Chapter One Mixture of Ideal Gases
|
|
- Primrose Johnston
- 5 years ago
- Views:
Transcription
1 herodynacs II AA Chapter One Mxture of Ideal Gases. Coposton of a Gas Mxture: Mass and Mole Fractons o deterne the propertes of a xture, we need to now the coposton of the xture as well as the propertes of the ndvdual coponents. here are two ways to descrbe the coposton of a xture: ether by specfyng the nuber of oles of each coponent, called olar analyss, or by specfyng the ass of each coponent, called gravetrc analyss. Consder a gas xture coposed of coponents. he ass of the xture tot s the su of the asses of the ndvdual coponents, and the ole nuber of the xture N tot s the su of the ole nubers of the ndvdual coponents and n n+ n n n (.) tot 2 tot he rato of the ass of a coponent to the ass of the xture s called the ass fracton f, and the rato of the ole nuber of a coponent to the ole nuber of the xture s called the ole fracton y: f and tot y n (.2) ntot A lstng of the ass fractons of the coponents of a xture s soetes referred to as a gravetrc analyss. A lstng of the ole fractons of the coponents of a xture ay be called a olar analyss. An analyss of a xture n ters of ole fractons s also called a voluetrc analyss. he su of the ass fractons or ole fractons for a xture s equal to unty..e y and he ass of a substance can be expressed n ters of the ole nuber n and olar ass M of the substance as nm. hen the average olar ass a xture can be expressed as M nm avr tot ntot ntot n tot ym Copled by Ydneachew M. Page of 8 f (.3)
2 herodynacs II AA he gas constant R s dfferent for each gas and s deterned fro R u R (.4) M Where Ru s the unversal gas constant and M s the olar ass (also called olecular weght) of the gas. he constant R u s the sae for all substances, and ts value s J / Kol. K. he average gas constant of a xture can be expressed as R avr R M u avr (.5) he olar ass of a xture can also be expressed as M n (.6) Mass and ole fractons of a xture are related by f nm M y nm M (.6).2 P-v- Behavor of Ideal Gas Mxtures Many therodynac applcatons nvolve xtures of deal gases. hat s, each of the gases n the xture ndvdually behaves as an deal gas. An deal gas s defned as a gas whose olecules are spaced far apart so that the behavor of a olecule s not nfluenced by the presence of other olecules a stuaton encountered at low denstes. he P-v- behavor of an deal gas s expressed by the sple relaton, whch s called the dealgas equaton of state. Pv R (.7) he P-v- behavor of real gases s expressed by ore coplex equatons of state or by Pv ZR, where Z s the copressblty factor. he predcton of the P-v- behavor of gas xtures s usually based on two odels: Dalton s law of addtve pressures and Aagat s law of addtve volues. Both odels are descrbed and dscussed below. Copled by Ydneachew M. Page 2 of 8
3 herodynacs II AA Dalton s law of addtve pressures: he pressure of a gas xture s equal to the su of the pressures each gas would exert f t exsted alone at the xture teperature and volue. Fgure. Dalton s law of addtve pressures for a xture of two deal gases. Aagat s law of addtve volues: he volue of a gas xture s equal to the su of the volues each gas would occupy f t exsted alone at the xture teperature and pressure. Fgure.2 Aagat s law of addtve volues for a xture of two deal gases. For deal gases, these two laws are dentcal and gve dentcal results. Dalton s and Aagat s laws can be expressed as follows: Dalton s law: P PV (, ) (.8) Aagat s law: V VV (, ) (.9) In these relatons, P s called the coponent pressure and V s called the coponent volue. he rato P /P s called the pressure fracton and the rato V /V s called the volue fracton of coponent. For deal gases, P and V can be related to y by usng the deal-gas relaton for both the coponents and the gas xture: PV (, ) nr u / V n y (.0) P n R / V n u VV (, ) nr u / P n y (.) V n R / P n u Copled by Ydneachew M. Page 3 of 8
