Lecture 2 Thermodynamics and stability October 30, 2009
|
|
- Moses Caldwell
- 6 years ago
- Views:
Transcription
1 The tablty of thn (oft) flm Lecture 2 Thermodynamc and tablty October 30, 2009 Ian Morron 2009
2 Revew of Lecture 1 The djonng preure a jump n preure at the boundary. It doe not vary between the plate. 1 G Π ( h) = A h T P σ σ,, 1, 2, N P h P 2π RR F y Π h dh R + R Force between 2 phere: 1 2 ( ) ( ) G(h) 1 2 y ( ) G h 1 Π ( h) = h 2 G 0 = σ σ σ = S 0 G ( ) ( ) = 0 0 l lv 3 h Curve 1 Stable Curve 2 Metatable Curve 3 - Untable Ian Morron
3 Joah Wllard Gbb JOSIAH WILLARD GIBBS Born Feb. 11, 1839 Ded Apr. 22, 1903 PROFESSOR OF MATHEMATICAL PHYSICS IN YALE UNIVERSITY, Ian Morron
4 Gbb nterfacal phae Denty Interfacal Phae σ Dtance du = TdS pdv +σ da + μdn U = TS pv +σ A+ μ n p μ SdT Vdp + Adσ+ n dμ = 0 S dt V dp+ n dμ = 0 SdT Vdp+ ndμ = 0 dμ = dμ = dμ Dfferental of total energy Total energy Gbb-Duhem equaton For each bulk phae At equlbrum ( S S S ) dt ( V V V ) dp+ Adσ+ ( n n n ) dμ = 0 σ σ S = S S S V = V V V n = n n n σ σ σ Adσ + S dt V dp + nd μ = 0 σ Subtractng and renamng. Gbb adorpton otherm: Surface concentraton: n σ= = Γ μ A μ σ d d d μ Γ = n σ A -2 mol m Ian Morron
5 Gbb urface phae F = C P+ 2 Gbb adorpton otherm: n σ dσ= dμ = Γdμ A The urface exce: Γ = n σ A -2 mol m For a 2-component ytem: Surface Surface Phae Phae dσ=γ1dμ 1+Γ2dμ2 wth the Gbb-Duhem relaton Xd 1 μ 1 + Xd 2 μ 2 = 0 G gve dσ=γ2dμ2 and the urface-exce concentraton G X 2 Γ 2 =Γ2 Γ1 X1 Dtance ndependent of the dvdng urface. Denty D Denty old Dtance Component 2 Component 1 2 component, 2 component, 2 phae 1 phae Ian Morron
6 Interactng adorpton layer? Interfacal Phae Surface Phae Surface Phae Surface Phae Component 2 Component 2 Denty Denty Denty old Denty old Component 1 Component 1 σ Dtance Dtance Dtance Dtance 2 phae, 2 component 1 phae, 2 component Surface Phae Bulk h Phae Surface Phae X Γ =Γ Γ G X1 X 1 and X 2 are no longer contant. They depend on h. ty Den old Component 2 Component 1 old Den ty h a new degree of freedom Dtance 1 lqud phae, 2 component Ian Morron
7 du = TdS pdv + μ dn G = U - TS + pv ** Thermodynamc of thn flm* G Π ( h) = A h σ σ T, P, 1, 2, N r plate dg = SdT + VdP + μdn + A Ψ dσ AΠdh Ψ dσ =Ψ dσ +Ψ dσ plate j j j j = 1 j j (,,, σ, σ, ) (,,, σ, σ, ) GTPN h = AΠ TPN kdk+ G h= h G = h the free energy of Gbb model ncludng the adorpton at urface. r dg = d G μdn Ψ1dσ1 Ψ 2dσ2 = SdT + VdP + Ndμ + A( σ1dψ 1+ σ2dψ2) AΠdh = 1 = 1 A Gbb dd, we hall do, ubtract the unform properte of the bulk: V = k V k S = S Sk = S Vkk k k N = N N = N V n k k, k k k = μ ( σ Ψ + σ Ψ ) Π dg S dt Nd A 1d 1 2d 2 A dh = 1, r **Rowlnon and Wdom, Appendx 1 - Thermodynamc * Parallel plate. Ian Morron
