3-1 Introduction: 3-2 Spontaneous (Natural) Process:

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1 - 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) Process: * Eulbrum state: rest state Noneulbrum state: spontaneous change to eulbrum * Spontaneous process s rreversble case : mxng of two gases case : contact of two bodes at dfferent temperature * Isolated system: no mass and energy transfer wth surroundng.e. constant U,, m Closed system: no mass transfer, but energy transfer exsts constant m Open system: both mass and energy transfer Introducton to the hermodynamcs of Materals

2 Entropy and Degree of Irreversblty: () converson of work to heat () heat flow down a temperature gradent processes: (), W(weght fall), (heat produced) () (heat flow), (), W(weght fall), (heat produced) [()+() ()] process () s more rreversble than () compare process (): process (): > () < () we call S and S = S s a measure of degree of rreversblty Introducton to the hermodynamcs of Materals

3 Reversble Processes: * Irreversblty s zero and no degradaton * he process path passes through a contnuum of eulbrum states * It s an magnary path * Each step s under an nfntesmally small drvng force Example of Reversble & Irreversble Process: Evaporaton and Condensaton of water * Frctonless pston Heat reservor at Eulbrum: PHO() = Pext Introducton to the hermodynamcs of Materals

4 Process : sudden fnte change of P () decrease pressure: (Pext- P) spontaneous evaporaton heat absorbed, (w ) assume: mole HO evaporated molar volume of HO vapor work done by system: W=(Pext- P) () ncrease pressure: (Pext- P)+ P spontaneous condensaton exothermc (w ) work done on system: W=-Pext. ()+() permanent change n external agency: ( P.) Process : nfntesmal change of pressure δp 0 (Pext+δp) Pext then (δp.) 0 W=(Pext-δp)~Pext W=-(Pext+δp)~-Pext no permanent change! If the process s nfntely slow, then a complete reversblty s approached Introducton to the hermodynamcs of Materals

5 Entropy and Reversble Heat:. Evaporaton Only: work done by system for rreversble process: W=(Pext- P) work done by system for reversble process: Wrev=Wmax=Pext. U ndep. of path Urev=rev-Wmax (Rev) Urrev=-W (Irrev) deg (degraded heat) (rev-)=(wmax-w)>0 Less heat s transferred to cylnder from reservor durng rreversble process * Reversble process: S reservor=- rev S cylnder= rev = S reservor + S cylnder=0 Stot * Irreversble process: Sreservor=- Scylnder= + deg = + rev = rev Stot= deg = rev = Srr>0 (entropy produced) Scylnder= + S rr = S trans. + S produced and ( S cylnder) rev=( S cylnder) rr Introducton to the hermodynamcs of Materals

6 . Condensaton only: work done on system for rreversble process: W=(Pext+ P) work done on system for reversble process: Wrev=Wmn= Pext. deg=(w-wmn)= -(rev-) >0 * Reversble condensaton: Sreservor= rev Scylnder=- rev Stot=0 * Irreversble condensaton: Sreservor= Scylnder=- + deg =- rev Stot= deg = Srr >0 (entropy produced) Scylnder= S trans+ S produced ( S cylnder) rev=( S cylnder) rr state state (cylnder only) rev = S=S-S= Srr = Strans for reversble process: Srr ( Sproduced)=0 + Sproduced Introducton to the hermodynamcs of Materals

7 Summary. Entropy of an solated system ncreases, whch system undergoes an rreversble process. Stot>0. Entropy s not created ( Sp=0) for a reversble process. Stot=0, Ssys=- Ssurroundng (Entropy transferred from one part to another). Entropy s a state functon. ( Scylnder)rev=( Scylnder)rr (system: cylnder) Reversble Isothermal Compresson of one mole deal gases (, ) (, ) < d=0, U=0, =W W P R ln W<0, work done ON system Reversble dabatc Expanson of deal gas (P, ) Rev (P, ) P>P (Expanson) dabatc: =0 (Reversble + dabatc): P γ =const =0 Eual Entropy (Isentropc) (P, ) Irrev (P, ) > ( Heat produced by degradaton after rreversble adabatc expanson remans n gas) More rreversble and U Introducton to the hermodynamcs of Materals

8 Propertes of Heat Engnes work done η (Effcency) = heat nput * For a Carnot cycle process: two rev. sothermal two rev. adabatc any thermodynamc substance w Carnot Engne s an deal engne whch has the maxmum effcency W=W+W-W-W4=(area CD) Introducton to the hermodynamcs of Materals

9 =- One cycle, U=0, W== - ηc=effcency= w = (η >η) Greater effcency could be obtaned by two methods () =, f w >w(η >η).e. ( - ) >(- ) < () w =w f < - = - then < consder two engnes combned together: () take = w = - = - -w=-+ f w -w= (- )>0 work (w -w) >0 s obtaned from (- ) heat only from one reservor mpossble!! Prelmnary statement of nd law: homsen prncple: t s mpossble, by a cyclc process, to take heat from heat from a reservor and convert t to work, wthout transferrng heat to another cold reservor Introducton to the hermodynamcs of Materals

