Chemistry 163B Winter 2014 notes for ΔS UNIVERSE and Thermodynamic Tools

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1 notes for ΔS UNIERSE and hermodnamic ools goals Chemistr 163B DS of the UNIERSE and Deriving hermodnamic Relationships 1. ΔS universe > 0 2. Mawell-Euler Relationships 3. ΔS Φ = ΔH Φ / Φ (Φ is phase transtion) Challenged enmanship Notes nd Law of hermodnamics in terms of entrop S universe 0 S is a SAE FUNCION rev S rev irrev irrev toda soon : S S 0 S tem oundings universe disorder increases 3 4 the entrop of the UNIERSE increases towards a universal EA SOU ds Stem S Stem S? Stem S 0 S tem + S oundings = S?? = S UNIERSE UNIERSE lotkin's Entrop S > 0 Clark s Entrop # 2 Acrlic EA SOU 6 1

2 notes for ΔS UNIERSE and hermodnamic ools BU ALAS: S tem < 0 (order) if S oundigns > 0 (disorder) Raff s Samm et 0 nr(300 K) int 20L AC nr(300 K) int 40L w=0 q=0 ΔU=0 Δ=0 oor Sam? Smart Leigh S oundings > 0 S tem < 0 7 ΔS=R ln 2 (isothermal reversible) 8 trepanation, the mind and the brain. reveris, 1525, England trepanation and the second law REERSIBLE Oouch, di q S= should have been oor Chem163B a music major!! student thought I ll fi that! S= S= REERSIBLE H. Bosch, 1480, Dutch eru, ~ 1000AD, pre-incan remember same initial and final states of tem: S Sreversible S final reversible S initial irreversible final initial so how will reversible and irreversible processes between same initial and final states of tem differ??? Stem Soundings S universe 0 ( = for reversible, > for irreversible) S oundings will differ 11 tools for evaluating thermodnamic relationships: starting relationships definitions: U ª internal energ H ª U + A ª U S G ª H S relationships from 1 st and 2 nd Laws: [no change of material (dn i =0) and, onl work (dw other =0)] nc d nc d du dw d rev ds ds 12 2

3 notes for ΔS UNIERSE and hermodnamic ools differential relationships eample of Mawell-Euler ( dg=-s d + d ) U ª internal energ H ª U + A ª U S G ª H S du dw d rev ds ds du ds d U( S, ) ds dh du d d dh ds d H( S, ) ds d da du ds Sd da Sd d A(, ) ds d d dg dh ds Sd dg Sd d G(, ) so: what about: thus: dg S d d G (, ): G G dg d d G G S and G = G S 1 st and 2 nd Laws math, total differential Mawell-Euler Relationship from dg Euler-Mawell relationships (handout #4 Math Comments) Euler-Mawell relationships du ds d S S d, d d d, M d N d M N 15 dh ds d dasd d dgsd d S S S S S S 16 entrop variations with and finite changes from derivatives: isothermal volume change S C S C S S 17 S S ds(, ) d d isothermal d 0 S ds d d S S 12, const ds d d nr S 1 d nr general for no work other; no change of composition S ds d for ideal gas : nr 2 ln 1 [ note: same as S qrev, q for isothermal volume change] rev

4 notes for ΔS UNIERSE and hermodnamic ools calculating entrop (see summar on review handout) S for equilibrium phase transition for phase transition at equilibrium conditions (e.g.) H 2 O() H 2 O (g, 1atm, 373K) or H 2 O() H 2 O (s, 1atm, 273K) H qreversible S H HW6 #35 S for H 2 O() ö H 2 O (s, 1atm, 263K) hermodnamics and Black Holes (and other cosmolog?) End of Lecture hermodnamics and Black Holes (and other cosmolog?) ΔS universe < 0???? tem with entrop S falls into black hole (r < r s ) hermodnamics of Black Holes Eric Monkman, Matthew J. Farrar Department of hsics and Astronom McMaster Universit, Hamilton, ON L8S 4M whole tem gets sucked into black hole includes entrop what happens to the entrop of the universe? What happened to the 2 nd law of thermodnamics??? r s 23 4

5 notes for ΔS UNIERSE and hermodnamic ools Striking Similarit 2 nd Law of hermodnamics: ds 0 vs. Hawking Area heorem: da 0 a coincidence? Bekenstein, 1973, sas no Hawking, Bekenstein derived entrop of black hole: S BH = A/4 Generalized Second Law (GSL) In words: he common entrop in the black-hole eterior plus the black-hole entrop never decreases. Bekenstein, J. Black Holes and Entrop, hs. Rev. D., 7, 2333, (1973). In math: ΔS BH + ΔS c 0 (S c is common entrop to the eterior) 5