8 dg = S dt Ndμ A( σ1dψ 1+ σ2dψ2) AΠ dh = 0 = 1, r Thermodynamc of thn flm - 2 Snce the LHS a total dfferental, o the RHS, o 1 N Π = A h μ μ μ,, Ψ, Ψ h,,, Ψ, Ψ N Π= dμ A h μ h a modfed σ,, Ψ1, Ψ2 Gbb equaton. dσ= dμ = Γdμ A n N A Π Γ = A μ h h, dh the exce adorpton due to djonng preure. Note that we do not know how much exce on ether plate! Ian Morron
9 dg = S dt Ndμ A( σ1dψ 1+ σ2dψ2) AΠ dh = 0 = 1, r Thermodynamc of thn flm S Π = A h T 1 A μ,, Ψ, Ψ ( h= ) 1 2 Π S S = dh T h h, h, μ,, Ψ, Ψ If we know Π=Π( ht Ψ Ψ μ),, 1, 2, 1 2 the exce entropy due to djonng preure. We have (,,, σ, σ, ) (,,, σ, σ, ) GTPN h = AΠ TPN kdk+ G S S Vkk k = h= h So all the thermodynamc functon can be calculated. The ret tattcal mechanc, oft matter calng, etc Ian Morron
10 1 G Π ( h) = A h σ σ Stablty of flm between parallel plate TP,, 1, 2, N Stable Sabewhen 2 G > 0 2 h dπ h d P P Untable: 1 G dh dh Π ( h) = A h Π ( h) < 0 Aumng all other thermodynamc value RTS. hh ( ) ( ) 0 = = 0 If the change n thckne not by a p, ( q ) tate at a hgher free energy o that: reverble path, then the (non-equlbrum) Π ( h) Π ( h) h non eq < h eq Some untable flm wll be table to fat eg e.g. Gbb-Marangon tablty a ncreae perturbaton: n lqud urface tenon wth expanon becaue urfactant adorpton low. Ian Morron Not preented durng Lecture 2.
11 2π RR 2π RR F y R h dh F y h dh F y h dh ( ) 2 π Π( ) ( ) Π( ) ( ) Π( ) p r r R1+ R2 n Ω y y y Stablty of flm between convex bode F y The change n force wth dtance : = gπ ( y ) Stablty of the equlbrum : df < 0 Hence: Π ( y ) > 0 dy < ( ) 0 If the change n thckne not tby a reverble path, then df df df non eq eq the (non-equlbrum) tate or dy dy dy at a hgher force o that: df non eq < > gπ( y) e.g. If the collon of charged partcle more rapd than the tme for the urface charge to equlbrate, the dperon may appear to be more table than t really. But, nteracton between convex urface are more lkely to be at equlbrum than parallel plate. Ian Morron 2009 Not preented durng Lecture 2. 23
12 Component of djonng preure What overlap? Electromagnetc feld from the random, quantum fluctuaton of electron n all the three phae. (Dperon force.) Statc electrc feld from charged urface. Interacton between molecule or polymer adorbed on the urface. Layered tructurng of olvent molecule, olute molecule or dpered phae. Ian Morron Not preented durng Lecture 2.
