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HelmholtzandGibbsEnergiesChapt22 6 10Tues Officehours 24 I FreeEnergy AHelmholtzFreeEnergy Define A U TS

recallduTdsPdVG 224

dA dU Tds SdT TdS PDVTds Sdt dA Pdu Sdt 2 22 17

also dAdUTds sdTdqPedVTds Sdt G before 2217 at const TV da v dq Tds 4 eq.ro astchaptifTdSZdq Spontaneous

if r.h.si Loro Spontaneous

DAIMIO 5 22.53 B GibbsFreeEnergy G U Tst PV H TS 6 522.117

dGdUTdsSdTtPdVtVdP a sdTtVdP

at const Pex T

dG tp dqTds 8

Gpp 0 note CDGqp O inipliesequilibrium

C Work andFreeEnergy DA dqTdStdw SDT

lo

ifreversible defTds0 dw maximum

at const T reversible

A f dwma OA Wmax workdonebysystem g E 22.9J

ThusArbeit isappropriate

ifotherkindsofworkhappen

dW dw PexdV il otherwork

then dG dqtdw DexdVtPdVtVdPTds Sdt 44

at const TP reversible

G tp dw ma B 122.16

D MoreonA G

AGf DbrAAF Ar etc Formation traction

worklikethoseforH

II SomeUsefulRelationships

ABasic Definitions know H U CPVj A U TSjG UTStPV

HUtPV HTS

B BasicDifferentials Know 1derive

Liable22.5ft dU Tds PdVjdH TdStVdp dA Sdt PdVj dG SdTtVdP

AsideExamla Bayof TBH

3H 7 Hfc4001 141298tfcpdT GSH Tablewillcanbeusedinall exams

C MaxwellRelationships ingeneral df gdXthdY secondderivative foranexactdifferential fy f y g fg yandh f x

ConsiderGCT dG I pdTtIE dP CH

Iftp S y 2246,2247

nowtake2ndDer

Getafe.ITtsDt EfEeHp fEtv 457P so ftp.t IpjfEvHIIhEFlsEElpjlIIhs

ffIsh Eblen.D

DWorkingEquations 1 NIV du43 rdTt dV lb

I Hr Cr Tt

Hath ff f ktCf CH ray Maxwell nd4 T LITv P 122.223

du GdTtLTC h P dV 181 EquationofStateforU

foridealgas P nR SoITT_OCidgas fatter22.227

for vdg file nffnb aft µdw aunt

2 Http dH f vdTt f tdVCdoasexercise Or wecando

seehandou BDCI pdTtLIpHdP 19 Cp 20

ftppdHTdStudPtaa9apTffp

ttVdHCpdTtLV II pTdP Cay KIIT a 3 Entropy SCTV

dS f dTtCffhdV 122 reminderdU TdS PdV duv TdS C dT so F f IST tf v 23 122443 sodS dTt hdV 441

EDT t E ki dVExercise d Hf p Hi ICENT

ExerciseshowdSCTP dT Fpdp 125

III MoreGibbsEnergy AGeneral GUTstPV dG sdTtVdP IfsfV p SGD e.g G f IpetdP SHIP en'ted fdP VDP

BTempVariations GU TAPE HTS

ft p S G 1271

recall fifth 5 so

ftp.E fzftff p tfLTIEIp HIT

qf f GtHI p tEEHpEI tf

1 Gibbs Helmholtz 281 22.603

Plot DHT vs IT also 2gqqf OH Go slopeOH integrating

oGf dE OH Hz fi 137t oftenconst oversmall1changes

C PressureVariations for UFO DG p Vdp 1 Incompressiblespecies Of VAP 31 22 57

2 Gases DG G G nRTlnP4p 34

Suppose P was 1bar GE GE G0tnRTnP4p0 SB 1g

Supposegasisnonideal

Gz G tnRTlmfp0 34 22.687forfugacity where f fugacity effectivepressure in termsof afugacitycoefficient 10

f p E5 22.737 Consider realand idealgases

yal ideas GmGin

p fPVmdP RThe plsVmddP RThrMp

whereP istheactualpressure and P issome referencepressure

dothis subtract

subtmtoipiSPCVmVm.idJdP RT ffi lnPpD RTlnfj.I.l'D ifwechoose P O f p but tryofVm VmiddP

gg

ln9 Y dP Where theRtp jVmµ Rpt 2 PIT lowTlowP fcp CO2 highThighPgf P fY

oe 4 ig

I 500C P

II Deformation of solids A Basicconcepts

I WorkandForce simpleuniaxialdeformation W214dL 39

manysolidsobeyHooke'sLaw f k L Lo 140 ke forceconstant

then W tzkGLLok 141

forcecoast k 42

2 StressStrain Modulus stress 0 fA 5 9 break

strain C O

qLo stress yeildModulus E CEtrain

So WSfdE o0dE xk Vo de 143 Volume

Assumesnovolumechange Getstrickybecause ifvolume doeschange it can takealot ofenergy

B ReversibleExtension dU dqtdw TdS PdVtfdL and dA Sdt PdVtfdL 44

then fYIHv.EC v.r TGHu.tl44a Theforcehastwo components at V const

InternalEnergyandEntropy Maxwell CIEu.EC i ycC45

asidedA r SdTtfdLthenfPFhyttTfIftvL 149 pT T metal jogging polymerssomeglasses Bmg Eagan.mgr oooo Somnath rppmmceramic µ Bisons

mooeoutofLattice y Mumsposition incU chainststraighten

C Calculations decreasesentropy

1 Rubberbandstretchesquickly hot radibatic retraction cools

CIII tEsH I anycorrectnotes T ECLICV heatcapacity at constant length

Y0 differentthanCu

CITIs E Ht 48 since 4T because 0T was positivewithstretching

2 hangrubber hand w weight heat it T.FI tCIfIE LFHIFhE EfIthne.aafie 49

fotherobberbandshouldgetshorter

I Mixtures A Chemical Potential

Consider G TPni na nx dG ftp.n.na Tt IFHnndPtlInfhpn.dn

define14 HIMp.niQ.dk ED Mi Yeni n no 154

Suppose onestarted at Zeromaterial at constantTandP hi

o5dG SEMidniO or G hiMi 152

whereforasinglecoment MA a

dtfff.am GamC5ia

forasinglecomponent MA isthemolarGibbsfreeEnergy Supposespecies iexists intwoplaces then for thespontaneoustransfer

of dni fromAtoB t fa thenDG Headni t HBdNico

1537

ooo MiB A A Bso

B Mixtures 7 wrongsignoriginallyCorrect

GCTP GED tRTln4pctGD

for amixtureofAinequil withapuresubstance

Maa.LTpj ffotRTlnppo ff.tn rec34

i7 ifDalton'sLawholds Pa XaP

i.e ArtHz

soffmiffTEMEtRTln HEtRTlnPptRTlnXa 154

ManTT4aPwetRTenXA El

C MixingofIdealGases DGmix naMa tRTlnXa tMB MB4RTlnXB

NathanNBMIM naRTlnXAtnBRTlnXB DtotalRTXalnXatXBlnXB 155

genera NwaRTEXilnXi i

for Osp f p Dsm NRExilnxi 156 20329 on i is1