Topic 6&7 Entropy and the 2 nd & 3 rd Laws
|
|
- Meredith Griffin
- 6 years ago
- Views:
Transcription
1 pc 6&7 Entrpy and the 2 nd & rd Laws ntent & Objectves: hapters 6 and 7 cncern entrpy and ts calculatn n deal gas systems. hapter 6 dscusses the need fr a thermdynamc state functn capable f predctng the drectn f natural prcesses. he 2 nd Law ntrduces such a functn, the entrpy, whch prvdes a crtern fr spntanety and equlbrum n slated systems. We wll dscuss the mcrscpc bass fr entrpy (.e. the relatnshp t dsrder but the emphass n hapter 6 wll be n the thermdynamc cnsequences f the 2 nd Law, manly usng deal gases fr llustratn. he rd Law, whch establshes an abslute scale fr entrpy, s dscussed n hapter 7. ere we wll lk at the statstcal mechancal calculatn f abslute entrpes f deal gases n rder t better understand the nature f entrpy, as well as dscuss hw standard entrpes are btaned frm calrmetrc data. Readng: M&S hapters 5-6, Mathhapter E Other Surces: 2 nd Law: Rck h. 4; arrngtn h. 6 rd Law and Statstcal alculatns: Rck h. 6 & 14; Ptzer hapters 5-6 he Meanng f Entrpy: P. W. Atkns, he Secnd Law (Scentfc Amercan Lbrary, New Yrk, 1984 h. -4. Entrpy and he 2 nd Law Numerus expermental bservatns suggest a fundamental drectnalty t natural prcesses. strcally, these bservatns were summarzed n terms f restrctns n the peratn f heat engnes. w famus statements f the 2 nd Law can be paraphrased: lausus Statement (1850: N engne wrkng n a cycle can transfer energy frm a cld bdy t a ht bdy and have n ther effect. Planck-Kelvn Statement (1851: It s mpssble t cnstruct a devce whch perates n a cycle and has n ther effect than t prduce wrk by extractng heat frm a reservr at a sngle temperature. he mdern statement f the 2 nd Law f hermdynamcs we wll emply s here exsts an extensve state functn f a system, termed the entrpy, S, such that fr any change n thermdynamc state δq ds, where the equalty apples nly f the change s carred ut reversbly. Nte the mprtance f the cncept f reversblty n ths statement. Recall that a reversble (r quas-statc prcess s ne n whch the system evlves thrugh a successn f quasequlbrum states. be truly reversble a prcess must be carred ut nfntely slwly. All real prcesses are therefre rreversble t sme extent. 1
2 Fr any prcess ne can rewrte the lausus nequalty f the 2 nd Law as an equalty by ntrducng the dea f entrpy prductn δq ds = δ S prd + δs prd s the entrpy generated durng a prcess va the creatn and dsspatn f gradents n temperature r pressure, by frctnal effects, etc. In an (dealzed reversble prcess, wheren such effects are cmpletely elmnated, δqrev ds = Many real prcesses can be treated as beng reversble t a gd apprxmatn. In addtn, even f the prcess f nterest s nt reversble, t s ften useful t calculate the entrpy change between the endpnts f the prcess usng ths expressn fr sme reversble path. Interpretatns f Entrpy and Irreversblty he 1 st Law establshes the equalty f wrk and heat as frms f energy whereas the 2 nd Law recgnzes the dfferental utlty ( qualty f these energy frms. Mechancal wrk can be vewed as the cherent (rdered mtns f mlecules, whereas heat nvlves chatc (dsrdered mtn. he fundamental rreversblty f all natural prcesses ( tme s arrw stems frm the fact that change n the drectn rder dsrder s verwhelmngly mre prbable than s the reverse prcess. he physcal prncple behnd the 2 nd Law s that energy tends t dsperse bth spatally and n terms f ts cherence (Atkns. lausus (1865 succnctly summarzed the 1 st and 2 nd Laws n the statement: he energy f the unverse s cnstant; the entrpy tends tward a maxmum. he statstcal mechancal nterpretatn f entrpy n an slated system s: S( N,, U = k ln Ω( N,, U where Ω ( N,, U s the number f quantum states (each equally prbably cnsstent wth the macrscpc cnstrants f fxed N,, and U. Mre generally the entrpy can be expressed n any ensemble by: S = k p ln p General nsequences f the 2 nd Law In an slated system, δq=0 and the system entrpy prvdes a crtern fr spntanety and equlbrum: ds > 0 fr any spntaneus prcess n an slated system ds = 0 fr a slated system at equlbrum 2
3 .e. slated systems evlve twards a state f maxmal entrpy. Engnes, refrgeratrs, and heat pumps are devces that perate n a cyclc manner t effect transfrmatns between wrk and heat. Such devces are maxmally effcent when run reversbly. Fr reversble peratn, effcency s lmted slely by the tw temperatures between whch the devce perates. Smple analyss based n cmbned applcatn f the 1 st and 2 nd Laws t ne cycle f peratn f the devce rev rev U = w + q + ql = 0 (1 st rev rev q ql Law S = + = 0 (2 nd Law prvdes the theretcal maxmum effcences shwn n the fllwng schematc. L Effcences f hermdynamc evces = eat Engne surce q q L w w Effcency = q L L exhaust = Refrgeratr eat Pump Ar nd. ktchen huse utdrs q q L w q L w L L q w L q L w L L L ce bx utdrs huse Real devces have smaller effcences than these lmtng values and can nly apprach them when surces f entrpy prductn are mnmzed. Nte that these lmtng thermdynamc effcences are cmpletely ndependent f the partculars f the devces; they depend nly n the rat f the tw temperatures nvlved. Such effcences can therefre used t establsh the true thermdynamc scale f temperature.
