Relaxation in Glass: Review of Thermodynamics. Lecture 10: Thermodynamic Functions

Transcription

1 Reaxation in a: Review of hermodynamic Lecture 10: hermodynamic Function

2 2 nd Law of hermodynamic irreveribe procee Exercie for omework: Conider the two procee: Reveribe equiibrium heating of ice from -25 C to 0 C, meted at 0 C and then reveriby warmed to 25 C Irreveribe non-equiibrium meting of ice from -25C to water at 25 C Exercie: What i 2O, urr and univ for each proce? ake Cpice = 2.1J/g- o C, Cpwater = 4.2J/g- o C, = J/g meting wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 2

3 Exercie for omework: Reveribe proce: ytem = urrounding 2 O K Cp ice d q met K K K K Cp water d urrounding K K Cp ice d q met K K K Cp water d univere 2 O urrounding 0 wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 3

4 Exercie for omework: Irreveribe proce: ytem = urrounding 2 O K K Cp ice d q met K K K Cp water d urrounding q ice urrounding K Cp K ice d q met K Cp K water d univere 2 O urrounding 0 0 wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 4

5 2 nd Law of hermodynamic irreveribe procee For irreveribe procee, the entropy change in the ytem i ti the ame o ong a the ytem change between the two ame initia and fina tate, the entropy i a tate function owever, the entropy change in the univere i now nonzero, we do more than exchange diorder between the ytem and urrounding, we create more diorder in the univere in the irreveribe procee q d irr univ ytem urrounding 0 wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 5

6 2 nd Law of hermodynamic Direction toward equiibrium o for an ioated ytem, the entropy can be ued to te the direction of pontaneou change, the direction that increae the entropy of the ytem he chaenge of coure i to do cience on ioated ytem, we need a function that operate under condition that are more common Contant and? Contant t and? Let ee if we can invent a function that wi give u the ame abiity to predict the poition of equiibrium, but for a ytem that i contained under more commony ued condition wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 6

7 2 nd Law of hermodynamic Direction toward equiibrium Conider procee at contant and oume: du q d U A q du d da, 0 d q d du d du d d 0 conider d 0 at td=d d=0 d d d d d U d 0 conider d U d d U he emhotz Function decreae for pontaneou procee unti it reache a minimum where after at equiibrium i i unchanged for procee taking pace ermann Ludwig Ferdinand von emhotz Augut 31, 1821 eptember 8, 1894 wa a erman phyician and phyicit wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 7

8 2 nd Law of hermodynamic Direction toward equiibrium o the emhotz Function, A,, tart out high and decreae toward equiibrium wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 8

9 2 nd Law of hermodynamic Direction toward equiibrium Conider procee at contant emperature and reure du q d conider d 0 q du d d d d d q q d U d 0 d du d reca U du d d 0 d d 0 conider d 0 d d d d d 0 d, 0 wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 9

10 2 nd Law of hermodynamic Direction toward equiibrium o the ibb function decreae for pontaneou procee and reache a minimum at equiibrium for procee taking pace at contant and, d = d = 0 d, 0 Joiah Wiard ibb February 11, 1839 Apri 28, 1903 wa an American theoretica phyicit, chemit, and mathematician. e devied much of the theoretica foundation for chemica thermodynamic a we a phyica chemitry / iki/j i h d wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 10

11 2 nd Law of hermodynamic Direction toward equiibrium o the ibb function decreae for pontaneou procee and reache a minimum at equiibrium for procee taking pace at contant and, d = d = 0 d, 0 wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 11

12 2 nd Law of hermodynamic hermodynamic Function Our thermodynamic function o far U q w U A U heir derivative form du d q w d d d d d d d d da d d d d d d d d d d d d d wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 12

13 2 nd Law of hermodynamic hermodynamic Function heir natura variabe: d U d U du U U, A A d d d, d d d d A d A da A A,, Exercie: What are the 8 gradient of thee function? For exampe? U wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 13

14 hermodynamic Function 1 t Derivative he firt derivative function U U U U A A ome are more uefu than other other wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 14

15 hermodynamic Function 1 t Derivative Conider the ibb Free- Energy Function For a ga phae g g g g For a oid phae For a oid phae For a iquid phae wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 15

16 hermodynamic Function 1 t Derivative Conider the ibb Free-Energy Function d d d d 2 1 d d wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 16

17 hermodynamic Function 1 t Derivative < < g g g o, o, o, v,,, o o o 0, Cp m 0 Cp d d m Cp o 0, d 0 met 0, m 0 o met b m b m Cp d Cp d o vap b g Cp d wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 17

18 hermodynamic Function 1 t Derivative emperature Dependence of the Entropy wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 18

19 hermodynamic Function 1 t Derivative emperature dependence of the ibb Free-Energy g g wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 19

20 hermodynamic Function 1 t Derivative < < g g g wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 20

21 hermodynamic Function 2 nd Derivative he thermodynamic function we ue are tate function, and tate function variabe have the property of being exact property of being exact hat i, the formation of their econd derivative i independent of the order of differentiation: y x F y x F,, y x F y x F x y y x y x x y,, 2 2 x y y x wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 21

22 hermodynamic Function 2 nd Derivative When thi i appied to thermodynamic function, we ca them the Maxwe reationhip and we get the foowing: U U Exercie: here are four, write out the remaining three: du d d d d d da d d d d d wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 22

23 hermodynamic Function 2 nd Derivative Maxwe Reation: du d d d d d da d d d d d wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 23

24 hermodynamic Function 2 nd Derivative ome are more uefu than other 2 2 d d d d wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 24

25 omework Exercie for next time: Derive an expreion for the foowing quantity in term of eaiy meaured quantitie and appy it to iquid id B 2 O 3 ighty above it meting point and crytaine B 2 O 3 ighty beow it meting point wmartin@iatate.edu MI: Reaxation in a - Lecture 10 hermodynamic Function 25