10 () engne w = - engne -w=-+ ake w =w - = +- f (- )= (- )=>0 heat = s transferred from (low t) to (heght t) mpossble!! Clausus prncple: It s mpossble to transfer heat from a cold to a hot reservor wthout convertng a certan work to heat hermodynamc emperature Scale * ll reversble Carnot cycles operatng between the same upper and lower temperature must have the same (maxmum) effcency, t s ndependent of workng substance and s c f '( t, t ) a functon only of temperatures t,t f ( t, t )? * consder two Carnot cycles (t,t)+(t,t)=(t,t) f ( t, t ) f ( t, t) f ( t, t) f ( t f ( t, t, t ) ) f ( t, t ) f(t,t) ndep. of t f(t,t)=f(t)/f(t) f(t,t)=f(t)/f(t) Introducton to the hermodynamcs of Materals

11 F( t) F( t ) Kelvn: the smplest functon!! Defne: F(t), F(t) and c low temp() has a lmtng value absolute! not relatve zero temperature of cold reservor =0, s η=00% Kelvn emperature scale Ideal gas temperature scale proof: one mole deal gas, Carnot cycle (), Reversble, sothermal expanson at U=0, w R ln () C, Rev. ada. Expanson ( =0, w U Cvd Cv ) ()C D, Rev. soth. Comp. at U=0, w R ln D C (4)D, Rev. ada. Comp. 4 ( =0, w U Cvd Cv ) otal work w w w w w 4 R ln R ln D C (),() P=P, PCC=PDD (),(4) P γ =PCC γ, PDD γ =P γ C w R D C ln R ln R( ) ln D Introducton to the hermodynamcs of Materals

12 Introducton to the hermodynamcs of Materals ln )ln ( R R w c nd Law of hermodynamcs c.e. 0 * ny cycle be broken down nto many Carnot cycles 0 0 cyclc ntegral 令 ds rev 0 ds rev For loop : 0 ) ( ) ( 0 S S S S ds ds ds nd Law of hermodynamcs: () Entropy functon: S ds rev rev S S S () Entropy of an solated system: 0 S SU, 0 Eulbrum process: SU,=0 Non-eulbrum process: SU,>0 Entropy s ncreased!! or ds 0

13 Maxmum Work for reversble process state state U-U=-W * and W can vary dependng on path (degree of rreversblty) ds system t ds rr st law du sys t W t du sys w ds sys w ds du sys w ds sys du sys ds rr rr dsrr>o w ds sys du ) ( sys w S S ) ( U U ) (.e. Wmax=(S-S)-(U-U) and dsrr=0 Reversble process (path) has maxmum work.# If heat s absorbed (transferred) durng a process rev> (rreversble) See example (Ex): Introducton to the hermodynamcs of Materals

14 Crteron for Eulbrum * spontaneous change state (non-eul.) Irrev. State (eul.) of an solated system Stot=(S-S)>0, S>S entropy S reachng eul. t eulbrum SU,=Smax * Consder a chemcal reaton: + = C+D Isolated system: constant When SU, = Smax Eul. State has a fxed composton mass (M) Internal energy (U) olume () (ds)u, 0 >0, non-eul. = 0, eul. Introducton to the hermodynamcs of Materals

15 Combned statement of st and nd Laws. st law: du=δ-δw nd law: ds rev for reversble mechancal work δwrev=p du=ds-p pplcaton restrctons: ()Reversble ()closed system (const. composton & mass) ()mechancal work only In general reversble: du=ds-p-δw + dn. U=U(S,) U du S v U ds s U U, P S v s. S=S(U,) S S ds du U P ds du S U v P 4. du=ds-p (ds)u, 0 mples (du)s, 0 for a constant S, system: at eul. US,=Umn * du=ds-p-δw du P ds δw dsu, 0, δw 0 dus,=- δw 0 U Introducton to the hermodynamcs of Materals

16 dus, and at eul. US,=Umn δw can be chemcal work or electrc work w' dn U n nj, S, dn Ex: (p. 56) compare S, W,, for one mole deal gas () Reversble, sothermal expanson, (<) () Free expanson (adabatc + constant ) Sol: () d=0, U=0 rev wrev P R ln >0 吸熱 S rev R ln () Free expanson, d=0, =W=0 (no work done) Entropy s a state functon, rev Srr( free.expasojn) Srev S S ds du P P R S rr R ln R a.e. no heat absored, and no work done c.p. (),() Wrev-Wfree expanson= Wrev= rev Free expanson s the lmt of rreversblty at whch all potental work s degraded to heat and create entropy. ds Introducton to the hermodynamcs of Materals

17 Ex: 5 moles deal gas, Cv=.5R, γ= 5, adabatc expanson (P=50 atm P=0 atm, =00 K) =? () Reversble process, =? () Irreversble: W=4000J, =? =?, =?, S()rr=? Sol: nr (). 46 lters P (Rev. + da.) P γ =P γ P lters P P 58 K nr note: =0, U n Cvd ncv ( ) 5 R(58 00) 8854 J W=- U= J ds du P du nr S nc v d nr nc v ln nr ln R S 5 ln 5 R ln 0.05R 0. ( J / K) Reversble dabatc S=0 () (Irrev. + da), =0 U=-W=-4000 J U n =6 K C d nc nr P v v lters R ( ) 5 ( 00) 4000 = Srr state state Srev Introducton to the hermodynamcs of Materals

18 Rev: ds du P du S rev ncv d nr nr nc v d nr nc v ln nr ln Srr R ln 5 R ln ( J / K) = Srev=4 (J/K) S() S() Introducton to the hermodynamcs of Materals