Effects of high RH on α-pinene SOA phase partitioning

Size: px
Start display at page:

Download "Effects of high RH on α-pinene SOA phase partitioning"

Transcription

1 Effets f hgh RH n α-pnene SA phase parttnng Götebrg summer shl 26/06/2008 Nenne Prsle PhD student Chemstry, CCAR, Unv. Cpenhagen, Denmark nlp@kem.ku.dk 26/06/2008 Götebrg, Nenne Prsle 1 Mtvatn Current atmspher mdels annt aunt fr bserved rgan aersl mass. Identfy mehansms that ntrbute t nreasng predted sendary rgan aersl (SA) mass. The nfluene f humdty n SA gas-partle phase parttnng s ne suh ptental effet. 26/06/2008 Götebrg, Nenne Prsle 2/28 1

2 utlne parttnng thery» why expet a humdty effet n SA phase parttnng? the experments prelmnary results» what dd we bserve?» future wrk/hallenges my ther PhD prjet» surfatant parttnng n atvatng lud drplets 26/06/2008 Götebrg, Nenne Prsle 3/28 The expermental system rg rg H 2 2 (G) 3 rgan prduts [H 2 ] (P) rg H 2!!! rgans and water parttn nt a sngle ndensed phase 2

3 SA phase parttnng referene: Prest and Dnahue (EST 2006) the effetve gas phase saturatn mass nentratn *» related t the partal pressure f a spees n slutn» the saturatn vapr pressure f the pure lqud spees, wth the prpertes the spees psesses n a gven slutn the parttnng effent ξ» rat f the mass nentratn f a spees n slutn t the ttal mass nentratn n gas phase and slutn 26/06/2008 Götebrg, Nenne Prsle 5/28 Effetve gas phase saturatn nentratn, * 0 p = p γ χ Rault s law, G p = W, P *, P RT W = χ, P W 0, G p, Pγ W = RT, P, P deal gas law mass fratn n slutn effetve gas phase saturatn mass nentratn 26/06/2008 Götebrg, Nenne Prsle 6/28 3

4 * depends n SA mpstn * depends n the partle mpstn» atvty effent» mean mlar weght * = p 0, P γ W RT mpstn hange => * hange f» atvty effent hange» mean mlar weght hange χ χ : ' *'' *' '' γ W = γ W '' ' '' ' 26/06/2008 Götebrg, Nenne Prsle 7/28 Parttnng effent, ξ A 1 = 1+ ξ * = A ξ 26/06/2008 Götebrg, Nenne Prsle 8/28 4

5 RH effet n SA phase parttnng nreasng RH => SA hygrsp grwth f water and rgans mx n slutn» nrease absrbng A» derease W avg => derease * (f pseud-deal) bth wll nrease ξ => nrease resultng A 1 ξ = 1+ * A A W,, ξ, *, ξ, A * wet shft A 26/06/2008 Götebrg, Nenne Prsle 9/28 * wet shft - depends n ntal A larger effet f * wet shft smaller A (dry) r C RG µg m -3 A ~70% RH > 80% experments 26/06/2008 Götebrg, Nenne Prsle 10/28 5

6 Expermental setup purfed ar H 2 ar heater heated nlet 2) RH ramp 5% - 85% α-pnene aetntrle RH meter purfed ar 12 m 3 Tefln reatr SMPS purfed ar 2-butanl T ntrlled AMS purfed ar dffusn drer PTRMS atmzers AS slutn 1) make SA 3 generatr 2 Expermental setup purfed ar ar heater H 2 heated nlet α-pnene aetntrle RH meter purfed ar 12 m 3 Tefln reatr SMPS purfed ar 2-butanl T ntrlled AMS purfed ar dffusn drer PTRMS atmzers AS slutn 3 generatr 2 6

7 Hygrsp grwth max RH ~85% partles take up water at RH ~65% RH ~65% DRH(pure AS) = 80% 26/06/2008 Götebrg, Nenne Prsle 13/28 Aersl mass mpstn tmeseres (AMS) Mass Cnentratn (µg m -3 ) AS α-pnene RH ramp RH~65% Water Ammnum Ntrate Sulphate rgans Chlrde ttal aersl mass - wall lss ntamnatn? lletn effeny 0 11: :00 13:00 14:00 15:00 16:00 17:00 Date and Tme 26/06/2008 Götebrg, Nenne Prsle 14/28 7

8 bserved SA mass grwth +20% -nludng ntamnatn? 26/06/2008 Götebrg, Nenne Prsle 15/28 Predted SA mass grwth referenes: Prest and Dnahue (EST 2006) Chang and Pankw (apd 2008) We bserved: A ~20% fr A ~15 µg m -3 at RH ~85% +25% Cnsstent wet shft : *(dry)/*(wet) ~1.5 ±0.5 26/06/2008 Götebrg, Nenne Prsle 16/28 8

9 bserved SA water ntent frm hygrsp grwth α-pnene SA dameter GF=1.08 at RH=85% [Varutbangkul et al., ACP 2006, 2367] rrespnds t aersl χ(h 2 )=0.75 rrespnds t derease n W avg frm W SA by fatr 3 26/06/2008 Götebrg, Nenne Prsle 17/28 Humdty effet n SA mass? at mst (nl. ntamnatn), we bserved an a-pnene SA mass grwth f ~20%» we dd nt see a large RH effet n SA mass the bserved SA mass grwth s nsstent wth a * wet shft f ~1.5» ths s abut half the * wet shft expeted frm the effet f pure SA hygrsp grwth n A W avg there may be an addtnal γ-effet n *:» pseud-dealty nt vald assumptn» γ rg nreasng wth water uptake (n surprse) 26/06/2008 Götebrg, Nenne Prsle 18/28 9

10 Partle phase separatn expermental evdene (P rg ) rg H 2 W avg effet smaller fr gven ttal water uptake f aqueus phase separates frm absrbng rgan phase (P Aq ) rg H 2 rg rg H 2 2 (G) 26/06/2008 Götebrg, Nenne Prsle 19/28 Future wrk ntamnatn rretn => better nstran SA grwth phase separatn: water ntent f absrbng rgan phase atvty effents: AIM mdel nludng rgans experments w. ther terpenes/mxed terpenes 26/06/2008 Götebrg, Nenne Prsle 20/28 10

