Review of Classical Thermodynamics

Transcription

1 Revew of Classcal hermodynamcs Physcs 4362, Lecture #1, 2 Syllabus What s hermodynamcs? 1

2 [A law] s more mpressve the greater the smplcty of ts premses, the more dfferent are the knds of thngs t relates, and the more extended ts range of applcablty. herefore, the deep mpresson whch classcal thermodynamcs made on me. It s the only physcal theory of unversal content whch I am convnced, that wthn the framework of applcablty of t basc concepts wll never be overthrown. Albert Ensten hermodynamcs Classcal Statstcal Knetc heory he descrpton of a physcal system Macroscopc Mcroscopc 2

3 Classcal hermodynamcs Macroscopc approach General propertes of the system Macroscopc varables Statstcal hermodynamcs Mcroscopc approach Specfc propertes of the system Mcroscopc varables Knetc heory Mcroscopc approach Specfc propertes of the system Mcroscopc varables 3

4 Physcal System Mcroscopc model Experment Method Mechancs Statstcs hermodynamc System conssts of very large number of partcles has the boundary has the surroundngs 4

5 hermodynamc system he part of the unverse treated at a gven problem, whch state can be completely determned by gven thermodynamc varables. Macroscopc approach reats system as a whole Macroscopc varables Mcroscopc approach reats system as collecton of partcles Mcroscopc varables 5

6 hermodynamc varables Extensve Intensve hermodynamc State hermodynamc State hermodynamc varables are well defned for all volume elements of the system large enough that macroscopc descrpton can be appled hermodynamc varables are not changng wth tme 6

7 hermodynamc state Macrostate Mcrostate Interacton between the system and ts envronment Equlbrum Mechancal hermal Chemcal 7

8 emperature hermal Equlbrum An Illustraton of the Zeroth Law of hermodynamcs 8

9 Zero Law of hermodynamcs wo or more systems n mutual thermal equlbrum-that s, wth no tendency of heat to flow through the conductng walls connectng them all have the same temperature. Or when two systems are n thermal equlbrum wth the thrd system, they are n thermal equlbrum wth each other and all the three systems have the same temperature. Equaton of State and Exstence of emperature Emprcal emperature and hermometers 9

10 A Constant-Volume Gas hermometer A Constant-Volume Gas hermometer Cp emperature Scales 10

11 Reference ponts of Kelvn Scale Absolute zero rple pont of water K Ideal Gas hermometer 3 Cp3 p K p p Klm p 3 0 p3 3 V Determnng Absolute Zero 11

12 Celsus and Fahrenhet Scales tc o t F 9 t 5 C 32 o hermodynamc Process Heat ransfer 12

13 Insulatng (adabatc) wall hermally conductng (dathermc) wall Work Work W Fdx 13

14 Work done by gas n a cylnder W pdv Sgn Conventon Work s postve f t s done by the system Work s negatve f t s done on the system Work dfferental of work s nexact dfferental s not functon of state depends on the process 14

15 Work done by gas n the cylnder Work done by a gas n the contaner W Fdx pdv Work done by a gas n the contaner over a cycle 15

16 Work done n adabatc process does not depend on the choce of the path Internal Energy U 2 U1 Wad Fdx ad he Frst Law of hermodynamcs du Q W U U Q W

17 he Frst Law of hermodynamcs When a system changes from an ntal state 1 to a fnal state 2, the sum of work W and the heat Q, whch t receves from surroundngs s determned by the states 1 and 2, t does not depend n the ntermedate process. hermodynamc Process hermodynamc Process Reversble Irreversble 17

18 Reversble process If the system under consderaton changes from orgnal state 1 to fnal state 2 and ts envronment changes from state a to state b, then n some way t s possble to return the system from 2 to 1 and n the same tme return the envronment from b to a, the process (1,a) to (2,b) s sad to be reversble. Heat ransfer and Work Heat Engne produces useful work works through a cycle exchanges heat wth envronment 18