13 Expermental evdence Derjagun, B.V.; Rabnovch, Y.I.; Churaev, N.V. Drect meaurement of molecular force Nature, 272, , r Frt drect meaurement were reported n Frt Englh report n Quartz, platnum, gold n ar. Gla thread n water. Gla thread n water. = 2 π ( ) 12 u F rr 1 2 Rabnovch, Ya.I.; Derjagun, B.V.; Churaev, N.V. Drect meaurement of long-range urface force n ga and lqud d meda. Adv. Collod Interface Sc., 16, 63 78, Ian Morron 2009 Not preented durng Lecture 2. 25
14 Polymolecular adorbed layer? Water on mca Intal After collape Thee dtance are much larger than Debye length. For example: 0.1 N LCl on polhed damond wa 75 nm at 900 dyne/cm 2. The Debye length hould be about 1 nm. Nor t van der Waal force becaue of the extreme entvty to the dolved component. Derjagun, B.; Kuakov, M.; Lebedva. Range of molecular l acton of urface and polymolecular olvate (adorbed) layer. C.R. Acad. Soc. URSS, 1939, 23(7), nm Ian Morron 2009 Not preented durng Lecture 2. 26
15 Polywater Rabnovch, Y.I.; Derjagun, B.V. Interacton of hydrophobzed flament n aqueou-electrolyte oluton. Collod Surf., 30, , Ian Morron 2009 Not preented durng Lecture 2. 27
16 Polywater Ice-nne Ice-nne a fctonal materal conceved by wrter Kurt Vonnegut n h novel Cat' Cradle. It uppoed to be a more table polymorph of water than common ce (Ice I h ) whch ntead of meltng at 0 Celu (32 Fahrenhet), melt at 45.8 C (1144 F) (114.4 F). When ce-nne come nto contact wth lqud water below 45.8 C (whch thu effectvely upercooled), t act a a eed crytal, and caue the oldfcaton (freezng) of the entre body of water whch quckly crytallze a ce-nne. A global catatrophe nvolvng freezng the Earth' ocean by mple contact wth cenne ued a a plot devce n Vonnegut' novel. (wkpeda.com) Future oberver wll chuckle quetly over Derjagun dcomfture centfc htory wll ee Derjagun a a great phycal chemt who ha domnated theory and experment n urface and collod cence for ffty year... Let the lat word on polywater be thoe of Derjagun: It wa not a matter of belef, t wa a matter of performng better experment. Pethca, B.A. Book revew: Polywater by F. Frank, MIT Pre: J. Collod Interface Sc., 21, 607, Bor Vladmrovch Derjagun, Ian Morron 2009 Not preented durng Lecture 2. 28
17 Iraelachvl, J. Intermolecular and urface force, 2 nd ed.; Academc Pre: Amterdam; Jacob box Surface force apparatu: Two mca urface, atomcally mooth, accuracy to 1 Å. At the 10 Å cale flud properte, uch a relaxaton tme, can be tme greater than n the bulk. Djonng preure only mentoned twce n th (terrfc) book, once wth negatve Hamaker contant and once wth electrotatc repulon.) Ian Morron 2009 Not preented durng Lecture 2. 29
Introduction to Interfacial Segregation. Xiaozhe Zhang 10/02/2015
Introducton to Interfacal Segregaton Xaozhe Zhang 10/02/2015 Interfacal egregaton Segregaton n materal refer to the enrchment of a materal conttuent at a free urface or an nternal nterface of a materal.
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 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 informationLecture 3 Electrostatic effects November 6, 2009
The stablty of thn (soft) flms Lecture 3 Electrostatc effects November 6, 009 Ian Morrson 009 Revew of Lecture The dsjonng pressure s a jump n pressure at the boundary. It does not vary between the plates.
More informationCHAPTER X PHASE-CHANGE PROBLEMS
Chapter X Phae-Change Problem December 3, 18 917 CHAPER X PHASE-CHANGE PROBLEMS X.1 Introducton Clacal Stefan Problem Geometry of Phae Change Problem Interface Condton X. Analytcal Soluton for Soldfcaton
More informationEffect of the adsorption component of the disjoining pressure on foam film drainage
Collod J. 75 (2013) 176-180 [arxv 1209.4745] Effect of the adorpton component of the djonng preure on foam flm dranage Stoyan I. Karakahev 1, Anh V. Nguyen 2 and Roumen Tekov 1 1 Department of Phycal Chemtry,
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 informationYou must not circulate this book in any other binding or cover and you must impose this same condition on any acquirer.
6 Interfacal thermodynamc: Gbb equaton Luuk K. Koopal Chapter 6, Interfacal thermodynamc: Gbb equaton n Interface Scence, Second edton, 008, Wagenngen Unverty, Wagenngen, The Netherland. Avalable va: http://www.reearchgate.net/profle/luuk_koopal
More informationProblem #1. Known: All required parameters. Schematic: Find: Depth of freezing as function of time. Strategy:
BEE 3500 013 Prelm Soluton Problem #1 Known: All requred parameter. Schematc: Fnd: Depth of freezng a functon of tme. Strategy: In thee mplfed analy for freezng tme, a wa done n cla for a lab geometry,
More information3) Thermodynamic equation to characterize interfaces
3) Thermodynamc equaton to characterze nterfaces 3.1) Gbbs Model Realty: rapd contnuous change of chemcal and thermodynamc propertes Replaced by model (constant propertes up to the surface) uv bulk uv
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 informationReview of Classical Thermodynamics
Revew of Classcal hermodynamcs Physcs 4362, Lecture #1, 2 Syllabus What s hermodynamcs? 1 [A law] s more mpressve the greater the smplcty of ts premses, the more dfferent are the knds of thngs t relates,
More informationThe stability of thin (soft) films
The tability of thin (oft) film Lecture 5 Stability of thin film Long range force* November, 9 e.g. Diperion, electrotatic, polymeric Review of Lecture The dijoining preure i a jump in preure at the boundary.