11 Take-hme message #1 The predted effet f RH n SA gas-partle phase parttnng s hghly dependent n the assumed dry SA vlatlty dstrbutn. 26/06/2008 Götebrg, Nenne Prsle 21/28 Take-hme message #2 If the partle phase separates nt dstnt rgan and aqueus phases, the effet f a gven ttal water uptake nt the aersl phase n SA gas-partle phase parttnng wll be muh less than f the water and rgans parttn nt a sngle absrbng rgan aersl phase. 26/06/2008 Götebrg, Nenne Prsle 22/28 11

12 Surfatants n lud drplet atvatn lud drplet atvatn: Köhler thery surfatant parttnng n an aqueus drplet results and future wrk 26/06/2008 Götebrg, Nenne Prsle 23/28 Clud drplet atvatn Köhler equatn S= pw 4ν σ = aw exp w 0 pw RTd S atvatn rtal pnt (S,d) atvated drplet d>d d 26/06/2008 Götebrg, Nenne Prsle 24/28 12

13 Surfatant parttnng => greater predted S and S Srjamaa et al. (ap 2004) H 3 C surfatants derease σ fatty ad sdum salts: sdum laurate - preferentally nentrate n the surfae» surfae-bulk parttnng mrsp drplets have large surfae area-t-bulk vlume rat smaller equlbrum surfae area and bulk vlume nentratns Na + S = p p w 0 w = a w 4ν wσ exp RTd a w lwered less σ lwered less 26/06/2008 Götebrg, Nenne Prsle 25/28 Prsle et al. (Tellus B 2008) d 13

14 Take-hme message #3 If the surfatant prpertes are aunted fr n predtng lud drplet atvatn, the effet f surfatant parttnng between the drplet bulk and surfae must be aunted fr n bth Kelvn and Rault terms f the Köhler equatn, else partle rtal supersaturatns are nsderably underestmated. 26/06/2008 Götebrg, Nenne Prsle 27/28 Thank yu see yu at EAC2008! Aknwledgements are due:» Prfs. Nel Dnahue and Spyrs Pands (CMU)» Gab Engelhart (CMU)» Prf. Ar Laaksnen (FMI)» Rkka Srjamaa (Unv. Kup), Tm Raatkanen (FMI)» CCAR, BACCI & EUCAARI 26/06/2008 Götebrg, Nenne Prsle 28/28 14

Chem 204A, Fall 2004, Mid-term (II)

Chem 204A, Fall 2004, Mid-term (II) Frst tw letters f yur last name Last ame Frst ame McGll ID Chem 204A, Fall 2004, Md-term (II) Read these nstructns carefully befre yu start tal me: 2 hurs 50 mnutes (6:05 PM 8:55 PM) 1. hs exam has ttal

More information

Module 7: Solved Problems

Module 7: Solved Problems Mdule 7: Slved Prblems 1 A tn-walled nentr tube eat exanger f 019-m lengt s t be used t eat denzed water frm 40 t 60 at a flw rate f 5 kg/s te denzed water flws trug te nner tube f 30-mm dameter wle t

More information

Chapter 6 : Gibbs Free Energy

Chapter 6 : Gibbs Free Energy Wnter 01 Chem 54: ntrductry hermdynamcs Chapter 6 : Gbbs Free Energy... 64 Defntn f G, A... 64 Mawell Relatns... 65 Gbbs Free Energy G(,) (ure substances)... 67 Gbbs Free Energy fr Mtures... 68 ΔG f deal

More information

Chapter 3, Solution 1C.

Chapter 3, Solution 1C. COSMOS: Cmplete Onlne Slutns Manual Organzatn System Chapter 3, Slutn C. (a If the lateral surfaces f the rd are nsulated, the heat transfer surface area f the cylndrcal rd s the bttm r the tp surface

More information

Approach: (Equilibrium) TD analysis, i.e., conservation eqns., state equations Issues: how to deal with

Approach: (Equilibrium) TD analysis, i.e., conservation eqns., state equations Issues: how to deal with Schl f Aerspace Chemcal D: Mtvatn Prevus D Analyss cnsdered systems where cmpstn f flud was frzen fxed chemcal cmpstn Chemcally eactng Flw but there are numerus stuatns n prpulsn systems where chemcal

More information

Analysis The characteristic length of the junction and the Biot number are

Analysis The characteristic length of the junction and the Biot number are -4 4 The temerature f a gas stream s t be measured by a thermule. The tme t taes t regster 99 erent f the ntal ΔT s t be determned. Assumtns The juntn s sheral n shae wth a dameter f D 0.00 m. The thermal

More information

Thermodynamics of Materials

Thermodynamics of Materials Thermdynamcs f Materals 14th Lecture 007. 4. 8 (Mnday) FUGACITY dg = Vd SdT dg = Vd at cnstant T Fr an deal gas dg = (RT/)d = RT dln Ths s true fr deal gases nly, but t wuld be nce t have a smlar frm fr

More information

BME 5742 Biosystems Modeling and Control

BME 5742 Biosystems Modeling and Control BME 5742 Bsystems Mdeln and Cntrl Cell Electrcal Actvty: In Mvement acrss Cell Membrane and Membrane Ptental Dr. Zv Rth (FAU) 1 References Hppensteadt-Peskn, Ch. 3 Dr. Rbert Farley s lecture ntes Inc Equlbra

More information

Physic 231 Lecture 33

Physic 231 Lecture 33 Physc 231 Lecture 33 Man pnts f tday s lecture: eat and heat capacty: Q cm Phase transtns and latent heat: Q Lm ( ) eat flw Q k 2 1 t L Examples f heat cnductvty, R values fr nsulatrs Cnvectn R L / k Radatn

More information

Transient Conduction: Spatial Effects and the Role of Analytical Solutions

Transient Conduction: Spatial Effects and the Role of Analytical Solutions Transent Cnductn: Spatal Effects and the Rle f Analytcal Slutns Slutn t the Heat Equatn fr a Plane Wall wth Symmetrcal Cnvectn Cndtns If the lumped capactance apprxmatn can nt be made, cnsderatn must be