4 herodynacs II AA herefore P V n y (.2) P V n he quantty y P s called the partal pressure (dentcal to the coponent pressure for deal gases), and the quantty y V s called the partal volue (dentcal to the coponent volue for deal gases). Note that for an deal-gas xture, the ole fracton, the pressure fracton, and the volue fracton of a coponent are dentcal..3 Propertes of Gas Mxture Dalton s law was re-forulated by Gbbs to nclude a second stateent on the propertes of xtures. he cobned stateent s nown as the Gbbs-Dalton law, and s as follows he nternal energy, enthalpy, and entropy of a gaseous xture are respectvely equal to the sus of the nternal energes, enthalpes, and entropes, of the consttuents. Each consttuent has that nternal energy, enthalpy and entropy, whch t could have f t occuped alone that volue occuped by the xture at the teperature of the xture. hs stateent leads to the followng equatons : ( u) u + u u Or 2 2 ( u) u (.3) u f u (.4) ( h) h + h h Or ( h) 2 2 h (.5) h f h (.6) ( s) s + s s Or 2 2 ( s) s (.7) s f s (.8).4 Adabatc Mxng of Perfect Gases Fgure.3 shows two gases A and B separated fro each other n a closed vessel by a thn daphrag. If the daphrag s reoved or punctured then the gases x and each then occupes Copled by Ydneachew M. Page 4 of 8
5 herodynacs II AA the total volue, behave as f the other gas were not present. hs process s equvalent to a free expanson of each gas, and s rreversble. he process can be splfed by the assupton that t s adabatc; ths eans that the vessel s perfectly therally nsulated and there wll therefore be an ncrease n entropy of the syste. Fgure.3 Gases before and after xture In a free expanson process, the nternal energy ntally s equal to the nternal energy fnally. U nc A vaa + nc B vbb and U2 ( nc + nc ) A va B vb If ths result s extended to any nuber of gases, we have (.9) U nc v and U2 nc U hen U U 2 nc v 2 nc v nc v U nc v v (.20) When two streas of flud eet to for a coon strea n steady flow, they gve another for of xng Copled by Ydneachew M. Page 5 of 8
6 herodynacs II AA Fgure.4 Flud xture Applyng steady-flow energy equaton to the xng secton (neglectng changes n netc and potental energy), we get h + h + Q h + h + W A A B B A A2 B B2 In case of adabatc flow: Q 0, and also W 0 n ths case Also h c p, hence, h + h h + h A A B B A A2 B B2 c + c c + c A pa A B pb B A pa B pb (.2) (.22) (.23) For any nuber of gases ths becoes c c p p c p c Also, C p Mc p and M /n p nc p c p (.24) nc p Hence, nc p (.25) Copled by Ydneachew M. Page 6 of 8
7 herodynacs II AA Eqns. (9.28) and (9.29) represent one condton whch ust be satsfed n an adabatc xng process of perfect gas n steady flow. In a partcular proble soe other nforaton ust be nown (e.g., specfc volue or the fnal pressure) before a coplete soluton s possble..5 Mxng of Ideal Gases ntally at dfferent Pressure and eperature Consder three deal gases A, B and C ntally at dfferent pressure and teperature and separated by parttons. Let the gases be xed by reovng the parttons. he total volue and ass occuped by the xture are gven by V VA + VB + VC and A + B + C (.26) In ters of the xng asses, the nternal energy of the gases after xng can be related to the nternal energy of the gases before xng by expresson: u aua + bub + cuc (.27) Snce u for a perfect gas s equal to c v, ths relaton ay be rewrte as: cv acvaa + bcvbb + ccvcc (.28) c + c + c c a va a b vb b c vc c (.29) v c + c + c c + c + c a va a b vb b c vc c a va b vb c vc (.30) Applng the perfect gas law.e, PV R PV c PV c PV c Ra Rb Rc PV c PV c PV c R R R a a va b b vb c c vc a a va b b vb c c vc a a b b c c (.3) Multplyng each ters n the nuerator and denonator of equaton by the respectve olecular weghts: Copled by Ydneachew M. Page 7 of 8
8 herodynacs II AA M PV c M PV c M PV c MR a a MR b b MR c c M PV c M PV c M PV c MR MR MR a a a va b b b vb c c c vc a a a va b b b vb c c c vc a a a b b b c c c (.32) he product Mc v s the sae for deal gases and the product MRR u s a constant for all deal gases. Cancellaton of these quanttes fro equaton results n: Where : RPV/ PV a a + PV b b + PV c c PV PV PV a a b b c c a b c PV + PV + PV R (.33) a a b b c c (.34) If the pressure are all equal before xng then, then fro equaton, the resultng xng teperature wll be obtaned fro: Va + Vb + Vc V V V a b c a b c (.35) If the volue are all equal before xng then, then fro equaton, the resultng xng teperature wll be obtaned fro: Pa + Pb + Pc Pa Pb Pc a b c (.38) Copled by Ydneachew M. Page 8 of 8
Chapter 13. Gas Mixtures. Study Guide in PowerPoint. Thermodynamics: An Engineering Approach, 5th edition by Yunus A. Çengel and Michael A.