4 he mbned 1 st and 2 nd Laws and Entrpy hanges Fr a reversble change n whch nly P wrk s perfrmed, δ w rev = Pd and the 1 st Law can be wrtten du = δ qrev Pd. Furthermre, fr a reversble prcess the 2 nd Law states that δ q rev = ds, s that a cmbnatn f the tw laws leads t: du = ds Pd hs equatn shfts attentn away frm the prcess rentatn f the 1 st and 2 nd Laws and places t n the state functns f a system n equlbrum. (he rev subscrpt s therefre rrelevant and mtted here. Usng ths relatn ne can easly determne hw entrpy changes wth,, and P: 1 U ds = d + P + d Of mst nterest nw are the relatns: S = ds = S P P 1 d + P = P dp whch allw ne t determne schrc r sbarc changes n S wth based n a knwledge f ( r P (. Entrpy hanges n Ideal Gases Fr an deal gas ( U / = ( / P = 0 s that fr any reversble prcess the abve equatns fr ds can be smplfed t: IG nr IG P nr ds = d + d ds = d dp P Fr a reversble sthermal expansn: S IG = nr ln( 2 / 1 = nr ln( P2 / P1 Fr a reversble adabatc expansn S = 0. (Any reversble adabatc expansn, whether f an deal gas r nt, s a cnstant entrpy r sentrpc prcess. If s ndependent f temperature (as fr a mnatmc deal gas ne has: S IG IG ( 2, 2 S ( 1, 1 = ln( 2 / 1 + nr ln( 2 / 1 IG IG S ( 2, P2 S ( 1, P1 = P ln( 2 / 1 nr ln( P2 / P1 Mxtures f deal gases prvde an mprtant reference fr thnkng abut mxtures f real substances. A result knwn as Gbbs therem states that the entrpy f a mxture f deal gases at a gven and sme ttal s the sum f the entrpes that each gas wuld have f t alne were t ccupy the ttal vlume. Usng ths result, the sthermal mxng f deal gases results n an entrpy f mxng mx S IG S ( mxture y S (pure = R y ln y 4
5 were y s the mle fractn f speces. he rd Law f hermdynamcs & Practcal Abslute Entrpes he rd Law f hermdynamcs serves t defne the zer f the entrpy scale. Several statements f ths law have been prpsed: Nernst (1906: Fr any sthermal prcess S 0 as 0. Nernst (1912: he abslute zer f temperature s unattanable. Planck (1912: he entrpy f a chemcally hmgeneus sld r lqud substance has the value zer at the abslute zer f temperature. We wll adpt the defntn ffered n the textbk: Every substance has a fnte pstve entrpy, but at zer Kelvn the entrpy may becme zer, and des s n the case f perfectly crystallne substances. hs last statement s n keepng wth the statstcal mechancal defntn f entrpy n terms f rder at 0 K systems n equlbrum shuld exst n ther lwest energy quantum states, whch shuld have a degeneracy (Ω f 1 (r at least f rder 1. Adptng the cnventn S=0 at =0 K defnes the scale f rd Law r practcal abslute entrpes. Gven ths cnventn the entrpy at any temperature can be determned frm an ntegratn f heat capacty data f the frm: P ( tr1 S ( = d tr1 trn P ( d hs expressn ncrprates ntegratns ver P ( n regns where a sngle phase exsts, as well as the dscntnuus changes that ccur at phase transtns tr S tr = tr he supercrpts n these expressns dente standard state cndtns (P = 1 bar and the standard state f the cmpund f nterest. he caveat practcal appled t the entrpes determned n ths manner s a remnder that tw surces f dsrder / entrpy are gnred n these rd -Law entrpes the entrpy asscated wth nuclear spns and the entrpy f stpc mxng. Snce nucle are cnserved n chemcal prcesses, t s nt necessary t accunt fr ether f these ptental surces f dsrder n thermchemcal calculatns (except perhaps n the case f 2. 5
6 Sme representatve P ( data and the resultng S ( data are pltted belw: 80 eat apacty f r 2 00 Entrpy f r 2 eat apacty P / (J ml -1 K fusn vaprzatn Entrpy S / (J ml -1 K fus S vap S emperature /K emperature /K ata taken frm M. W. hase, Jr., NIS-JANAF hermchemcal ables, 4 th Edtn (AS, AIP & NSRS, he dtted lnes at lw temperatures are smply guesses. Lw emperature eat apactes It s mprtant t understand the behavr f heat capactes as 0 because t s always necessary t extraplate avalable data t 0 n rder t calculate rd Law entrpes. he rd Law requrement that S 0 as 0 (r at least that S reman fnte mples that P 0 as 0 Statstcal mechancal mdels fr the behavr f slds at lw temperature prvde useful relatns fr the lmtng lw-temperature dependence f P (. Fr example, the ebye thery (1912 s an extensn f the Ensten mdel dscussed prevusly. It prvdes the crrect lmtng behavr f the heat capacty due t crystal lattce vbratns fr mst nncrystallne nnmetallc crystals. he predctns f the ebye mdel can be summarzed: ( = 9 R Θ Θ / 0 u 4 e u du u 2 ( e 1 where Θ s the ebye temperature, a characterstc f a gven sld, whch s usually treated as an emprcal cnstant. Examples f fts f expermental data t ths functnal frm are llustrated belw. 6