More information

6.2. Measurement of freezing point depression

6.2. Measurement of freezing point depression 6.2. easureent f freezng pnt depressn I. asks: Deternatn f nentratn f urea slutn y easurng freezng pnt depressn. Investgatn f freezng pnt depressn n ase f ttal and partal dssatn. Iprtant nepts Phase equlru,

More information

Natural Circulation Systems

Natural Circulation Systems Natural Crulatn Systems Natural rulatn lays an mrtant rle n the ln term ln f reatr systems durn adent ndtns, and n the strae f sent fuels. Cnsder the fllwn smle reresentatn f a reatr lant system eratn

More information

_J _J J J J J J J J _. 7 particles in the blue state; 3 particles in the red state: 720 configurations _J J J _J J J J J J J J _

_J _J J J J J J J J _. 7 particles in the blue state; 3 particles in the red state: 720 configurations _J J J _J J J J J J J J _ Dsrder and Suppse I have 10 partcles that can be n ne f tw states ether the blue state r the red state. Hw many dfferent ways can we arrange thse partcles amng the states? All partcles n the blue state:

More information

A.P. CHEMISTRY. SOLUTIONS AND ACID BASE CHEMISTRY. p 1

A.P. CHEMISTRY. SOLUTIONS AND ACID BASE CHEMISTRY. p 1 A.P. CHEMISTRY. SOLUTIONS AND ACID BASE CHEMISTRY. p 1 (Nte: questins 1 t 14 are meant t be dne WITHOUT calculatrs!) 1.Which f the fllwing is prbably true fr a slid slute with a highly endthermic heat

More information

(element) But, we do NOT know G!!! Correct, but not applicable! Free Energy Problems: o r. products. reactants. o f. reactants.

(element) But, we do NOT know G!!! Correct, but not applicable! Free Energy Problems: o r. products. reactants. o f. reactants. SANDARD fr hemcal Rxns prducts G p G reactants r But, we d NO knw G!!! rrect, but nt applcable! prducts G f G reactants f f (element) 0 f standard Gbbs free energy f frmatn Free Energy Prblems: 5. Prf.

More information

Heat exchanger. Heat exchanger

Heat exchanger. Heat exchanger s are deves n w eat s transferred between tw fluds at dfferent teperatures wtut any xng f fluds. type. Dret eat transfer type 2. Strage type 3. Dret ntat type ttps://www.faebk./0000085304058/vdes/96230780490756/.

More information

Chemical Engineering 160/260 Polymer Science and Engineering. Lecture 15: Molecular Aspects of Polymer Rheology February 21, 2001

Chemical Engineering 160/260 Polymer Science and Engineering. Lecture 15: Molecular Aspects of Polymer Rheology February 21, 2001 Chemial Engineering 160/260 Plymer Siene and Engineering Leture 15: Mleular Aspets f Plymer Rhelgy February 21, 2001 Objetives! T intrdue the nept f saling analysis t aunt fr the nentratin and mleular

More information

4. The material balances for isothermal ideal reactor models

4. The material balances for isothermal ideal reactor models Summay Geneal mateal balane f eatng system Bath eat Cntnuus-flw eats: CST (Cntnuus Sted Tank eat) P (Plug lw eat) Steady state f CST and P Desgn tasks : utlet (fnal nvesn), gven vlume f eat x vlume f eat,

More information

SIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES

SIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES SIMULATION OF THREE PHASE THREE LEG TRANSFORMER BEHAVIOR UNDER DIFFERENT VOLTAGE SAG TYPES Mhammadreza Dlatan Alreza Jallan Department f Electrcal Engneerng, Iran Unversty f scence & Technlgy (IUST) e-mal:

More information

Lucas Imperfect Information Model

Lucas Imperfect Information Model Lucas Imerfect Infrmatn Mdel 93 Lucas Imerfect Infrmatn Mdel The Lucas mdel was the frst f the mdern, mcrfundatns mdels f aggregate suly and macrecnmcs It bult drectly n the Fredman-Phels analyss f the

More information

3. Be able to derive the chemical equilibrium constants from statistical mechanics.

3. Be able to derive the chemical equilibrium constants from statistical mechanics. Lecture #17 1 Lecture 17 Objectves: 1. Notaton of chemcal reactons 2. General equlbrum 3. Be able to derve the chemcal equlbrum constants from statstcal mechancs. 4. Identfy how nondeal behavor can be

More information

Diodes Waveform shaping Circuits. Sedra & Smith (6 th Ed): Sec. 4.5 & 4.6 Sedra & Smith (5 th Ed): Sec. 3.5 & 3.6

Diodes Waveform shaping Circuits. Sedra & Smith (6 th Ed): Sec. 4.5 & 4.6 Sedra & Smith (5 th Ed): Sec. 3.5 & 3.6 des Waefrm shapng Cruts Sedra & Smth (6 th Ed): Se. 4.5 & 4.6 Sedra & Smth (5 th Ed): Se. 3.5 & 3.6 Tw-prt netwrks as buldng blks Reall: Transfer funtn f a tw-prt netwrk an be fund by slng ths rut ne.

More information

Section 3: Detailed Solutions of Word Problems Unit 1: Solving Word Problems by Modeling with Formulas

Section 3: Detailed Solutions of Word Problems Unit 1: Solving Word Problems by Modeling with Formulas Sectn : Detaled Slutns f Wrd Prblems Unt : Slvng Wrd Prblems by Mdelng wth Frmulas Example : The factry nvce fr a mnvan shws that the dealer pad $,5 fr the vehcle. If the stcker prce f the van s $5,, hw

More information

Diodes Waveform shaping Circuits

Diodes Waveform shaping Circuits des Waefrm shapng Cruts Leture ntes: page 2-2 t 2-31 Sedra & Smth (6 th Ed): Se. 4.5 & 4.6 Sedra & Smth (5 th Ed): Se. 3.5 & 3.6 F. Najmabad, ECE65, Wnter 212 Tw-prt netwrks as buldng blks Reall: Transfer