Chapter 3 Gas Mxtures Study Gude n PowerPont to accopany Therodynacs: An Engneerng Approach, 5th edton by Yunus A. Çengel and Mchael A. Boles The dscussons n ths chapter are restrcted to nonreactve deal-gas
More informationChapter 12 Lyes KADEM [Thermodynamics II] 2007
Chapter 2 Lyes KDEM [Therodynacs II] 2007 Gas Mxtures In ths chapter we wll develop ethods for deternng therodynac propertes of a xture n order to apply the frst law to systes nvolvng xtures. Ths wll be
More informationStudy of the possibility of eliminating the Gibbs paradox within the framework of classical thermodynamics *
tudy of the possblty of elnatng the Gbbs paradox wthn the fraework of classcal therodynacs * V. Ihnatovych Departent of Phlosophy, Natonal echncal Unversty of Ukrane Kyv Polytechnc Insttute, Kyv, Ukrane
More informationChemical Engineering 160/260 Polymer Science and Engineering. Lecture 10 - Phase Equilibria and Polymer Blends February 7, 2001
Checal Engneerng 60/60 Polyer Scence and Engneerng Lecture 0 - Phase Equlbra and Polyer Blends February 7, 00 Therodynacs of Polyer Blends: Part Objectves! To develop the classcal Flory-Huggns theory for
More informationPHYS 1443 Section 002 Lecture #20
PHYS 1443 Secton 002 Lecture #20 Dr. Jae Condtons for Equlbru & Mechancal Equlbru How to Solve Equlbru Probles? A ew Exaples of Mechancal Equlbru Elastc Propertes of Solds Densty and Specfc Gravty lud
More informationFermi-Dirac statistics
UCC/Physcs/MK/EM/October 8, 205 Fer-Drac statstcs Fer-Drac dstrbuton Matter partcles that are eleentary ostly have a type of angular oentu called spn. hese partcles are known to have a agnetc oent whch
More informationOn Pfaff s solution of the Pfaff problem
Zur Pfaff scen Lösung des Pfaff scen Probles Mat. Ann. 7 (880) 53-530. On Pfaff s soluton of te Pfaff proble By A. MAYER n Lepzg Translated by D. H. Delpenc Te way tat Pfaff adopted for te ntegraton of
More informationUniversity of Washington Department of Chemistry Chemistry 452/456 Summer Quarter 2013
Lecture 8/8/3 Unversty o Washngton Departent o Chestry Chestry 45/456 Suer Quarter 3 A. The Gbbs-Duhe Equaton Fro Lecture 7 and ro the dscusson n sectons A and B o ths lecture, t s clear that the actvty
More informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationSolution Thermodynamics
Soluton hermodynamcs usng Wagner Notaton by Stanley. Howard Department of aterals and etallurgcal Engneerng South Dakota School of nes and echnology Rapd Cty, SD 57701 January 7, 001 Soluton hermodynamcs
More informationXII.3 The EM (Expectation-Maximization) Algorithm
XII.3 The EM (Expectaton-Maxzaton) Algorth Toshnor Munaata 3/7/06 The EM algorth s a technque to deal wth varous types of ncoplete data or hdden varables. It can be appled to a wde range of learnng probles
More informationPhysical Chemistry I for Biochemists. Lecture 18 (2/23/11) Announcement
Physcal Chestry I or Bochests Che34 Lecture 18 (2/23/11) Yoshtaka Ish Ch5.8-5.11 & HW6 Revew o Ch. 5 or Quz 2 Announceent Quz 2 has a slar orat wth Quz1. e s the sae. ~2 ns. Answer or HW5 wll be uploaded
More informationTHERMODYNAMICS of COMBUSTION
Internal Cobuston Engnes MAK 493E THERMODYNAMICS of COMBUSTION Prof.Dr. Ce Soruşbay Istanbul Techncal Unversty Internal Cobuston Engnes MAK 493E Therodynacs of Cobuston Introducton Proertes of xtures Cobuston
More information,..., k N. , k 2. ,..., k i. The derivative with respect to temperature T is calculated by using the chain rule: & ( (5) dj j dt = "J j. k i.
Suppleentary Materal Dervaton of Eq. 1a. Assue j s a functon of the rate constants for the N coponent reactons: j j (k 1,,..., k,..., k N ( The dervatve wth respect to teperature T s calculated by usng
More informationDepartment of Mechanical Engineering ME 322 Mechanical Engineering Thermodynamics. Ideal Gas Mixtures II. Lecture 32
Departent of Mechanical Engineering ME 322 Mechanical Engineering Therodnaics Ideal Gas Mixtures II Lecture 32 The Gibbs Phase Rule The nuber of independent, intensive properties required to fix the state
More informationSystem in Weibull Distribution
Internatonal Matheatcal Foru 4 9 no. 9 94-95 Relablty Equvalence Factors of a Seres-Parallel Syste n Webull Dstrbuton M. A. El-Dacese Matheatcs Departent Faculty of Scence Tanta Unversty Tanta Egypt eldacese@yahoo.co
More informationElastic Collisions. Definition: two point masses on which no external forces act collide without losing any energy.