More informationAPPLICATIONS: CHEMICAL AND PHASE EQUILIBRIA
5.60 Sprn 2007 Lecture #28 pae PPLICTIOS: CHMICL D PHS QUILIBRI pply tattcal mechanc to develop mcrocopc model for problem you ve treated o far wth macrocopc thermodynamc 0 Product Reactant Separated atom
More informationa for save as PDF Chemistry 163B Introduction to Multicomponent Systems and Partial Molar Quantities
a for save as PDF Chemstry 163B Introducton to Multcomponent Systems and Partal Molar Quanttes 1 the problem of partal mmolar quanttes mx: 10 moles ethanol C 2 H 5 OH (580 ml) wth 1 mole water H 2 O (18
More informationLecture 2 Grand Canonical Ensemble GCE
Lecture 2 Grand Canoncal Ensemble GCE 2.1 hermodynamc Functons Contnung on from last day we also note that thus, dω = df dµ µd = Sd P dv dµ (2.1) P = V = S = From the expresson for the entropy, we therefore
More informationChemistry. Lecture 10 Maxwell Relations. NC State University
Chemistry Lecture 10 Maxwell Relations NC State University Thermodynamic state functions expressed in differential form We have seen that the internal energy is conserved and depends on mechanical (dw)
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 informationProblem Free Expansion of Ideal Gas
Problem 4.3 Free Expanon o Ideal Ga In general: ds ds du P dv P dv NR V dn Snce U o deal ga ndependent on olume (du=), and N = cont n the proce: dv In a ere o nntemal ree expanon, entropy change by: S
More informationCHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS
CHAPTER 9 LINEAR MOMENTUM, IMPULSE AND COLLISIONS 103 Phy 1 9.1 Lnear Momentum The prncple o energy conervaton can be ued to olve problem that are harder to olve jut ung Newton law. It ued to decrbe moton
More information3. 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 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 informationEffect of adding an ideal inert gas, M
Effect of adding an ideal inert gas, M Add gas M If there is no change in volume, then the partial pressures of each of the ideal gas components remains unchanged by the addition of M. If the reaction
More informationSome properties of the Helmholtz free energy
Some properties of the Helmholtz free energy Energy slope is T U(S, ) From the properties of U vs S, it is clear that the Helmholtz free energy is always algebraically less than the internal energy U.
More informationIntroduction to Statistical Methods
Introducton to Statstcal Methods Physcs 4362, Lecture #3 hermodynamcs Classcal Statstcal Knetc heory Classcal hermodynamcs Macroscopc approach General propertes of the system Macroscopc varables 1 hermodynamc
More information8 Waves in Uniform Magnetized Media
8 Wave n Unform Magnetzed Meda 81 Suceptblte The frt order current can be wrtten j = j = q d 3 p v f 1 ( r, p, t) = ɛ 0 χ E For Maxwellan dtrbuton Y n (λ) = f 0 (v, v ) = 1 πvth exp (v V ) v th 1 πv th
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 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 informationThermodynamics and statistical mechanics in materials modelling II
Course MP3 Lecture 8/11/006 (JAE) Course MP3 Lecture 8/11/006 Thermodynamcs and statstcal mechancs n materals modellng II A bref résumé of the physcal concepts used n materals modellng Dr James Ellott.1
More informationLecture 3 Clausius Inequality
Lecture 3 Clausius Inequality Rudolf Julius Emanuel Clausius 2 January 1822 24 August 1888 Defined Entropy Greek, en+tropein content transformative or transformation content The energy of the universe
More information10.40 Appendix Connection to Thermodynamics and Derivation of Boltzmann Distribution
10.40 Appendx Connecton to Thermodynamcs Dervaton of Boltzmann Dstrbuton Bernhardt L. Trout Outlne Cannoncal ensemble Maxmumtermmethod Most probable dstrbuton Ensembles contnued: Canoncal, Mcrocanoncal,
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 informationElectrical double layer: revisit based on boundary conditions
Electrcal double layer: revst based on boundary condtons Jong U. Km Department of Electrcal and Computer Engneerng, Texas A&M Unversty College Staton, TX 77843-318, USA Abstract The electrcal double layer
More informationThe Euler Equation. Using the additive property of the internal energy U, we can derive a useful thermodynamic relation the Euler equation.