More information

6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS

6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS 6. ELUTRIATION OF PARTICLES FROM FLUIDIZED BEDS Elutratn s the prcess n whch fne partcles are carred ut f a fludzed bed due t the flud flw rate passng thrugh the bed. Typcally, fne partcles are elutrated

More information

Dynamic simulation of multi-effect falling-film evaporator: Milk powder production plant

Dynamic simulation of multi-effect falling-film evaporator: Milk powder production plant Dynam smulatn f mult-effet fallng-flm evapratr: Mlk pwder prdutn plant Fateme Medhat Bjnurd, Mhammad Al Fanae *, Had Zhree Department f Chem. Eng., Faulty f Eng., Ferdws Unversty f Mashhad, I. R. Iran

More information

Chapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune

Chapter 7. Systems 7.1 INTRODUCTION 7.2 MATHEMATICAL MODELING OF LIQUID LEVEL SYSTEMS. Steady State Flow. A. Bazoune Chapter 7 Flud Systems and Thermal Systems 7.1 INTODUCTION A. Bazune A flud system uses ne r mre fluds t acheve ts purpse. Dampers and shck absrbers are eamples f flud systems because they depend n the

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

Design of Analog Integrated Circuits

Design of Analog Integrated Circuits Desgn f Analg Integrated Crcuts I. Amplfers Desgn f Analg Integrated Crcuts Fall 2012, Dr. Guxng Wang 1 Oerew Basc MOS amplfer structures Cmmn-Surce Amplfer Surce Fllwer Cmmn-Gate Amplfer Desgn f Analg

More information

Exploiting vector space properties for the global optimization of process networks

Exploiting vector space properties for the global optimization of process networks Exptng vectr space prpertes fr the gbal ptmzatn f prcess netwrks Juan ab Ruz Ignac Grssmann Enterprse Wde Optmzatn Meetng March 00 Mtvatn - The ptmzatn f prcess netwrks s ne f the mst frequent prblems

More information

Relationships Between Frequency, Capacitance, Inductance and Reactance.

Relationships Between Frequency, Capacitance, Inductance and Reactance. P Physics Relatinships between f,, and. Relatinships Between Frequency, apacitance, nductance and Reactance. Purpse: T experimentally verify the relatinships between f, and. The data cllected will lead

More information

PHYSICS 536 Experiment 12: Applications of the Golden Rules for Negative Feedback

PHYSICS 536 Experiment 12: Applications of the Golden Rules for Negative Feedback PHYSICS 536 Experment : Applcatns f the Glden Rules fr Negatve Feedback The purpse f ths experment s t llustrate the glden rules f negatve feedback fr a varety f crcuts. These cncepts permt yu t create

More information

Final Exam Spring 2014 SOLUTION

Final Exam Spring 2014 SOLUTION Appled Opts H-464/564 C 594 rtland State nverst A. La Rsa Fnal am Sprng 14 SOLTION Name There are tw questns 1%) plus an ptnal bnus questn 1%) 1. Quarter wave plates and half wave plates The fgures belw

More information

Gasometric Determination of NaHCO 3 in a Mixture

Gasometric Determination of NaHCO 3 in a Mixture 60 50 40 0 0 5 15 25 35 40 Temperature ( o C) 9/28/16 Gasometrc Determnaton of NaHCO 3 n a Mxture apor Pressure (mm Hg) apor Pressure of Water 1 NaHCO 3 (s) + H + (aq) Na + (aq) + H 2 O (l) + CO 2 (g)

More information

NAME TEMPERATURE AND HUMIDITY. I. Introduction

NAME TEMPERATURE AND HUMIDITY. I. Introduction NAME TEMPERATURE AND HUMIDITY I. Intrductin Temperature is the single mst imprtant factr in determining atmspheric cnditins because it greatly influences: 1. The amunt f water vapr in the air 2. The pssibility

More information

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).

Three charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter). Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)

More information

Autumn 2012 CHEM452B Bruce H. Robinson 322 Gould Hall HW 10(A) Homework 10A KEY (there will not be a 10B) 2

Autumn 2012 CHEM452B Bruce H. Robinson 322 Gould Hall HW 10(A) Homework 10A KEY (there will not be a 10B) 2 Autumn 0 CHEM45B Bruce H. Rbinsn Guld Hall HW 0(A) Hmewrk 0A KEY (there will nt be a 0B) QA) Let c be the speed f sund in air. he square f the speed f sund, () f the gas with respect t the change in the

More information

WYSE Academic Challenge 2014 Sectional Physics Exam SOLUTION SET. [ F][ d] [ t] [ E]

WYSE Academic Challenge 2014 Sectional Physics Exam SOLUTION SET. [ F][ d] [ t] [ E] WYSE Aaem Challenge 0 Setnal hss Exam SOLUTION SET. Crret answer: E Unts Trque / unts pwer: [ r ][ ] [ E] [ t] [ r ][ ][ t] [ E] [ r ][ ][ t] [ ][ ] [ r ][ t] [ ] m s m s. Crret answer: D The net external

More information

Wp/Lmin. Wn/Lmin 2.5V

Wp/Lmin. Wn/Lmin 2.5V UNIVERITY OF CALIFORNIA Cllege f Engneerng Department f Electrcal Engneerng and Cmputer cences Andre Vladmrescu Hmewrk #7 EEC Due Frday, Aprl 8 th, pm @ 0 Cry Prblem #.5V Wp/Lmn 0.0V Wp/Lmn n ut Wn/Lmn.5V

More information

Regents Chemistry Period Unit 3: Atomic Structure. Unit 3 Vocabulary..Due: Test Day

Regents Chemistry Period Unit 3: Atomic Structure. Unit 3 Vocabulary..Due: Test Day Name Skills: 1. Interpreting Mdels f the Atm 2. Determining the number f subatmic particles 3. Determine P, e-, n fr ins 4. Distinguish istpes frm ther atms/ins Regents Chemistry Perid Unit 3: Atmic Structure

More information

CHEM 116 Concentrations and Colligative Properties

CHEM 116 Concentrations and Colligative Properties UMass stn, Chem 116 CHEM 116 Cncentratins and Clligative Prperties FSG is Mndays 11:00 am Lecture 10 Prf. Sevian and Tuesdays 3:30 pm bth in S-1-89 Tday s agenda Ways f expressing cncentratin Clligative