Elastc Collsons Defnton: to pont asses on hch no external forces act collde thout losng any energy v Prerequstes: θ θ collsons n one denson conservaton of oentu and energy occurs frequently n everyday
More informationEXAMPLES of THEORETICAL PROBLEMS in the COURSE MMV031 HEAT TRANSFER, version 2017
EXAMPLES of THEORETICAL PROBLEMS n the COURSE MMV03 HEAT TRANSFER, verson 207 a) What s eant by sotropc ateral? b) What s eant by hoogeneous ateral? 2 Defne the theral dffusvty and gve the unts for the
More informationThermodynamics General
Thermodynamcs General Lecture 1 Lecture 1 s devoted to establshng buldng blocks for dscussng thermodynamcs. In addton, the equaton of state wll be establshed. I. Buldng blocks for thermodynamcs A. Dmensons,
More informationMultipoint Analysis for Sibling Pairs. Biostatistics 666 Lecture 18
Multpont Analyss for Sblng ars Bostatstcs 666 Lecture 8 revously Lnkage analyss wth pars of ndvduals Non-paraetrc BS Methods Maxu Lkelhood BD Based Method ossble Trangle Constrant AS Methods Covered So
More informationLecture. Polymer Thermodynamics 0331 L Chemical Potential
Prof. Dr. rer. nat. habl. S. Enders Faculty III for Process Scence Insttute of Chemcal Engneerng Department of Thermodynamcs Lecture Polymer Thermodynamcs 033 L 337 3. Chemcal Potental Polymer Thermodynamcs
More informationApplied Mathematics Letters
Appled Matheatcs Letters 2 (2) 46 5 Contents lsts avalable at ScenceDrect Appled Matheatcs Letters journal hoepage: wwwelseverco/locate/al Calculaton of coeffcents of a cardnal B-splne Gradr V Mlovanovć
More informationLecture-24. Enzyme kinetics and Enzyme inhibition-ii
Lecture-24 Enzye knetcs and Enzye nhbton-ii Noncopette Inhbton A noncopette nhbtor can bnd wth enzye or wth enzye-substrate coplex to produce end coplex. Hence the nhbtor ust bnd at a dfferent ste fro
More informationSupplementary Notes for Chapter 9 Mixture Thermodynamics
Supplementary Notes for Chapter 9 Mxture Thermodynamcs Key ponts Nne major topcs of Chapter 9 are revewed below: 1. Notaton and operatonal equatons for mxtures 2. PVTN EOSs for mxtures 3. General effects
More informationOur focus will be on linear systems. A system is linear if it obeys the principle of superposition and homogenity, i.e.
SSTEM MODELLIN In order to solve a control syste proble, the descrptons of the syste and ts coponents ust be put nto a for sutable for analyss and evaluaton. The followng ethods can be used to odel physcal
More information1.3 Hence, calculate a formula for the force required to break the bond (i.e. the maximum value of F)
EN40: Dynacs and Vbratons Hoework 4: Work, Energy and Lnear Moentu Due Frday March 6 th School of Engneerng Brown Unversty 1. The Rydberg potental s a sple odel of atoc nteractons. It specfes the potental
More information( ) 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 informationPhysics 123. Exam #1. October 11, 2006
hyscs Exa # October, 006 roble /0 roble /0 roble /0 roble 4 /0 roble 5 /0 roble 6 /0 roble 7 /0 roble 8 /0 roble 9 /0 roble 0 /0 Total /00 Free-Response robles: lease show all work n order to receve partal
More informationTransfer Functions. Convenient representation of a linear, dynamic model. A transfer function (TF) relates one input and one output: ( ) system
Transfer Functons Convenent representaton of a lnear, dynamc model. A transfer functon (TF) relates one nput and one output: x t X s y t system Y s The followng termnology s used: x y nput output forcng
More informationSolutions for Homework #9
Solutons for Hoewor #9 PROBEM. (P. 3 on page 379 n the note) Consder a sprng ounted rgd bar of total ass and length, to whch an addtonal ass s luped at the rghtost end. he syste has no dapng. Fnd the natural
More informationNAME and Section No. it is found that 0.6 mol of O
NAME and Secton No. Chemstry 391 Fall 7 Exam III KEY 1. (3 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). In the reacton 3O O3 t s found that.6 mol of O are consumed. Fnd
More informationThermodynamics Second Law Entropy
Thermodynamcs Second Law Entropy Lana Sherdan De Anza College May 8, 2018 Last tme the Boltzmann dstrbuton (dstrbuton of energes) the Maxwell-Boltzmann dstrbuton (dstrbuton of speeds) the Second Law of
More informationProblem Set #6 solution, Chem 340, Fall 2013 Due Friday, Oct 11, 2013 Please show all work for credit
Problem Set #6 soluton, Chem 340, Fall 2013 Due Frday, Oct 11, 2013 Please show all work for credt To hand n: Atkns Chap 3 Exercses: 3.3(b), 3.8(b), 3.13(b), 3.15(b) Problems: 3.1, 3.12, 3.36, 3.43 Engel
More informationDepartment of Mechanical Engineering ME 322 Mechanical Engineering Thermodynamics. Ideal Gas Mixtures. Lecture 31
Departet of echacal Egeerg E 322 echacal Egeerg Therodyacs Ideal Gas xtures Lecture 31 xtures Egeerg Applcatos atural gas ethae, ethae, propae, butae, troge, hydroge, carbo doxde, ad others Refrgerats
More information4.2 Chemical Driving Force