7 (frm K. S. Ptzer, hermdynamcs, rd Edtn (McGraw-ll, he lmtng behavr predcted by the ebye thery s: 4 12π / R 5Θ fr ( / Θ << 1 (and / R fr ( / Θ >> 1 Nte the scalng f by a sngle characterstc parameter Θ. hs scalng mples that ( / Θ s a unversal functn fr all slds that ft the ebye mdel. hs crrespndng states behavr s ndeed bserved fr mnatmc slds, but nt fr slds f mre cmplcated mlecules r ns. wever, the lmtng dependence as 0 s general. At lw enugh temperatures ther mechansms f energy strage may becme mprtant. One such mechansm s the electrnc heat capacty due t valence electrns n a metal. he cntrbutn f ths mechansm can be calculated usng an electrn gas mdel. he result s: 2 π = = ( el / R A n 2 F where n s the number f valence electrns and F s the Ferm temperature (ε F /k where ε F s the energy f the hghest ccuped state at 0 K; F ~10 4 K s typcal. he relatve magntudes f electrnc and lattce vbratnal heat capactes fr tw smple metals are tabulated belw: Electrnc eat apacty n ypcal Metals 2 K 0 K Sld F Abs (el ( el (el ( el /(10 4 K Acalc /(10-4 R ( tt /(10-4 R ( tt u Al ata frm Ptzer and N. W. Aschrft and N.. Mermn, Sld State Physcs (Suanders llege,
8 In lght f these tw mechansms, the lmtng lw-temperature behavr f crystals s usually: P a + b a S ( + b as 0 as 0 Fr nn-metals the 1 term s absent, and the entrpy s smply related t the bserved 1 heat capacty: S ( ( P as 0. rd -Law ntegratns therefre ften start 1 wth the value S = ( fr the lwest temperature measured. ( mn P mn Statstcal Mechancal alculatn f the Entrpes f Ideal Gases he machnery develped n hapters & 4 prvdes the means fr calculatng the entrpes f deal gases based n mlecular cnstants btaned frm spectrscpc measurements. Recall that the relatn between S, the ttal system parttn functn Q(N,,, and the N mlecular parttn functn q(, (where Q( N,, = q(, / N! can be wrtten: ln Q ln q S = k ln Q + k = Nk ln q k ln N! + Nk N, Usng Sterlng s apprxmatn, ln N! N ln N N, and chsng N=N A ths equatn becmes: q ln q S / R = 1+ ln + N A he mlecular parttn functn can be wrtten q(, = qtrans (, qrt ( qvb ( qel ( where the ndvdual peces were descrbed n pcs &4 : q trans 2πMk a (, = 2 h 2 / 2 = Λ q q rt rt 1 ( σ Θ rt 1/ 2 π ( σ Θ A rt Θ rt Θ rt 1/ 2 (lnear mlecules (nnlnear mlecules q vb ( vb e ( = (1 f fvb Θvb / 2 ( qh = ( Θvb / = 1 = 1 e As a result f ths factrzatn, the entrpy f an deal gas, just lke the energy, s a sum f translatnal, rtatnal, vbratnal, and electrnc cntrbutns: 8
9 Fr lnear mlecules: 5/ 2 N 5 S e e ln ln R = Θ N + + Λ A σθrt = 1 e and fr nnlnear mlecules: S R / vb Θ / ln(1 e vb + Θ vb / 1 1/ 2 5/ 2 1/ 2 / 2 N = e e ln ln + rt rt rt N + π Λ A A σ Θ Θ Θ 6 = 1 Θ e ln g / e1 vb Θ / ln(1 e vb + Θ vb / 1 ln g e1 Gas-phase entrpes calculated n ths way can be cmpared wth practcal abslute entrpes, derved frm ntegratn f calrmetrc data assumng S ( 0 K = 0. In mst cases the tw methds agree t wthn expermental uncertantes. Sme cmparsns are prvded belw. able 14-4 frm P. A. Rck, hemcal hermdynamcs (Unversty Press ks,