More information

V. Electrostatics Lecture 27a: Diffuse charge at electrodes

V. Electrostatics Lecture 27a: Diffuse charge at electrodes V. Electrstatcs Lecture 27a: Dffuse charge at electrdes Ntes by MIT tudent We have talked abut the electrc duble structures and crrespndng mdels descrbng the n and ptental dstrbutn n the duble layer. Nw

More information

CIRCLE YOUR DIVISION: Div. 1 (9:30 am) Div. 2 (11:30 am) Div. 3 (2:30 pm) Prof. Ruan Prof. Naik Mr. Singh

CIRCLE YOUR DIVISION: Div. 1 (9:30 am) Div. 2 (11:30 am) Div. 3 (2:30 pm) Prof. Ruan Prof. Naik Mr. Singh Frst CIRCLE YOUR DIVISION: Dv. 1 (9:30 am) Dv. (11:30 am) Dv. 3 (:30 m) Prf. Ruan Prf. Na Mr. Sngh Schl f Mechancal Engneerng Purdue Unversty ME315 Heat and Mass ransfer Eam #3 Wednesday Nvember 17 010

More information

Turbulent Nonpremixed Flames

Turbulent Nonpremixed Flames School of Aerospace Engneerng Turbulent Nonpremxed Flames Jerry Setzman. 5 Mole Fracton.15.1.5 CH4 HO HCO x 1 Temperature Methane Flame.1..3 Dstance (cm) 15 1 5 Temperature (K) TurbulentNonpremxed -1 School

More information

Energy Inputs and Outputs

Energy Inputs and Outputs Energy Inputs and Outputs Sun Earth ultravilet visible infrared Bth Sun and Earth behave as blackbdies (absrb 100% incident radiatin; emit radiatin at all wavelengths in all directins) Earth receives energy

More information

Problem Set 5 Solutions - McQuarrie Problems 3.20 MIT Dr. Anton Van Der Ven

Problem Set 5 Solutions - McQuarrie Problems 3.20 MIT Dr. Anton Van Der Ven Prblem Set 5 Slutns - McQuarre Prblems 3.0 MIT Dr. Antn Van Der Ven Fall Fall 003 001 Prblem 3-4 We have t derve the thermdynamc prpertes f an deal mnatmc gas frm the fllwng: = e q 3 m = e and q = V s

More information

GASES. PV = nrt N 2 CH 4 CO 2 O 2 HCN N 2 O NO 2. Pressure & Boyle s Law Temperature & Charles s Law Avogadro s Law IDEAL GAS LAW

GASES. PV = nrt N 2 CH 4 CO 2 O 2 HCN N 2 O NO 2. Pressure & Boyle s Law Temperature & Charles s Law Avogadro s Law IDEAL GAS LAW GASES Pressure & Byle s Law Temperature & Charles s Law Avgadr s Law IDEAL GAS LAW PV = nrt N 2 CH 4 CO 2 O 2 HCN N 2 O NO 2 Earth s atmsphere: 78% N 2 21% O 2 sme Ar, CO 2 Sme Cmmn Gasses Frmula Name

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

WYSE Academic Challenge 2004 Sectional Physics Solution Set

WYSE Academic Challenge 2004 Sectional Physics Solution Set WYSE Acadec Challenge 004 Sectnal Physcs Slutn Set. Answer: e. The axu pssble statc rctn r ths stuatn wuld be: ax µ sn µ sg (0.600)(40.0N) 4.0N. Snce yur pushng rce s less than the axu pssble rctnal rce,

More information

What characteristics distinguish irreversible (real) transformations from reversible (idealized) transformations?

What characteristics distinguish irreversible (real) transformations from reversible (idealized) transformations? bbs Free Eergy: ptaety ad Equlbrum What haratersts dstgush rreversble real trasfrmats frm reversble dealzed trasfrmats? t every stage f a reversble trasfrmat the system departs frm ulbrum ly ftesmally.

More information

Lecture 10 Adiabatic Processes

Lecture 10 Adiabatic Processes ASME231 Atmsheri hermdynamis NC A& State U Deartment f Physis Dr. Yuh-Lang Lin htt://meslab.rg ylin@nat.edu Leture 10 Adiabati Presses (Se.3.5 f Hess) [Classial equatin editr: 0 dq ] Definitin: If a thermdynami

More information

Mass Transfer Processes

Mass Transfer Processes Mass Transfer Processes S. Majd Hassanzadeh Department of Earth Scences Faculty of Geoscences Utrecht Unversty Outlne: 1. Measures of Concentraton 2. Volatlzaton and Dssoluton 3. Adsorpton Processes 4.

More information

Chapter Outline 4/28/2014. P-V Work. P-V Work. Isolated, Closed and Open Systems. Exothermic and Endothermic Processes. E = q + w

Chapter Outline 4/28/2014. P-V Work. P-V Work. Isolated, Closed and Open Systems. Exothermic and Endothermic Processes. E = q + w Islated, Clsed and Open Systems 9.1 Energy as a Reactant r a Prduct 9.2 Transferring Heat and Ding Wrk 9.5 Heats f Reactin and Calrimetry 9.6 Hess s Law and Standard Heats f Reactin 9.7 Heats f Reactin

More information

Spring 2002 Lecture #17

Spring 2002 Lecture #17 1443-51 Sprng 22 Lecture #17 r. Jaehn Yu 1. Cndtns fr Equlbrum 2. Center f Gravty 3. Elastc Prpertes f Slds Yung s dulus Shear dulus ulk dulus Tday s Hmewrk Assgnment s the Hmewrk #8!!! 2 nd term eam n

More information

Chapter 9 Gibbs Energy for Reactions Involving Components Not in Their Standard State

Chapter 9 Gibbs Energy for Reactions Involving Components Not in Their Standard State 1 Chater 9 Gbbs Energy fr Reatns Invlvng Cnents Nt n Ther Standard State Chater 6 desrbed hw enthaly and entry data ay be used t alulate the Gbbs energy hange fr a reatn at any T when all the nvlved reatants

More information

Module B3. VLoad = = V S V LN

Module B3. VLoad = = V S V LN Mdule B Prblem The -hase lads are cnnected n arallel. One s a urely resste lad cnnected n wye. t cnsumes 00kW. The secnd s a urely nducte 00kR lad cnnected n wye. The thrd s a urely caacte 00kR lad cnnected

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

15-69C Under the conditions of complete combustion with stoichiometric amount of air.