4.2. CHEMICL DRIVING FORCE 103 4.2 Chemcal Drvng Force second effect of a chemcal concentraton gradent on dffuson s to change the nature of the drvng force. Ths s because dffuson changes the bondng n a
More informationG4023 Mid-Term Exam #1 Solutions
Exam1Solutons.nb 1 G03 Md-Term Exam #1 Solutons 1-Oct-0, 1:10 p.m to :5 p.m n 1 Pupn Ths exam s open-book, open-notes. You may also use prnt-outs of the homework solutons and a calculator. 1 (30 ponts,
More informationPhysics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum. Physics 3A: Linear Momentum
Recall that there was ore to oton than just spee A ore coplete escrpton of oton s the concept of lnear oentu: p v (8.) Beng a prouct of a scalar () an a vector (v), oentu s a vector: p v p y v y p z v
More informationAppendix II Summary of Important Equations
W. M. Whte Geochemstry Equatons of State: Ideal GasLaw: Coeffcent of Thermal Expanson: Compressblty: Van der Waals Equaton: The Laws of Thermdynamcs: Frst Law: Appendx II Summary of Important Equatons
More information...Thermodynamics. If Clausius Clapeyron fails. l T (v 2 v 1 ) = 0/0 Second order phase transition ( S, v = 0)
If Clausus Clapeyron fals ( ) dp dt pb =...Thermodynamcs l T (v 2 v 1 ) = 0/0 Second order phase transton ( S, v = 0) ( ) dp = c P,1 c P,2 dt Tv(β 1 β 2 ) Two phases ntermngled Ferromagnet (Excess spn-up
More informationIrreversible Work of Separation and Heat-Driven Separation
J. Phys. Che. B 004, 08, 6035-604 6035 Irreversble Wor of Separaton and Heat-Drven Separaton Anatoly M. Tsrln and Vladr Kazaov*, Progra Syste Insttute, Russan Acadey of Scence, set. Botc, PerejaslaVl-Zalesy,
More informationNumerical Heat and Mass Transfer
Master degree n Mechancal Engneerng Numercal Heat and Mass Transfer 06-Fnte-Dfference Method (One-dmensonal, steady state heat conducton) Fausto Arpno f.arpno@uncas.t Introducton Why we use models and
More informationThe Parity of the Number of Irreducible Factors for Some Pentanomials
The Party of the Nuber of Irreducble Factors for Soe Pentanoals Wolfra Koepf 1, Ryul K 1 Departent of Matheatcs Unversty of Kassel, Kassel, F. R. Gerany Faculty of Matheatcs and Mechancs K Il Sung Unversty,
More informationHomework Chapter 21 Solutions!!
Homework Chapter 1 Solutons 1.7 1.13 1.17 1.19 1.6 1.33 1.45 1.51 1.71 page 1 Problem 1.7 A mole sample of oxygen gas s confned to a 5 lter vessel at a pressure of 8 atm. Fnd the average translatonal knetc
More information1 Review From Last Time
COS 5: Foundatons of Machne Learnng Rob Schapre Lecture #8 Scrbe: Monrul I Sharf Aprl 0, 2003 Revew Fro Last Te Last te, we were talkng about how to odel dstrbutons, and we had ths setup: Gven - exaples
More informationObtaining U and G based on A above arrow line: )
Suary or ch,,3,4,5,6,7 (Here soe olar propertes wthout underlne) () he three laws o herodynacs - st law: otal energy o syste (SYS) plus surroundng (SUR) s conserved. - nd law: otal change o entropy o the
More informationEnergy, Entropy, and Availability Balances Phase Equilibria. Nonideal Thermodynamic Property Models. Selecting an Appropriate Model
Lecture 4. Thermodynamcs [Ch. 2] Energy, Entropy, and Avalablty Balances Phase Equlbra - Fugactes and actvty coeffcents -K-values Nondeal Thermodynamc Property Models - P-v-T equaton-of-state models -
More informationCOS 511: Theoretical Machine Learning
COS 5: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #0 Scrbe: José Sões Ferrera March 06, 203 In the last lecture the concept of Radeacher coplexty was ntroduced, wth the goal of showng that
More informationDesigning Fuzzy Time Series Model Using Generalized Wang s Method and Its application to Forecasting Interest Rate of Bank Indonesia Certificate
The Frst Internatonal Senar on Scence and Technology, Islac Unversty of Indonesa, 4-5 January 009. Desgnng Fuzzy Te Seres odel Usng Generalzed Wang s ethod and Its applcaton to Forecastng Interest Rate
More informationI wish to publish my paper on The International Journal of Thermophysics. A Practical Method to Calculate Partial Properties from Equation of State
I wsh to publsh my paper on The Internatonal Journal of Thermophyscs. Ttle: A Practcal Method to Calculate Partal Propertes from Equaton of State Authors: Ryo Akasaka (correspondng author) 1 and Takehro
More informationFinal Exam Solutions, 1998
58.439 Fnal Exa Solutons, 1998 roble 1 art a: Equlbru eans that the therodynac potental of a consttuent s the sae everywhere n a syste. An exaple s the Nernst potental. If the potental across a ebrane
More informationA quote of the week (or camel of the week): There is no expedience to which a man will not go to avoid the labor of thinking. Thomas A.
A quote of the week (or camel of the week): here s no expedence to whch a man wll not go to avod the labor of thnkng. homas A. Edson Hess law. Algorthm S Select a reacton, possbly contanng specfc compounds
More informationAt zero K: All atoms frozen at fixed positions on a periodic lattice.