10 When actvatn barrers prevent cmplete relaxatn, frzen-n cnfguratnal entrpy can persst n the sld state dwn t 0 K. In such cases S ( 0 K 0 and as a result the entrpy deduced frm calrmetrc measurements at hgher temperatures s less than that btaned frm calculatns (r ther means. Mst nstances f frzen-n entrpy are fund n glassfrmng substances and n crystals f quas-symmetrc mlecules whch can adpt nearly equvalent rentatns n the sld state. Examples n the latter categry are als llustrated n part (b f the prevus tabulatn. Entrpes f Reactn r S he standard entrpy f reactn, r S (, s the entrpy asscated wth cmplete cnversn f reactants t prducts f a mlar quantty f the reactn (as wrtten. All speces are n pure frm at the standard pressure f 1 bar and at sme specfed temperature. entng a chemcal reactn by ν = 0, the standard entrpy f reactn can be A calculated frm practcal abslute entrpes va: r S ( = ν S ( Interpretng and Estmatng the Magntudes f S and r S Entrpy s a drect measure f the number f states avalable t a system va Ω = exp( S / R. A few generalzatns cncernng the magntude f S / R are: - he entrpes f slds cnfrmng t the ebye mdel can be estmated at temperatures greater than Θ frm the equatn: S / R ln( / Θ he entrpes f fusn f mnatmc slds are usually n the range f 1.0R t 1.7R. (Rare gases have values near 1.7R; mst metals have values nearer t 1.R. Lattces cmpsed f sngle ns behave as mnatmc slds wth entrpes f fusn n the range 1.2R 1.7R per n. Mlecular substances f smlar structure have apprxmately equal values f the sum f the entrpes f fusn and any sld-sld transtns that may exst. - he entrpes f vaprzatn at the blng temperature f a lqud and 1 bar pressure are clse t 10.5R fr mst nn-asscated substances. hs bservatn s knwn as rutn s rule (frmulated n he entrpes f smerc sets f mlecules can ften be ranked accrdng t the nature f the bndng present. Entrpy ncreases wth flexblty. yclc and branched structures tend t reduce the number f cnfguratns accessble t a mlecule and these bndng patterns therefre reduce the value f S / R. Snce the entrpes f gases are typcally much larger than the entrpes f cndensed phases under standard cndtns, the sgn and apprxmate magntude f reactn entrpes are ften determned by the change n the numbers f gas-phase speces n reactn. 10
_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 informationChapter 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 informationProblem 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 informationApproach: (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 informationThermodynamics 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 informationV. 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 informationPhysic 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 informationChapter 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 informationSIMULATION 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 informationLecture 12. Heat Exchangers. Heat Exchangers Chee 318 1
Lecture 2 Heat Exchangers Heat Exchangers Chee 38 Heat Exchangers A heat exchanger s used t exchange heat between tw fluds f dfferent temperatures whch are separated by a sld wall. Heat exchangers are
More information(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 informationChapter 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 informationPhys 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 informationA New Method for Solving Integer Linear. Programming Problems with Fuzzy Variables
Appled Mathematcal Scences, Vl. 4, 00, n. 0, 997-004 A New Methd fr Slvng Integer Lnear Prgrammng Prblems wth Fuzzy Varables P. Pandan and M. Jayalakshm Department f Mathematcs, Schl f Advanced Scences,
More informationCHAPTER 3 ANALYSIS OF KY BOOST CONVERTER
70 CHAPTER 3 ANALYSIS OF KY BOOST CONERTER 3.1 Intrductn The KY Bst Cnverter s a recent nventn made by K.I.Hwu et. al., (2007), (2009a), (2009b), (2009c), (2010) n the nn-slated DC DC cnverter segment,
More informationWater 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 informationChem 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 informationIntroduction to Electronic circuits.
Intrductn t Electrnc crcuts. Passve and Actve crcut elements. Capactrs, esstrs and Inductrs n AC crcuts. Vltage and current dvders. Vltage and current surces. Amplfers, and ther transfer characterstc.