15-69C Under the conditions of complete combustion with stoichiometric amount of air. 15-43 Adabatc Flame emperature 15-68C Fr the case f stchmetrc amunt f pure xy snce we have the same amunt f chemcal energy released but a smaller amunt f mass t absrb t. 15-69C Under the cndtns f cmplete

More information

IGEE 401 Power Electronic Systems. Solution to Midterm Examination Fall 2004

IGEE 401 Power Electronic Systems. Solution to Midterm Examination Fall 2004 Jós, G GEE 401 wer Electrnc Systems Slutn t Mdterm Examnatn Fall 2004 Specal nstructns: - Duratn: 75 mnutes. - Materal allwed: a crb sheet (duble sded 8.5 x 11), calculatr. - Attempt all questns. Make

More information

Water vapour balance in a building moisture exposure for timber structures

Water vapour balance in a building moisture exposure for timber structures Jnt Wrkshp f COST Actns TU1 and E55 September 21-22 9, Ljubljana, Slvena Water vapur balance n a buldng msture expsure fr tmber structures Gerhard Fnk ETH Zurch, Swtzerland Jchen Köhler ETH Zurch, Swtzerland

More information

Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B]

Concept of Activity. Concept of Activity. Thermodynamic Equilibrium Constants [ C] [ D] [ A] [ B] Conept of Atvty Equlbrum onstnt s thermodynm property of n equlbrum system. For heml reton t equlbrum; Conept of Atvty Thermodynm Equlbrum Constnts A + bb = C + dd d [C] [D] [A] [B] b Conentrton equlbrum

More information

ME2142/ME2142E Feedback Control Systems. Modelling of Physical Systems The Transfer Function

ME2142/ME2142E Feedback Control Systems. Modelling of Physical Systems The Transfer Function Mdellng Physcal Systems The Transer Functn Derental Equatns U Plant Y In the plant shwn, the nput u aects the respnse the utput y. In general, the dynamcs ths respnse can be descrbed by a derental equatn

More information

PT326 PROCESS TRAINER

PT326 PROCESS TRAINER PT326 PROCESS TRAINER 1. Descrptn f the Apparatus PT 326 Prcess Traner The PT 326 Prcess Traner mdels cmmn ndustral stuatns n whch temperature cntrl s requred n the presence f transprt delays and transfer

More information

A/2 l,k. Problem 1 STRATEGY. KNOWN Resistance of a complete spherical shell: r rk. Inner and outer radii

A/2 l,k. Problem 1 STRATEGY. KNOWN Resistance of a complete spherical shell: r rk. Inner and outer radii Prblem 1 STRATEGY KNOWN Resstance f a cmplete sphercal shell: R ( r r / (4 π r rk sphere Inner an uter ra r an r, SOLUTION Part 1: Resstance f a hemsphercal shell: T calculate the resstance f the hemsphere,

More information

1/2 and e0 e s ' 1+ imm w 4 M s 3 πρ0 r 3 m. n 0 ktr. .Also,since n 0 ktr 1,wehave. 4 3 M sπρ 0 r 3. ktr. 3 M sπρ 0

1/2 and e0 e s ' 1+ imm w 4 M s 3 πρ0 r 3 m. n 0 ktr. .Also,since n 0 ktr 1,wehave. 4 3 M sπρ 0 r 3. ktr. 3 M sπρ 0 Chapter 6 6.1 Shw that fr a very weak slutin drplet (m 4 3 πr3 ρ 0 M s ), (6.8) can be written as e 0 ' 1+ a r b r 3 where a σ 0 /n 0 kt and b imm w / 4 3 M sπρ 0. What is yur interpretatin f thecnd and

More information

Conduction Heat Transfer

Conduction Heat Transfer Cnductn Heat Transfer Practce prblems A steel ppe f cnductvty 5 W/m-K has nsde and utsde surface temperature f C and 6 C respectvely Fnd the heat flw rate per unt ppe length and flux per unt nsde and per

More information

PHYSICS 212 MIDTERM II 19 February 2003

PHYSICS 212 MIDTERM II 19 February 2003 PHYSICS 1 MIDERM II 19 Feruary 003 Exam s losed ook, losed notes. Use only your formula sheet. Wrte all work and answers n exam ooklets. he aks of pages wll not e graded unless you so request on the front

More information

k T t T PHYS 2015 Week 13 E-M Waves, Interference Reading Journals Tuesday WebAssign due WEDNESDAY night

k T t T PHYS 2015 Week 13 E-M Waves, Interference Reading Journals Tuesday WebAssign due WEDNESDAY night PHYS 015 Week 13 -M Waves, Interferene Reading Jurnals Tuesday WebAssign due WDNSDAY night Test Friday: Chap 3 (Magneti indutin); Chap 33.1-4 (Indutane, self and mutual, energy, RL iruits). Chap 34 (Waves,

More information

Chapter 11: Atmosphere

Chapter 11: Atmosphere Chapter 11: Atmsphere Sectin 1: Atmspheric Basics Objectives 1. Describe the cmpsitin f the atmsphere. 2. Cmpare and cntrast the varius layers f the atmsphere. 3. Identify three methds f transferring energy

More information

Equation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process

Equation of State Modeling of Phase Equilibrium in the Low-Density Polyethylene Process Equaton of State Modelng of Phase Equlbrum n the Low-Densty Polyethylene Process H. Orbey, C. P. Boks, and C. C. Chen Ind. Eng. Chem. Res. 1998, 37, 4481-4491 Yong Soo Km Thermodynamcs & Propertes Lab.