September, 00 Readng: Chapter Four Homework: None Entropy and The Degree of Dsorder: Consder a sold crystallne materal: At zero K: All atoms frozen at fxed postons on a perodc lattce. Add heat to a fnte
More informationChemical Equilibrium. Chapter 6 Spontaneity of Reactive Mixtures (gases) Taking into account there are many types of work that a sysem can perform
Ths chapter deals wth chemcal reactons (system) wth lttle or no consderaton on the surroundngs. Chemcal Equlbrum Chapter 6 Spontanety of eactve Mxtures (gases) eactants generatng products would proceed
More informationAN ANALYSIS OF A FRACTAL KINETICS CURVE OF SAVAGEAU
AN ANALYI OF A FRACTAL KINETIC CURE OF AAGEAU by John Maloney and Jack Hedel Departent of Matheatcs Unversty of Nebraska at Oaha Oaha, Nebraska 688 Eal addresses: aloney@unoaha.edu, jhedel@unoaha.edu Runnng
More informationtotal If no external forces act, the total linear momentum of the system is conserved. This occurs in collisions and explosions.
Lesson 0: Collsons, Rotatonal netc Energy, Torque, Center o Graty (Sectons 7.8 Last te we used ewton s second law to deelop the pulse-oentu theore. In words, the theore states that the change n lnear oentu
More informationIf 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 informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More information1 Definition of Rademacher Complexity
COS 511: Theoretcal Machne Learnng Lecturer: Rob Schapre Lecture #9 Scrbe: Josh Chen March 5, 2013 We ve spent the past few classes provng bounds on the generalzaton error of PAClearnng algorths for the
More informationFinite Vector Space Representations Ross Bannister Data Assimilation Research Centre, Reading, UK Last updated: 2nd August 2003
Fnte Vector Space epresentatons oss Bannster Data Asslaton esearch Centre, eadng, UK ast updated: 2nd August 2003 Contents What s a lnear vector space?......... 1 About ths docuent............ 2 1. Orthogonal
More informationScattering by a perfectly conducting infinite cylinder
Scatterng by a perfectly conductng nfnte cylnder Reeber that ths s the full soluton everywhere. We are actually nterested n the scatterng n the far feld lt. We agan use the asyptotc relatonshp exp exp
More informationLeast Squares Fitting of Data
Least Squares Fttng of Data Davd Eberly Geoetrc Tools, LLC http://www.geoetrctools.co/ Copyrght c 1998-2014. All Rghts Reserved. Created: July 15, 1999 Last Modfed: February 9, 2008 Contents 1 Lnear Fttng
More informationLecture 6. Entropy of an Ideal Gas (Ch. 3)
Lecture 6. Entropy o an Ideal Gas (Ch. oday we wll acheve an portant goal: we ll derve the equaton(s o state or an deal gas ro the prncples o statstcal echancs. We wll ollow the path outlned n the prevous
More informationPART I: MULTIPLE CHOICE (32 questions, each multiple choice question has a 2-point value, 64 points total).
CHEMISTRY 123-07 Mdterm #2 answer key November 04, 2010 Statstcs: Average: 68 p (68%); Hghest: 91 p (91%); Lowest: 37 p (37%) Number of students performng at or above average: 58 (53%) Number of students
More informationFinding Dense Subgraphs in G(n, 1/2)
Fndng Dense Subgraphs n Gn, 1/ Atsh Das Sarma 1, Amt Deshpande, and Rav Kannan 1 Georga Insttute of Technology,atsh@cc.gatech.edu Mcrosoft Research-Bangalore,amtdesh,annan@mcrosoft.com Abstract. Fndng
More informationQuantum Particle Motion in Physical Space
Adv. Studes Theor. Phys., Vol. 8, 014, no. 1, 7-34 HIKARI Ltd, www.-hkar.co http://dx.do.org/10.1988/astp.014.311136 Quantu Partcle Moton n Physcal Space A. Yu. Saarn Dept. of Physcs, Saara State Techncal
More informationChemistry Department Al-kharj, October Prince Sattam Bin Abdulaziz University First semester (1437/1438)
Exercise 1 Exercises- chapter-1- Properties of gases (Part-2- Real gases Express the van der Waals paraeters a = 1.32 at d 6 ol 2 and b = 0.0436 d 3 ol 1 in SI base units? * The SI unit of pressure is
More informationRevision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax
.9.1: AC power analyss Reson: Deceber 13, 010 15 E Man Sute D Pullan, WA 99163 (509 334 6306 Voce and Fax Oerew n chapter.9.0, we ntroduced soe basc quanttes relate to delery of power usng snusodal sgnals.