More informationThermodynamics Partial Outline of Topics
Thermdynamics Partial Outline f Tpics I. The secnd law f thermdynamics addresses the issue f spntaneity and invlves a functin called entrpy (S): If a prcess is spntaneus, then Suniverse > 0 (2 nd Law!)
More informationFeedback Principle :-
Feedback Prncple : Feedback amplfer s that n whch a part f the utput f the basc amplfer s returned back t the nput termnal and mxed up wth the nternal nput sgnal. The sub netwrks f feedback amplfer are:
More informationTransient 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 informationCircuits Op-Amp. Interaction of Circuit Elements. Quick Check How does closing the switch affect V o and I o?
Crcuts Op-Amp ENGG1015 1 st Semester, 01 Interactn f Crcut Elements Crcut desgn s cmplcated by nteractns amng the elements. Addng an element changes vltages & currents thrughut crcut. Example: clsng a
More information4DVAR, according to the name, is a four-dimensional variational method.
4D-Varatnal Data Assmlatn (4D-Var) 4DVAR, accrdng t the name, s a fur-dmensnal varatnal methd. 4D-Var s actually a smple generalzatn f 3D-Var fr bservatns that are dstrbuted n tme. he equatns are the same,
More informationThermodynamics and Equilibrium
Thermdynamics and Equilibrium Thermdynamics Thermdynamics is the study f the relatinship between heat and ther frms f energy in a chemical r physical prcess. We intrduced the thermdynamic prperty f enthalpy,
More informationConservation of Energy
Cnservatn f Energy Equpment DataStud, ruler 2 meters lng, 6 n ruler, heavy duty bench clamp at crner f lab bench, 90 cm rd clamped vertcally t bench clamp, 2 duble clamps, 40 cm rd clamped hrzntally t
More informationPart One: Heat Changes and Thermochemistry. This aspect of Thermodynamics was dealt with in Chapter 6. (Review)
CHAPTER 18: THERMODYNAMICS AND EQUILIBRIUM Part One: Heat Changes and Thermchemistry This aspect f Thermdynamics was dealt with in Chapter 6. (Review) A. Statement f First Law. (Sectin 18.1) 1. U ttal
More informationelement k Using FEM to Solve Truss Problems
sng EM t Slve Truss Prblems A truss s an engneerng structure cmpsed straght members, a certan materal, that are tpcall pn-ned at ther ends. Such members are als called tw-rce members snce the can nl transmt
More information6. 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 informationCTN 2/23/16. EE 247B/ME 218: Introduction to MEMS Design Lecture 11m2: Mechanics of Materials. Copyright 2016 Regents of the University of California
Vlume Change fr a Unaxal Stress Istrpc lastcty n 3D Istrpc = same n all drectns The cmplete stress-stran relatns fr an strpc elastc Stresses actng n a dfferental vlume element sld n 3D: (.e., a generalzed
More informationCHEM Thermodynamics. Change in Gibbs Free Energy, G. Review. Gibbs Free Energy, G. Review
Review Accrding t the nd law f Thermdynamics, a prcess is spntaneus if S universe = S system + S surrundings > 0 Even thugh S system
More informationME2142/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 informationBME 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 informationChalcogenide Letters Vol. 11, No. 7, July 2014, p THE QUANTUM MECHANICAL STUDY OF CADMIUM SULFUR NANOPARTICLES IN BASIS OF STO s
Chalcgende Letters Vl. 11, N. 7, July 014, p. 35-364 THE QUNTUM MECHNICL STUDY OF CDMIUM SULFUR NNOPRTICLES IN BSIS OF STO s M.. RMZNOV *, F. G. PSHEV,. G. GSNOV,. MHRRMOV,. T. MHMOOD Baku State Unversty,
More informationPHYSICS 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 information15-69C 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 informationSection 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 informationA Note on the Linear Programming Sensitivity. Analysis of Specification Constraints. in Blending Problems
Aled Mathematcal Scences, Vl. 2, 2008, n. 5, 241-248 A Nte n the Lnear Prgrammng Senstvty Analyss f Secfcatn Cnstrants n Blendng Prblems Umt Anc Callway Schl f Busness and Accuntancy Wae Frest Unversty,
More informationWp/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 informationShell Stiffness for Diffe ent Modes
Engneerng Mem N 28 February 0 979 SUGGESTONS FOR THE DEFORMABLE SUBREFLECTOR Sebastan vn Herner Observatns wth the present expermental versn (Engneerng Dv nternal Reprt 09 July 978) have shwn that a defrmable
More informationLucas 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 information55:041 Electronic Circuits
55:04 Electrnc Crcuts Feedback & Stablty Sectns f Chapter 2. Kruger Feedback & Stablty Cnfguratn f Feedback mplfer S S S S fb Negate feedback S S S fb S S S S S β s the feedback transfer functn Implct
More informationConduction 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 informationChapter 5 rd Law of Thermodynamics
Entropy and the nd and 3 rd Chapter 5 rd Law o hermodynamcs homas Engel, hlp Red Objectves Introduce entropy. Derve the condtons or spontanety. Show how S vares wth the macroscopc varables,, and. Chapter
More informationALE 21. Gibbs Free Energy. At what temperature does the spontaneity of a reaction change?