19 Carnot Cycle for Ideal Gas he Second Law of hermodynamcs Expermental Evdence of the Second Law of hermodynamcs 19

20 Caratheodory s prncple: For a gven thermodynamc state of thermally unform system, there exsts another state whch s arbtrarly close to t but can not be reached from t by an adabatc change. heorem of Caratheodory If dfferental form M x, y,... dx N x, y,... dy... has a property that n the space of ts varables every arbtrary neghborhood of pont P contans other ponts whch are naccessble from P along a path correspondng to the soluton of ts dfferental equaton, then an ntegratng denomnator for the expresson exsts. Clausus prncple A process whch nvolves no change other than the transfer of heat from a hotter to a cooler body s rreversble, or t s mpossble for heat to transfer spontaneously from a colder to hotter body wthout causng other changes. 20

21 homson s (Kelvn s) prncple: A process n whch work s transformed nto heat wthout any other changes, s rreversble; or, t s mpossble to convert all the heat taken from a body of unform temperature nto work wthout causng other changes. Prncple of the mpossblty of the a perpetuum moble of the second knd It s mpossble to devse an engne operatng n a cycle whch does work by takng heat from a sngle heat reservor wthout producng any other change. General Carnot Cycle wo sothermal and two adabatc processes Effcency W Q Q Q 1 Q Q Q

22 Carnot s Prncple he effcency of a reversble Carnot cycle operatng between heat reservors R1 and R2 s unquely determned by the temperatures of the heart reservors and the effcency of any rreversble Carnot cycle operatng between the same heat reservors s less that the effcency of reversble Carnot engne Reversble Carnot Cycle Q Q Q K Q, 3 Clausus s nequalty for arbtrary cycle When a system performs a cycle whle n contact wth envronment and absorbs heat from the envronment at temperature, then the followng holds Q 0 22

23 Entropy S 1 reversble Q ds Q, Entropy s an extensve varable Second Law of hermodynamcs 2 1 L Q S, Q ds 23

24 hrd Law of hermodynamcs If one tres to reduce the temperature to absolute zero by repeatng the seres of operatons, each successve operaton yelds a smaller change of temperature and t appears that =0 wll never be reached. Nernst-Smon heorem S 0, 0 Infntesmal Reversble Process n the closed system du Q W, du ds pdv 24

25 Infntesmal Reversble Process n the open mult-component system Chemcal potental U N S, V, N j du ds pdv dn Other hermodynamc Functons Enthalpy H E pv Helmholtz free energy Gbbs free energy Grand potental F E S G E pv S F N Dfferentals of thermodynamc potentals dh ds Vdp dn, df Sd pdv dn, dg Sd Vdp dn d Sd pdv N d, 25

26 G N Gbbs-Duhem Relaton Sd Vdp Nd 0 Crtera for Equlbrum Q ds, du pdv ds, du pdv ds 0 26

27 Isolated System de=0, dv=0, dn=0 ds 0 S has ts maxmum at equlbrum he closed Isothermal system d=0, dn=0, dv=0 df 0, F has ts mnmum at equlbrum he closed Isobarc system d=0, dn=0, dp=0 dg 0, G has ts mnmum at equlbrum 27

28 he open Isothermal system d=0, d =0, dv=0 d 0, pv has ts mnmum at equlbrum Frst Partal dfferental coeffcents of thermodynamc potentals Measurable Propertes of the system he coeffcent of volume thermal expanson 1 V Compressblty V X 1 V V p X 28

29 Heat Capacty at constant volume C at constant pressure V C Q U S d p V V V Q H S d p p p he Cross-Dfferentaton Identty 2 2 W W W W x y y x xy yx p 1 U V V p V 1 H V p p 29

30 30 Maxwell s Relatons,,,. S V p S V p S V p S p V S p V S V p Example Show that nternal energy of a materal whose equaton of state has the form p=f(v) s ndependent of the volume.