More informationExcess Error, Approximation Error, and Estimation Error
E0 370 Statstcal Learnng Theory Lecture 10 Sep 15, 011 Excess Error, Approxaton Error, and Estaton Error Lecturer: Shvan Agarwal Scrbe: Shvan Agarwal 1 Introducton So far, we have consdered the fnte saple
More informationCHEMICAL ENGINEERING
Postal Correspondence GATE & PSUs -MT To Buy Postal Correspondence Packages call at 0-9990657855 1 TABLE OF CONTENT S. No. Ttle Page no. 1. Introducton 3 2. Dffuson 10 3. Dryng and Humdfcaton 24 4. Absorpton
More informationSolution Thermodynamics
CH2351 Chemcal Engneerng Thermodynamcs II Unt I, II www.msubbu.n Soluton Thermodynamcs www.msubbu.n Dr. M. Subramanan Assocate Professor Department of Chemcal Engneerng Sr Svasubramanya Nadar College of
More informationON THE NUMBER OF PRIMITIVE PYTHAGOREAN QUINTUPLES
Journal of Algebra, Nuber Theory: Advances and Applcatons Volue 3, Nuber, 05, Pages 3-8 ON THE NUMBER OF PRIMITIVE PYTHAGOREAN QUINTUPLES Feldstrasse 45 CH-8004, Zürch Swtzerland e-al: whurlann@bluewn.ch
More informationMultiplicative Functions and Möbius Inversion Formula
Multplcatve Functons and Möbus Inverson Forula Zvezdelna Stanova Bereley Math Crcle Drector Mlls College and UC Bereley 1. Multplcatve Functons. Overvew Defnton 1. A functon f : N C s sad to be arthetc.
More informationCollaborative Filtering Recommendation Algorithm
Vol.141 (GST 2016), pp.199-203 http://dx.do.org/10.14257/astl.2016.141.43 Collaboratve Flterng Recoendaton Algorth Dong Lang Qongta Teachers College, Haou 570100, Chna, 18689851015@163.co Abstract. Ths
More informationOutline. Unit Eight Calculations with Entropy. The Second Law. Second Law Notes. Uses of Entropy. Entropy is a Property.
Unt Eght Calculatons wth Entropy Mechancal Engneerng 370 Thermodynamcs Larry Caretto October 6, 010 Outlne Quz Seven Solutons Second law revew Goals for unt eght Usng entropy to calculate the maxmum work
More informationThermodynamics II. Department of Chemical Engineering. Prof. Kim, Jong Hak
Thermodynamcs II Department of Chemcal Engneerng Prof. Km, Jong Hak Soluton Thermodynamcs : theory Obectve : lay the theoretcal foundaton for applcatons of thermodynamcs to gas mxture and lqud soluton
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More informationV T for n & P = constant
Pchem 365: hermodynamcs -SUMMARY- Uwe Burghaus, Fargo, 5 9 Mnmum requrements for underneath of your pllow. However, wrte your own summary! You need to know the story behnd the equatons : Pressure : olume
More informationIntroduction to Vapor/Liquid Equilibrium, part 2. Raoult s Law:
CE304, Sprng 2004 Lecture 4 Introducton to Vapor/Lqud Equlbrum, part 2 Raoult s Law: The smplest model that allows us do VLE calculatons s obtaned when we assume that the vapor phase s an deal gas, and
More informationIncluded in this hand-out are five examples of problems requiring the solution of a system of linear algebraic equations.
he Lecture Notes, Dept. of heical Engineering, Univ. of TN, Knoville - D. Keffer, 5/9/98 (updated /) Eaple pplications of systes of linear equations Included in this hand-out are five eaples of probles
More informationCHEMICAL REACTIONS AND DIFFUSION
CHEMICAL REACTIONS AND DIFFUSION A.K.A. NETWORK THERMODYNAMICS BACKGROUND Classcal thermodynamcs descrbes equlbrum states. Non-equlbrum thermodynamcs descrbes steady states. Network thermodynamcs descrbes
More informationbetween standard Gibbs free energies of formation for products and reactants, ΔG! R = ν i ΔG f,i, we
hermodynamcs, Statstcal hermodynamcs, and Knetcs 4 th Edton,. Engel & P. ed Ch. 6 Part Answers to Selected Problems Q6.. Q6.4. If ξ =0. mole at equlbrum, the reacton s not ery far along. hus, there would
More informationLinear Multiple Regression Model of High Performance Liquid Chromatography
Lnear Multple Regresson Model of Hgh Perforance Lqud Chroatography STANISLAVA LABÁTOVÁ Insttute of Inforatcs Departent of dscrete processes odelng and control Slovak Acadey of Scences Dúbravská 9, 845
More informationOn the number of regions in an m-dimensional space cut by n hyperplanes
6 On the nuber of regons n an -densonal space cut by n hyperplanes Chungwu Ho and Seth Zeran Abstract In ths note we provde a unfor approach for the nuber of bounded regons cut by n hyperplanes n general
More information#64. ΔS for Isothermal Mixing of Ideal Gases