The Euler Equation Using the additive property of the internal energy U, we can derive a useful thermodynamic relation the Euler equation. Let us differentiate this extensivity condition with respect to
More informationThermodynamic Variables and Relations
MME 231: Lecture 10 Thermodynamic Variables and Relations A. K. M. B. Rashid Professor, Department of MME BUET, Dhaka Today s Topics Thermodynamic relations derived from the Laws of Thermodynamics Definitions
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 informationMS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7
2017 Spring Semester MS212 Thermodynamics of Materials ( 소재열역학의이해 ) Lecture Note: Chapter 7 Byungha Shin ( 신병하 ) Dept. of MSE, KAIST Largely based on lecture notes of Prof. Hyuck-Mo Lee and Prof. WooChul
More informationGeometrical Optics Mirrors and Prisms
Phy 322 Lecture 4 Chapter 5 Geometrcal Optc Mrror and Prm Optcal bench http://webphyc.davdon.edu/applet/optc4/default.html Mrror Ancent bronze mrror Hubble telecope mrror Lqud mercury mrror Planar mrror
More informationChapter 3. Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc.
Chapter 3 Property Relations The essence of macroscopic thermodynamics Dependence of U, H, S, G, and F on T, P, V, etc. Concepts Energy functions F and G Chemical potential, µ Partial Molar properties
More informationNot at Steady State! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Yes! Class 15. Is the following possible?
Chapter 5-6 (where we are gong) Ideal gae and lqud (today) Dente Partal preure Non-deal gae (next tme) Eqn. of tate Reduced preure and temperature Compreblty chart (z) Vapor-lqud ytem (Ch. 6) Vapor preure
More informationChapter 7 Four-Wave Mixing phenomena
Chapter 7 Four-Wave Mx phenomena We wll dcu n th chapter the general nonlnear optcal procee wth four nteract electromagnetc wave n a NLO medum. Frt note that FWM procee are allowed n all meda (nveron or
More informationFrequency dependence of the permittivity
Frequency dependence of the permttvty February 7, 016 In materals, the delectrc constant and permeablty are actually frequency dependent. Ths does not affect our results for sngle frequency modes, but
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 informationGouy-Chapman model (1910) The double layer is not as compact as in Helmholtz rigid layer.
CHE465/865, 6-3, Lecture 1, 7 nd Sep., 6 Gouy-Chapman model (191) The double layer s not as compact as n Helmholtz rgd layer. Consder thermal motons of ons: Tendency to ncrease the entropy and make the
More information5.60 Thermodynamics & Kinetics Spring 2008
MIT OpenCourseWare http://ocw.mt.edu 5.60 Thermodynamcs & Knetcs Sprng 2008 For nformaton about ctng these materals or our Terms of Use, vst: http://ocw.mt.edu/terms. 5.60 Sprng 2008 Lecture #29 page 1
More informationChapter 4: Partial differentiation
Chapter 4: Partial differentiation It is generally the case that derivatives are introduced in terms of functions of a single variable. For example, y = f (x), then dy dx = df dx = f. However, most of
More information) is the unite step-function, which signifies that the second term of the right-hand side of the
Casmr nteracton of excted meda n electromagnetc felds Yury Sherkunov Introducton The long-range electrc dpole nteracton between an excted atom and a ground-state atom s consdered n ref. [1,] wth the help
More informationPhysics 607 Exam 1. ( ) = 1, Γ( z +1) = zγ( z) x n e x2 dx = 1. e x2
Physcs 607 Exam 1 Please be well-organzed, and show all sgnfcant steps clearly n all problems. You are graded on your wor, so please do not just wrte down answers wth no explanaton! Do all your wor on
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 informationChapter 18, Part 1. Fundamentals of Atmospheric Modeling
Overhead Sldes for Chapter 18, Part 1 of Fundamentals of Atmospherc Modelng by Mark Z. Jacobson Department of Cvl & Envronmental Engneerng Stanford Unversty Stanford, CA 94305-4020 January 30, 2002 Types
More informationScattering of two identical particles in the center-of. of-mass frame. (b)
Lecture # November 5 Scatterng of two dentcal partcle Relatvtc Quantum Mechanc: The Klen-Gordon equaton Interpretaton of the Klen-Gordon equaton The Drac equaton Drac repreentaton for the matrce α and
More informationNo! Yes! Only if reactions occur! Yes! Ideal Gas, change in temperature or pressure. Survey Results. Class 15. Is the following possible?