More information

Voltammetry. Bulk electrolysis: relatively large electrodes (on the order of cm 2 ) Voltammetry:

Voltammetry. Bulk electrolysis: relatively large electrodes (on the order of cm 2 ) Voltammetry: Voltammetry varety of eletroanalytal methods rely on the applaton of a potental funton to an eletrode wth the measurement of the resultng urrent n the ell. In ontrast wth bul eletrolyss methods, the objetve

More information

Supporting information for: Large Protonation-Gated Photochromism of an OPE-Embedded Difurylperfluorocyclopentene

Supporting information for: Large Protonation-Gated Photochromism of an OPE-Embedded Difurylperfluorocyclopentene Eletrni Supplementary Material (ESI) fr Physial Chemistry Chemial Physis. This jurnal is the Owner Sieties 015 1/9 Supprting infrmatin fr: Large Prtnatin-Gated Phthrmism f an OPE-Embedded Difurylperflurylpentene

More information

HANSEN SOLUBILITY PARAMETERS IN CHROMATOGRAPHIC SCIENCES ADAM VOELKEL, K. ADAMSKA POZNAŃ UNIVERSITY OF TECHNOLOGY, POLAND

HANSEN SOLUBILITY PARAMETERS IN CHROMATOGRAPHIC SCIENCES ADAM VOELKEL, K. ADAMSKA POZNAŃ UNIVERSITY OF TECHNOLOGY, POLAND HANSN SOLUBILITY PARAMTRS IN CHROMATOGRAPHIC SCINCS ADAM OLKL, K. ADAMSKA POZNAŃ UNIRSITY OF TCHNOLOGY, POLAND SOLUBILITY PARAMTR THORY nergy f varzatn g l U ar U T d Chesve energy densty c c ch H w RT

More information

Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References

Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References Khmelnik S. I. Lrentz Fre, Ampere Fre and Mmentum Cnservatin Law Quantitative. Analysis and Crllaries. Abstrat It is knwn that Lrentz Fre and Ampere fre ntradits the Third Newtn Law, but it des nt ntradit

More information

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9.

If two volatile and miscible liquids are combined to form a solution, Raoult s law is not obeyed. Use the experimental data in Table 9. 9.9 Real Solutons Exhbt Devatons from Raoult s Law If two volatle and mscble lquds are combned to form a soluton, Raoult s law s not obeyed. Use the expermental data n Table 9.3: Physcal Chemstry 00 Pearson

More information

Measurement of Radiation: Exposure. Purpose. Quantitative description of radiation

Measurement of Radiation: Exposure. Purpose. Quantitative description of radiation Measurement of Radaton: Exposure George Starkschall, Ph.D. Department of Radaton Physcs U.T. M.D. Anderson Cancer Center Purpose To ntroduce the concept of radaton exposure and to descrbe and evaluate

More information

Phys 344 Ch 5 Lect 4 Feb 28 th,

Phys 344 Ch 5 Lect 4 Feb 28 th, hys 44 Ch 5 Lect 4 Feb 8 th, 009 1 Wed /4 Fr /6 Mn /9 Wed /11 Fr / 1 55 Dlute Slutn 56 Chemcal Equlbrum Revew Exam (C 107 S 60, 61 Bltzmann Statstcs Bnus: hys Sr hess resentatns @ 4pm HW17: 7,76,8 HW18:8,84,86,88,89,91

More information

Analytical Modeling of Natural Convection in Horizontal Annuli

Analytical Modeling of Natural Convection in Horizontal Annuli Analytcal Mdelng f Natural Cnvectn n Hrzntal Annul Peter Teertstra, M. Mchael Yvanvch, J. Rchard Culham Mcrelectrncs Heat Transfer Labratry Department f Mechancal Engneerng Unversty f Waterl Waterl, Ontar,

More information

Losses of Cigarette Smoke Particles in Oral Cavities

Losses of Cigarette Smoke Particles in Oral Cavities Le f Cgarette Smke Partcle n Oral Cavte O. Prce, B. Agharan, J. Schreter, C. U. Yurter, C. Dcken, and J. McAughey Aled eearch Acate, alegh, NC, USA Brth Amercan Tbacc, G&D BScence Dmetry, Suthamtn, UK

More information

Business. Class 3. Error in 4 th Edition (early printing) Specific Gravity (SG) A. Terminology Handout. Happy Monday! Terminology

Business. Class 3. Error in 4 th Edition (early printing) Specific Gravity (SG) A. Terminology Handout. Happy Monday! Terminology Class 3 Happy Mnday! Terminlgy Densities, MW, mle and, flw rates, and temperatures Pressure stuff next class Cnvert mass fractin t mle fractin Using a basis usiness Fr thse wh added the class late the

More information

SCHMIDT THEORY FOR STIRLING ENGINES

SCHMIDT THEORY FOR STIRLING ENGINES SHMIDT THOY FO STILING NGINS KOIHI HIATA Musashin-jjutaku 6-10, Gakuen -6-1, Musashimurayama, Tky 08, Japan Phne & Fax: +81-45-67-0086 e-mail: khirata@gem.bekkame.ne.jp url: http://www.bekkame.ne.jp/~khirata

More information

Homework for Diffraction-MSE 603: Solutions May 2002

Homework for Diffraction-MSE 603: Solutions May 2002 Hmewrk fr Diffratin-MSE 603: Slutins May 00 1. An x-ray beam f 1.5 Å impinges n a Ge single rystal sample with an inient angle θ lse t the ritial angle θ f the Ge surfae. Taking int aunt the absrptin,

More information

Heat Transfer and Friction Characteristics of Heat Exchanger Under Lignite Fly-Ash

Heat Transfer and Friction Characteristics of Heat Exchanger Under Lignite Fly-Ash The 20th Cnferene f Mehanial Engineering Netwrk f Thailand 18-20 Otber 2006, Nakhn Rathasima, Thailand Heat Transfer and Fritin Charateristis f Heat Exhanger Under ignite Fly-Ash Pipat Juangjandee 1*,

More information

Fall 2013 Physics 172 Recitation 3 Momentum and Springs

Fall 2013 Physics 172 Recitation 3 Momentum and Springs Fall 03 Physics 7 Recitatin 3 Mmentum and Springs Purpse: The purpse f this recitatin is t give yu experience wrking with mmentum and the mmentum update frmula. Readings: Chapter.3-.5 Learning Objectives:.3.