Name Chem 163 Sectin: Team Number: ALE 21. Gibbs Free Energy (Reference: 20.3 Silberberg 5 th editin) At what temperature des the spntaneity f a reactin change? The Mdel: The Definitin f Free Energy S
More informationA Note on Equivalences in Measuring Returns to Scale
Internatnal Jurnal f Busness and Ecnmcs, 2013, Vl. 12, N. 1, 85-89 A Nte n Equvalences n Measurng Returns t Scale Valentn Zelenuk Schl f Ecnmcs and Centre fr Effcenc and Prductvt Analss, The Unverst f
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 informationEntropy, Free Energy, and Equilibrium
Nv. 26 Chapter 19 Chemical Thermdynamics Entrpy, Free Energy, and Equilibrium Nv. 26 Spntaneus Physical and Chemical Prcesses Thermdynamics: cncerned with the questin: can a reactin ccur? A waterfall runs
More informationDesign 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 informationSELECTION OF MODEL PARAMETERS OF BIOGAS IC ENGINE. Karol Cupiał, Grzegorz Katolik
TEKA Km. Mt. Energ. Rln., 2006, 6A, 32 38 SELECTION OF MODEL PARAMETERS OF BIOGAS IC ENGINE Karl Cupał, Grzegrz Katlk Insttute f Internal Cmbustn Engnes and Cntrl Engneerng Techncal Unversty f Częstchwa
More informationChapters 29 and 35 Thermochemistry and Chemical Thermodynamics
Chapters 9 and 35 Thermchemistry and Chemical Thermdynamics 1 Cpyright (c) 011 by Michael A. Janusa, PhD. All rights reserved. Thermchemistry Thermchemistry is the study f the energy effects that accmpany
More informationVan der Waals-coupled electronic states in incommensurate double-walled carbon nanotubes
Kahu Lu* 1, Chenha Jn* 1, Xapng Hng 1, Jhn Km 1, Alex Zettl 1,2, Enge Wang 3, Feng Wang 1,2 Van der Waals-cupled electrnc states n ncmmensurate duble-walled carbn nantubes S1. Smulated absrptn spectra
More informationEE 204 Lecture 25 More Examples on Power Factor and the Reactive Power
EE 204 Lecture 25 Mre Examples n Pwer Factr and the Reactve Pwer The pwer factr has been defned n the prevus lecture wth an example n pwer factr calculatn. We present tw mre examples n ths lecture. Example
More informationAnalytical 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 informationChem 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 information4.8 Degradation of Elastomers by Heat and/or Radiation
4.8 Degradatn f Elastmers by Heat and/r Radatn M.It Japan Atmc Energy Research Insttute, Nuclear Educatn Center 2-28-49, Hnkmagme, Bunkyu-ku Tky, 113, JAPAN Abstract Ths artcle studed sme prblems n the
More informationAP CHEMISTRY CHAPTER 6 NOTES THERMOCHEMISTRY
AP CHEMISTRY CHAPTER 6 NOTES THERMOCHEMISTRY Energy- the capacity t d wrk r t prduce heat 1 st Law f Thermdynamics: Law f Cnservatin f Energy- energy can be cnverted frm ne frm t anther but it can be neither
More informationLecture 4. Macrostates and Microstates (Ch. 2 )
Lecture 4. Macrostates and Mcrostates (Ch. ) The past three lectures: we have learned about thermal energy, how t s stored at the mcroscopc level, and how t can be transferred from one system to another.
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 information14 The Boole/Stone algebra of sets
14 The Ble/Stne algebra f sets 14.1. Lattces and Blean algebras. Gven a set A, the subsets f A admt the fllwng smple and famlar peratns n them: (ntersectn), (unn) and - (cmplementatn). If X, Y A, then
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 informationOn the concentration dependence of the surface tension of liquid metallic alloys Theoretical basis Hungary, Miskolc, Egyetemvaros.