Survey Reult Chapter 5-6 (where we are gong) % of Student 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Hour Spent on ChE 273 1-2 3-4 5-6 7-8 9-10 11+ Hour/Week 2008 2009 2010 2011 2012 2013 2014 2015 2017 F17
More informationNote on the Electron EDM
Note on the Electron EDM W R Johnson October 25, 2002 Abstract Ths s a note on the setup of an electron EDM calculaton and Schff s Theorem 1 Basc Relatons The well-known relatvstc nteracton of the electron
More informationThe influence of Stern layer conductance on the. dielectrophoretic behaviour of latex nanospheres
The nfluence of Stern layer conductance on the delectrophoretc behavour of latex nanophere Mchael Pycraft Hughe* Bomedcal Engneerng Group, Unverty of Surrey, Guldford, GU2 7XH, UK Ncola Gavn Green Boelectronc
More informationTemperature. Chapter Heat Engine
Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the
More informationName: SID: Discussion Session:
Name: SID: Dscusson Sesson: Chemcal Engneerng Thermodynamcs 141 -- Fall 007 Thursday, November 15, 007 Mdterm II SOLUTIONS - 70 mnutes 110 Ponts Total Closed Book and Notes (0 ponts) 1. Evaluate whether
More informationNAME and Section No.
Chemstry 391 Fall 2007 Exam I KEY (Monday September 17) 1. (25 Ponts) ***Do 5 out of 6***(If 6 are done only the frst 5 wll be graded)*** a). Defne the terms: open system, closed system and solated system
More informationand Statistical Mechanics Material Properties
Statstcal Mechancs and Materal Propertes By Kuno TAKAHASHI Tokyo Insttute of Technology, Tokyo 15-855, JAPA Phone/Fax +81-3-5734-3915 takahak@de.ttech.ac.jp http://www.de.ttech.ac.jp/~kt-lab/ Only for
More informationIntroduction Statistical Thermodynamics. Monday, January 6, 14
Introduction Statistical Thermodynamics 1 Molecular Simulations Molecular dynamics: solve equations of motion Monte Carlo: importance sampling r 1 r 2 r n MD MC r 1 r 2 2 r n 2 3 3 4 4 Questions How can
More information4) It is a state function because enthalpy(h), entropy(s) and temperature (T) are state functions.
Chemical Thermodynamics S.Y.BSc. Concept of Gibb s free energy and Helmholtz free energy a) Gibb s free energy: 1) It was introduced by J.Willard Gibb s to account for the work of expansion due to volume
More informationV. Electrostatics. Lecture 25: Diffuse double layer structure
V. Electrostatcs Lecture 5: Dffuse double layer structure MIT Student Last tme we showed that whenever λ D L the electrolyte has a quas-neutral bulk (or outer ) regon at the geometrcal scale L, where there
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 informationHarmonic oscillator approximation
armonc ocllator approxmaton armonc ocllator approxmaton Euaton to be olved We are fndng a mnmum of the functon under the retrcton where W P, P,..., P, Q, Q,..., Q P, P,..., P, Q, Q,..., Q lnwgner functon
More informationIce crytal nucleaton, growth and breakage modellng n a craped urface heat exchanger H. Benkhelfa (a, M. Arellano (a,b G. Alvarez (b, D. Flck (a (a UMR n 45 AgroParTech/INRA, Ingénere-Procédé-Alment, 6
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 informationThe Second Law of Thermodynamics (Chapter 4)
The Second Law of Thermodynamics (Chapter 4) First Law: Energy of universe is constant: ΔE system = - ΔE surroundings Second Law: New variable, S, entropy. Changes in S, ΔS, tell us which processes made
More informationPhys 402: Raman Scattering. Spring Introduction: Brillouin and Raman spectroscopy. Raman scattering: how does it look like?
