatics WS Electic Foce an Fiel. Calculate the magnitue of the foce between two 3.60-µ C point chages 9.3 cm apat.. How many electons make up a chage of 30.0 µ C? 3. Two chage ust paticles exet a
More informationModeling of trickle bed reactor for hydrotreating of vacuum gas oils: effect of kinetic type on reactor modeling
17 th Euopean ymposium on Compute Aided Pocess Engineeing ECAPE17 V. Plesu and P.. Agachi (Editos) 007 Elsevie B.V. All ights eseved. 1 Modeling of tickle bed eacto fo hydoteating of vacuum gas oils: effect
More informationChapter Sixteen: Electric Charge and Electric Fields
Chapte Sixteen: Electic Chage and Electic Fields Key Tems Chage Conducto The fundamental electical popety to which the mutual attactions o epulsions between electons and potons ae attibuted. Any mateial
More information$ i. !((( dv vol. Physics 8.02 Quiz One Equations Fall q 1 q 2 r 2 C = 2 C! V 2 = Q 2 2C F = 4!" or. r ˆ = points from source q to observer
Physics 8.0 Quiz One Equations Fall 006 F = 1 4" o q 1 q = q q ˆ 3 4" o = E 4" o ˆ = points fom souce q to obseve 1 dq E = # ˆ 4" 0 V "## E "d A = Q inside closed suface o d A points fom inside to V =
More information6.641 Electromagnetic Fields, Forces, and Motion Spring 2005
MIT OpenouseWae http://ocw.mit.edu 6.641 Electomagnetic Fields, Foces, and Motion Sping 2005 Fo infomation about citing these mateials o ou Tems of Use, visit: http://ocw.mit.edu/tems. 6.641 Electomagnetic
More informationUniversal Gravitation
Chapte 1 Univesal Gavitation Pactice Poblem Solutions Student Textbook page 580 1. Conceptualize the Poblem - The law of univesal gavitation applies to this poblem. The gavitational foce, F g, between
More information