On the cncentratn dependence the surace tensn lqud metallc allys heretcal bass 1 G.Kaptay, kmkap@gld.un-msklc.hu 2 Z.Papp zltanp@da.ed.ac.uk 1 Pressr at the Department Physcal Chemstry the Unversty Msklc
More informationPhys. 344 Ch 7 Lecture 8 Fri., April. 10 th,
Phys. 344 Ch 7 Lecture 8 Fri., April. 0 th, 009 Fri. 4/0 8. Ising Mdel f Ferrmagnets HW30 66, 74 Mn. 4/3 Review Sat. 4/8 3pm Exam 3 HW Mnday: Review fr est 3. See n-line practice test lecture-prep is t
More informationLearn more at
Tensn and Expansn Analyss f Ppe-n-Ppe Rsers: Part A, Theretcal rmulatn Kevn Chuanjan Man, Bn Yue, Adam Szucs, Rcky Theth 2H ffshre nc. Hustn, TX, USA ABSTRACT Ths paper prvdes a mathematcal mdel fr accurate
More informationChemistry 20 Lesson 11 Electronegativity, Polarity and Shapes
Chemistry 20 Lessn 11 Electrnegativity, Plarity and Shapes In ur previus wrk we learned why atms frm cvalent bnds and hw t draw the resulting rganizatin f atms. In this lessn we will learn (a) hw the cmbinatin
More informationWYSE 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 informationAdvances in Engineering Research (AER), volume 102 Second International Conference on Mechanics, Materials and Structural Engineering (ICMMSE 2017)
Secnd Internatnal Cnference n Mechancs, Materals and Structural Engneerng (ICMMSE 2017) Materal Selectn and Analyss f Ol Flm Pressure fr the Flatng Rng Bearng f Turbcharger Lqang PENG1, 2, a*, Hupng ZHENG2,
More informationBig Data Analytics! Special Topics for Computer Science CSE CSE Mar 31
Bg Data Analytcs! Specal Tpcs fr Cmputer Scence CSE 4095-001 CSE 5095-005! Mar 31 Fe Wang Asscate Prfessr Department f Cmputer Scence and Engneerng fe_wang@ucnn.edu Intrductn t Deep Learnng Perceptrn In
More informationA brief overview of the principles of thermobarometry Cin-Ty Lee (2009)
A bref vervew f the prncples f thermbarmetry Cn-y Lee (2009) Hmgeneus tem Fr a ne phase tem (hmgeneus tem) characterzed by a fxed cmpstn, the state varable knwn as Gbbs Free energy G s defned as fllws:
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 informationLecture 17: Free Energy of Multi-phase Solutions at Equilibrium
Lecture 17: 11.07.05 Free Energy f Multi-phase Slutins at Equilibrium Tday: LAST TIME...2 FREE ENERGY DIAGRAMS OF MULTI-PHASE SOLUTIONS 1...3 The cmmn tangent cnstructin and the lever rule...3 Practical
More informationSection 10 Regression with Stochastic Regressors
Sectn 10 Regressn wth Stchastc Regressrs Meanng f randm regressrs Untl nw, we have assumed (aganst all reasn) that the values f x have been cntrlled by the expermenter. Ecnmsts almst never actually cntrl
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 informationRegression with Stochastic Regressors
Sectn 9 Regressn wth Stchastc Regressrs Meanng f randm regressrs Untl nw, we have assumed (aganst all reasn) that the values f x have been cntrlled by the expermenter. Ecnmsts almst never actually cntrl
More informationLecture 23: Lattice Models of Materials; Modeling Polymer Solutions
Lecture 23: 12.05.05 Lattice Mdels f Materials; Mdeling Plymer Slutins Tday: LAST TIME...2 The Bltzmann Factr and Partitin Functin: systems at cnstant temperature...2 A better mdel: The Debye slid...3
More information3-1 Introduction: 3-2 Spontaneous (Natural) Process:
- Introducton: * Reversble & Irreversble processes * Degree of rreversblty * Entropy S a state functon * Reversble heat engne Carnot cycle (Engne) * Crteron for Eulbrum SU,=Smax - Spontaneous (Natural)
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationWork and Heat Definitions
Wrk and eat Deinitins FL- Surrundings: Everything utside system + q -q + System: he part S the rld e are bserving. Wrk, : transer energy as a result unbalanced rces - eat, q: transer energy resulting rm
More informationChapter 17 Free Energy and Thermodynamics
Chemistry: A Mlecular Apprach, 1 st Ed. Nivald Tr Chapter 17 Free Energy and Thermdynamics Ry Kennedy Massachusetts Bay Cmmunity Cllege Wellesley Hills, MA 2008, Prentice Hall First Law f Thermdynamics
More informationCHAPTER 3: FEEDBACK. Dr. Wan Mahani Hafizah binti Wan Mahmud
CHPTER 3: FEEDBCK Dr. Wan Mahan Hafzah bnt Wan Mahmud Feedback ntrductn Types f Feedback dvantages, Characterstcs and effect f Negatve Feedback mplfers Crcuts wth negatve feedback Pstve feedback and Oscllatr
More informationFinal 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 informationLinear Plus Linear Fractional Capacitated Transportation Problem with Restricted Flow
Amercan urnal f Operatns Research,,, 58-588 Publshed Onlne Nvember (http://www.scrp.rg/urnal/ar) http://dx.d.rg/.46/ar..655 Lnear Plus Lnear Fractnal Capactated Transprtatn Prblem wth Restrcted Flw Kavta
More informationCHM112 Lab Graphing with Excel Grading Rubric
Name CHM112 Lab Graphing with Excel Grading Rubric Criteria Pints pssible Pints earned Graphs crrectly pltted and adhere t all guidelines (including descriptive title, prperly frmatted axes, trendline
More informationExperiment #3. Graphing with Excel
Experiment #3. Graphing with Excel Study the "Graphing with Excel" instructins that have been prvided. Additinal help with learning t use Excel can be fund n several web sites, including http://www.ncsu.edu/labwrite/res/gt/gt-
More informationChE 471: LECTURE 4 Fall 2003
ChE 47: LECTURE 4 Fall 003 IDEL RECTORS One f the key gals f chemical reactin engineering is t quantify the relatinship between prductin rate, reactr size, reactin kinetics and selected perating cnditins.