Phy 402: Raman Scatterng Sprng 2008 1 Introducton: Brlloun and Raman pectrocopy Inelatc lght catterng medated by the electronc polarzablty of the medum a materal or a molecule catter rradant lght from
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 informationChapter 5. Simple Mixtures Fall Semester Physical Chemistry 1 (CHM2201)
Chapter 5. Simple Mixtures 2011 Fall Semester Physical Chemistry 1 (CHM2201) Contents The thermodynamic description of mixtures 5.1 Partial molar quantities 5.2 The thermodynamic of Mixing 5.3 The chemical
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 informationOutline Review Example Problem 1. Thermodynamics. Review and Example Problems: Part-2. X Bai. SDSMT, Physics. Fall 2014
Review and Example Problems: Part- SDSMT, Physics Fall 014 1 Review Example Problem 1 Exponents of phase transformation : contents 1 Basic Concepts: Temperature, Work, Energy, Thermal systems, Ideal Gas,
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 informationESCI 341 Atmospheric Thermodynamics Lesson 12 The Energy Minimum Principle
ESCI 341 Atmospheric Thermodynamics Lesson 12 The Energy Minimum Principle References: Thermodynamics and an Introduction to Thermostatistics, Callen Physical Chemistry, Levine THE ENTROPY MAXIMUM PRINCIPLE
More informationPHY688, Statistical Mechanics
Department of Physcs & Astronomy 449 ESS Bldg. Stony Brook Unversty January 31, 2017 Nuclear Astrophyscs James.Lattmer@Stonybrook.edu Thermodynamcs Internal Energy Densty and Frst Law: ε = E V = Ts P +
More informationPY2101 Classical Mechanics Dr. Síle Nic Chormaic, Room 215 D Kane Bldg
PY2101 Classcal Mechancs Dr. Síle Nc Chormac, Room 215 D Kane Bldg s.ncchormac@ucc.e Lectures stll some ssues to resolve. Slots shared between PY2101 and PY2104. Hope to have t fnalsed by tomorrow. Mondays
More informationChapter 11. Supplemental Text Material. The method of steepest ascent can be derived as follows. Suppose that we have fit a firstorder
S-. The Method of Steepet cent Chapter. Supplemental Text Materal The method of teepet acent can be derved a follow. Suppoe that we have ft a frtorder model y = β + β x and we wh to ue th model to determne
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 informationChapter 2. Electrode/electrolyte interface: ----Structure and properties
Chapter 2 Electrode/electrolyte nterface: ----Structure and propertes Electrochemcal reactons are nterfacal reactons, the structure and propertes of electrode / electrolytc soluton nterface greatly nfluences
More informationRelaxation in water /spin ice models
Relaxaton n water /spn ce models Ivan A. Ryzhkn Insttute of Sold State Physcs of Russan Academy of Scences, Chernogolovka, Moscow Dstrct, 1443 Russa Outlne specfcty of approach quaspartcles Jaccard s theory
More informationEnvr 210, Chapter 3, Intermolecular forces and partitioning Free energies and equilibrium partitioning chemical potential fugacity activity coef.
Envr 20, Chapter 3, Intermolecular forces and parttonng Free energes and equlbrum parttonng chemcal potental fugacty actvty coef. phase transfer- actvty coef and fugactes more on free energes and equlbrum
More informationModule 1 : The equation of continuity. Lecture 1: Equation of Continuity
1 Module 1 : The equaton of contnuty Lecture 1: Equaton of Contnuty 2 Advanced Heat and Mass Transfer: Modules 1. THE EQUATION OF CONTINUITY : Lectures 1-6 () () () (v) (v) Overall Mass Balance Momentum
More informationESCI 341 Atmospheric Thermodynamics Lesson 13 Phase Changes Dr. DeCaria
ESCI 341 Atmopherc Thermodynamc Leon 13 Phae Change Dr. DeCara Reference: Thermodynamc and an Introducton to Thermotattc, Caen Phyca Chemtry, Lene GENERAL A phae change a change between od, qud, or apor
More informationLecture 3. Interaction of radiation with surfaces. Upcoming classes
Radaton transfer n envronmental scences Lecture 3. Interacton of radaton wth surfaces Upcomng classes When a ray of lght nteracts wth a surface several nteractons are possble: 1. It s absorbed. 2. It s
More informationPreliminary Examination - Day 2 August 16, 2013