More information

Thermodynamics of solids 6. Multicomponent homogeneous nonreacting systems: solutions

Thermodynamics of solids 6. Multicomponent homogeneous nonreacting systems: solutions Thermdynamis f slids 6. Multimpnent hmgeneus nnreating systems: slutins Kwanghen Par Kyung Hee University Department f Nulear Engineering 6.. Partial mlar prperties Multimpnent System Speies:,, 3, 4,..

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

In the half reaction I 2 2 I the iodine is (a) reduced (b) oxidized (c) neither of the above

In the half reaction I 2 2 I the iodine is (a) reduced (b) oxidized (c) neither of the above 6.3-110 In the half reactin I 2 2 I the idine is (a) reduced (b) xidized (c) neither f the abve 6.3-120 Vitamin C is an "antixidant". This is because it (a) xidizes readily (b) is an xidizing agent (c)

More information

( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2.

( ) 1/ 2. ( P SO2 )( P O2 ) 1/ 2. Chemstry 360 Dr. Jean M. Standard Problem Set 9 Solutons. The followng chemcal reacton converts sulfur doxde to sulfur troxde. SO ( g) + O ( g) SO 3 ( l). (a.) Wrte the expresson for K eq for ths reacton.

More information

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014

University of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2014 Lecture 12 7/25/14 ERD: 7.1-7.5 Devoe: 8.1.1-8.1.2, 8.2.1-8.2.3, 8.4.1-8.4.3 Unversty o Washngton Department o Chemstry Chemstry 452/456 Summer Quarter 2014 A. Free Energy and Changes n Composton: The

More information

Homework #7. True False. d. Given a CFG, G, and a string w, it is decidable whether w ε L(G) True False

Homework #7. True False. d. Given a CFG, G, and a string w, it is decidable whether w ε L(G) True False Hmewrk #7 #1. True/ False a. The Pumping Lemma fr CFL s can be used t shw a language is cntext-free b. The string z = a k b k+1 c k can be used t shw {a n b n c n } is nt cntext free c. The string z =

More information

Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References

Content 1. Introduction 2. The Field s Configuration 3. The Lorentz Force 4. The Ampere Force 5. Discussion References Khmelnik. I. Lrentz Fre, Ampere Fre and Mmentum Cnservatin Law Quantitative. Analysis and Crllaries. Abstrat It is knwn that Lrentz Fre and Ampere fre ntradits the Third Newtn Law, but it des nt ntradit

More information

Formal Uncertainty Assessment in Aquarius Salinity Retrieval Algorithm

Formal Uncertainty Assessment in Aquarius Salinity Retrieval Algorithm Frmal Uncertainty Assessment in Aquarius Salinity Retrieval Algrithm T. Meissner Aquarius Cal/Val Meeting Santa Rsa March 31/April 1, 2015 Outline 1. Backgrund/Philsphy 2. Develping an Algrithm fr Assessing

More information

Chapter 8 Reduction and oxidation

Chapter 8 Reduction and oxidation Chapter 8 Reductin and xidatin Redx reactins and xidatin states Reductin ptentials and Gibbs energy Nernst equatin Disprprtinatin Ptential diagrams Frst-Ebswrth diagrams Ellingham diagrams Oxidatin refers

More information

How can standard heats of formation be used to calculate the heat of a reaction?

How can standard heats of formation be used to calculate the heat of a reaction? Name Chem 161, Sectin: Grup Number: ALE 28. Hess s Law and Standard Enthalpies Frmatin (Reerence: Chapter 6 - Silberberg 5 th editin) Imprtant!! Fr answers that invlve a calculatin yu must shw yur wrk

More information

Exercises H /OOA> f Wo AJoTHS l^»-l S. m^ttrt /A/ ?C,0&L6M5 INFERENCE FOR DISTRIBUTIONS OF CATEGORICAL DATA. tts^e&n tai-ns 5 2%-cas-hews^, 27%

Exercises H /OOA> f Wo AJoTHS l^»-l S. m^ttrt /A/ ?C,0&L6M5 INFERENCE FOR DISTRIBUTIONS OF CATEGORICAL DATA. tts^e&n tai-ns 5 2%-cas-hews^, 27% /A/ mttrt?c,&l6m5 INFERENCE FOR DISTRIBUTIONS OF CATEGORICAL DATA Exercses, nuts! A cmpany clams that each batch f ttse&n ta-ns 5 2%-cas-hews, 27% almnds, 13% macadama nuts, and 8% brazl nuts. T test ths

More information

On small defining sets for some SBIBD(4t - 1, 2t - 1, t - 1)

On small defining sets for some SBIBD(4t - 1, 2t - 1, t - 1) University f Wllngng Research Online Faculty f Infrmatics - Papers (Archive) Faculty f Engineering and Infrmatin Sciences 992 On small defining sets fr sme SBIBD(4t -, 2t -, t - ) Jennifer Seberry University

More information

Author(s) Nguyen, Thi Phuong Thao; Pham, Hung.

Author(s) Nguyen, Thi Phuong Thao; Pham, Hung. Title ESTIMATION OF CANCER RISK BY BENZEN FROM VEHICLES Authr(s) Kaga, Akikazu; Knd, Akira; Shi, S Nguyen, Thi Phung Tha; Pham, Hung Annual Reprt f FY 24, The Cre Citatin between Japan Siety fr the Prm

More information

A) 0.77 N B) 0.24 N C) 0.63 N D) 0.31 N E) 0.86 N. v = ω k = 80 = 32 m/s. Ans: (32) 2 = 0.77 N

A) 0.77 N B) 0.24 N C) 0.63 N D) 0.31 N E) 0.86 N. v = ω k = 80 = 32 m/s. Ans: (32) 2 = 0.77 N Q1. A transverse sinusidal wave travelling n a string is given by: y (x,t) = 0.20 sin (2.5 x 80 t) (SI units). The length f the string is 2.0 m and its mass is 1.5 g. What is the magnitude f the tensin

More information

Microfacet models for reflection and refraction

Microfacet models for reflection and refraction Mcrfacet mdels fr reflectn and refractn Steve Marschner Crnell Unversty CS 5625 Sprng 2016 (based n presentatn fr Walter, Marschner, L, and Trrance EGSR 07) Mcrfacet scatterng mdels Rugh delectrc surface

More information