More informationExploiting 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 informationEnergy & Work
rk Dne by a Cntant Frce 6.-6.4 Energy & rk F N m jule () J rk Dne by a Cntant Frce Example Pullng a Sutcae-n-heel Fnd the wrk dne the rce 45.0-N, the angle 50.0 degree, and the dplacement 75.0 m. 3 ( F
More informationMore 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 informationNomenclature: number of electrons e -1. electron charge F constant number, (columbs/moles of e -1 ) atomic number g
Quanttatve Analyss f Irreversbltes Causes Vltage Drp n Fuel cell (Smulatn) Hssen Ghadaman*, Dr. Yadlah Sabh** Department f Energy Engneerng, Scence and Research Branch Azad Unversty, Islamc Republc f IRAN
More informationMatter Content from State Frameworks and Other State Documents
Atms and Mlecules Mlecules are made f smaller entities (atms) which are bnded tgether. Therefre mlecules are divisible. Miscnceptin: Element and atm are synnyms. Prper cnceptin: Elements are atms with
More informationGeneral Chemistry II, Unit I: Study Guide (part I)
1 General Chemistry II, Unit I: Study Guide (part I) CDS Chapter 14: Physical Prperties f Gases Observatin 1: Pressure- Vlume Measurements n Gases The spring f air is measured as pressure, defined as the
More informationChapter 9: Quantization of Light
Chapter 9: Quantizatin Light 9.1 Planck s Quantum Thery 9.1.1 Distinguish between Planck s quantum thery and classical thery energy The undatin the Planck s quantum thery is a thery black bdy radiatin.
More information/ / Chemistry. Chapter 1 Chemical Foundations
Name Chapter 1 Chemical Fundatins Advanced Chemistry / / Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne
More informationAn Extended Regular Solution Model with Local Volume Fraction
() An Etended Regular Slutn Mdel wth cal Vlume Fractn Shgetsh KOBUCHI, Ken ISHIGE (Department f Enrnmental Scence and Engneerng, Graduate Schl f Scence and Engneerng, Yamaguch Unersty) Setsuk YONEZAWA
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
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 informationChapter 8 Predicting Molecular Geometries
Chapter 8 Predicting Mlecular Gemetries 8-1 Mlecular shape The Lewis diagram we learned t make in the last chapter are a way t find bnds between atms and lne pais f electrns n atms, but are nt intended
More informationlecture 5: Nucleophilic Substitution Reactions
lecture 5: Nuclephilic Substitutin Reactins Substitutin unimlecular (SN1): substitutin nuclephilic, unimlecular. It is first rder. The rate is dependent upn ne mlecule, that is the substrate, t frm the
More informationA) 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 informationLecture 7: Boltzmann distribution & Thermodynamics of mixing
Prof. Tbbtt Lecture 7 etworks & Gels Lecture 7: Boltzmann dstrbuton & Thermodynamcs of mxng 1 Suggested readng Prof. Mark W. Tbbtt ETH Zürch 13 März 018 Molecular Drvng Forces Dll and Bromberg: Chapters
More informationThermodynamic Considerations for Thermal Water Splitting Processes and High Temperature Electrolysis
INL/CON-8-4376 PEPINT Thermdynamc Cnsderatns fr Thermal Water Splttng Prcesses and gh Temperature Electrlyss IMECE 8 J. E. O Bren Nvember 8 Ths s a preprnt f a paper ntended fr publcatn n a jurnal r prceedngs.
More information