UNL - Department of Physics and Astronomy Preliminary Examination - Day August 16, 13 This test covers the topics of Quantum Mechanics (Topic 1) and Thermodynamics and Statistical Mechanics (Topic ). Each
More informationThe ChemSep Book. Harry A. Kooijman Consultant. Ross Taylor Clarkson University, Potsdam, New York University of Twente, Enschede, The Netherlands
The ChemSep Book Harry A. Koojman Consultant Ross Taylor Clarkson Unversty, Potsdam, New York Unversty of Twente, Enschede, The Netherlands Lbr Books on Demand www.bod.de Copyrght c 2000 by H.A. Koojman
More informationThe Chemical Potential
CHEM 331 Physical Chemistry Fall 2017 The Chemical Potential Here we complete our pivot towards chemical thermodynamics with the introduction of the Chemical Potential ( ). This concept was first introduced
More informationSolutions to exercises week 45 FYS2160
Solution to exercie week 45 FYS2160 Kritian Bjørke, Knut Oddvar Høie Vadla November 29, 2017 Schroeder 5.23 a) Writing Φ = U T S µn in term of infiniteimal change of the quantitie involved: dφ = du T ds
More informationUniversity 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 informationNon-Ideality Through Fugacity and Activity
Non-Idealty Through Fugacty and Actvty S. Patel Deartment of Chemstry and Bochemstry, Unversty of Delaware, Newark, Delaware 19716, USA Corresondng author. E-mal: saatel@udel.edu 1 I. FUGACITY In ths dscusson,
More informationBrief introduction to groups and group theory
Brief introduction to groups and group theory In physics, we often can learn a lot about a system based on its symmetries, even when we do not know how to make a quantitative calculation Relevant in particle
More informationChapter 6 The Effect of the GPS Systematic Errors on Deformation Parameters
Chapter 6 The Effect of the GPS Sytematc Error on Deformaton Parameter 6.. General Beutler et al., (988) dd the frt comprehenve tudy on the GPS ytematc error. Baed on a geometrc approach and aumng a unform
More informationElectrochemistry Thermodynamics
CHEM 51 Analytcal Electrochemstry Chapter Oct 5, 016 Electrochemstry Thermodynamcs Bo Zhang Department of Chemstry Unversty of Washngton Seattle, WA 98195 Former SEAC presdent Andy Ewng sellng T-shrts
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 informationThe Gibbs Phase Rule F = 2 + C - P
The Gibbs Phase Rule The phase rule allows one to determine the number of degrees of freedom (F) or variance of a chemical system. This is useful for interpreting phase diagrams. F = 2 + C - P Where F
More informationOn the SO 2 Problem in Thermal Power Plants. 2.Two-steps chemical absorption modeling
Internatonal Journal of Engneerng Reearch ISSN:39-689)(onlne),347-53(prnt) Volume No4, Iue No, pp : 557-56 Oct 5 On the SO Problem n Thermal Power Plant Two-tep chemcal aborpton modelng hr Boyadjev, P
More informationOutline Review Example Problem 1 Example Problem 2. Thermodynamics. Review and Example Problems. X Bai. SDSMT, Physics. Fall 2013
Review and Example Problems SDSMT, Physics Fall 013 1 Review Example Problem 1 Exponents of phase transformation 3 Example Problem Application of Thermodynamic Identity : contents 1 Basic Concepts: Temperature,
More informationData Provided: A formula sheet and table of physical constants are attached to this paper.
Data Provided: A formula sheet and table of physical constants are attached to this paper. DEPARTMENT OF PHYSICS AND ASTRONOMY Spring Semester (2016-2017) From Thermodynamics to Atomic and Nuclear Physics
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationElectrochemical Equilibrium Electromotive Force
CHM465/865, 24-3, Lecture 5-7, 2 th Sep., 24 lectrochemcal qulbrum lectromotve Force Relaton between chemcal and electrc drvng forces lectrochemcal system at constant T and p: consder Gbbs free energy
More informationChapters 18 & 19: Themodynamics review. All macroscopic (i.e., human scale) quantities must ultimately be explained on the microscopic scale.
Chapters 18 & 19: Themodynamcs revew ll macroscopc (.e., human scale) quanttes must ultmately be explaned on the mcroscopc scale. Chapter 18: Thermodynamcs Thermodynamcs s the study o the thermal energy
More information