#64 Carnot Heat Engne ΔS for Isothermal Mxng of Ideal Gases ds = S dt + S T V V S = P V T T V PV = nrt, P T ds = v T = nr V dv V nr V V = nrln V V = - nrln V V ΔS ΔS ΔS for Isothermal Mxng for Ideal Gases
More informationEstimation of the composition of the liquid and vapor streams exiting a flash unit with a supercritical component
Department of Energ oltecnco d Mlano Va Lambruschn - 05 MILANO Eercses of Fundamentals of Chemcal rocesses rof. Ganpero Gropp Eercse 8 Estmaton of the composton of the lqud and vapor streams etng a unt
More informationMain components of the above cycle are: 1) Boiler (steam generator) heat exchanger 2) Turbine generates work 3) Condenser heat exchanger 4) Pump
Introducton to Terodynacs, Lecture -5 Pro. G. Cccarell (0 Applcaton o Control olue Energy Analyss Most terodynac devces consst o a seres o coponents operatng n a cycle, e.g., stea power plant Man coponents
More informationFUZZY MODEL FOR FORECASTING INTEREST RATE OF BANK INDONESIA CERTIFICATE
he 3 rd Internatonal Conference on Quanttatve ethods ISBN 979-989 Used n Econoc and Busness. June 6-8, 00 FUZZY ODEL FOR FORECASING INERES RAE OF BANK INDONESIA CERIFICAE Agus aan Abad, Subanar, Wdodo
More informationQ e E i /k B. i i i i
Water and Aqueous Solutons 3. Lattce Model of a Flud Lattce Models Lattce models provde a mnmalst, or coarse-graned, framework for descrbng the translatonal, rotatonal, and conformatonal degrees of freedom
More informationLNG CARGO TRANSFER CALCULATION METHODS AND ROUNDING-OFFS
CARGO TRANSFER CALCULATION METHODS AND ROUNDING-OFFS CONTENTS 1. Method for determnng transferred energy durng cargo transfer. Calculatng the transferred energy.1 Calculatng the gross transferred energy.1.1
More informationITERATIVE ESTIMATION PROCEDURE FOR GEOSTATISTICAL REGRESSION AND GEOSTATISTICAL KRIGING
ESE 5 ITERATIVE ESTIMATION PROCEDURE FOR GEOSTATISTICAL REGRESSION AND GEOSTATISTICAL KRIGING Gven a geostatstcal regresson odel: k Y () s x () s () s x () s () s, s R wth () unknown () E[ ( s)], s R ()
More informationSolubilities and Thermodynamic Properties of SO 2 in Ionic
Solubltes nd Therodync Propertes of SO n Ionc Lquds Men Jn, Yucu Hou, b Weze Wu, *, Shuhng Ren nd Shdong Tn, L Xo, nd Zhgng Le Stte Key Lbortory of Checl Resource Engneerng, Beng Unversty of Checl Technology,
More informationChapter 3 Thermochemistry of Fuel Air Mixtures
Chapter 3 Thermochemstry of Fuel Ar Mxtures 3-1 Thermochemstry 3- Ideal Gas Model 3-3 Composton of Ar and Fuels 3-4 Combuston Stochometry t 3-5 The1 st Law of Thermodynamcs and Combuston 3-6 Thermal converson
More informationPhysics 181. Particle Systems
Physcs 181 Partcle Systems Overvew In these notes we dscuss the varables approprate to the descrpton of systems of partcles, ther defntons, ther relatons, and ther conservatons laws. We consder a system
More informationUniversity of Washington Department of Chemistry Chemistry 453 Winter Quarter 2015
Lecture 2. 1/07/15-1/09/15 Unversty of Washngton Department of Chemstry Chemstry 453 Wnter Quarter 2015 We are not talkng about truth. We are talkng about somethng that seems lke truth. The truth we want
More informationCHAPTER 14 GENERAL PERTURBATION THEORY
CHAPTER 4 GENERAL PERTURBATION THEORY 4 Introducton A partcle n orbt around a pont mass or a sphercally symmetrc mass dstrbuton s movng n a gravtatonal potental of the form GM / r In ths potental t moves
More informationPhysics 240: Worksheet 30 Name:
(1) One mole of an deal monatomc gas doubles ts temperature and doubles ts volume. What s the change n entropy of the gas? () 1 kg of ce at 0 0 C melts to become water at 0 0 C. What s the change n entropy
More informationXiangwen Li. March 8th and March 13th, 2001
CS49I Approxaton Algorths The Vertex-Cover Proble Lecture Notes Xangwen L March 8th and March 3th, 00 Absolute Approxaton Gven an optzaton proble P, an algorth A s an approxaton algorth for P f, for an
More informationAn Optimal Bound for Sum of Square Roots of Special Type of Integers
The Sxth Internatonal Syposu on Operatons Research and Its Applcatons ISORA 06 Xnang, Chna, August 8 12, 2006 Copyrght 2006 ORSC & APORC pp. 206 211 An Optal Bound for Su of Square Roots of Specal Type
More informationMolecular Speeds. Real Gasses. Ideal Gas Law. Reasonable. Why the breakdown? P-V Diagram. Using moles. Using molecules
Kinetic Theory of Gases Connect icroscopic properties (kinetic energy and oentu) of olecules to acroscopic state properties of a gas (teperature and pressure). P v v 3 3 3 But K v and P kt K v kt Teperature
More information