Thermal Physics 1: Thermodynamics and Statistical Mechanics, Lecture notes of Thermal Physics

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THEORY THERMODYNAMICS CHAPTER 1 e BAsic DERWirio~“g TD By: DEFICE THERNODY WamICS,., AS THE INVEsTIGATIO~ oF THE byw amical avd THERMAL PRoPEAr1 FS OF sopies, pEbucED En71 AREY PROM THE 197 ard 27° Lax oF THERMobyrAnice | wirro7 SPECULATION as TO THE Motpeviah coveriTuziew Sn DEScRIBES MaceoscoPic PROPERTIES OF sS7sTEMS - ris Ew TiRELy EMP AL Sie tavs oF THERRODYKAN IES om law a DEFWES TenPeraturRe T Bsc iw DEFINES ErERoy U a2 law a DERMES E~7ROPy S RD - Sa i: baw a GIVES MURERICAL VALYE TO ENTROPY BP epee EXCHANGE BE rWwEEW SYSTEA Ard sURROVH DI WGS Alves 4 OPEV $y7STEXR Slyes CLOSEn SYSTEr ise Qreaz) BxcHavGt perwEer systim Ard suRROUM DINGS “Aves a DilaTnERnar 57STRA “ive a ApIAbAric ()20L07ES) SYSTEM a VER/ 1SOLATED SYSTEM LEFF on 17S OWN wernt REACH AW Fai 1BRium STAZE LL LIDRIum <7ATE 5 SPEciFiBD By STATE VARIABLES fa A simple TD cycrérn REeavits orty 2 STATE VARIABLES Quire EQuitr BRIvM ft 4 i 1 Ko hish oe iS are Two TD cysTEMS ape w THERMAL conTAclh, Tuey wile ABACH THERMAL FevieiBRiUA ‘Tue ees Ae! pel THERES hywabied, a. TWO $ysrems ARE SEPARATELY in THERMAL EQUILIBRIUM wirn A TRD S¥87EM_ THEN THEY MUST ALSO BE IN 7uERMAL EQUILIBRIUM wir FACH OTHER Brus LAw_LEabs TO THE CovcEertT OF TEMPERATURE a T oF A SYSTEM 1s A BULK PHysieAr PRePERTY me i THERMAL EQ@viciBRium vary OwF swoTméR HAVE THE. € ME PERATURE SCALES a LInEAR VARIATION Ti Sat od a O = CONSTANT SAME TErrerarvRE T x 2 Senk PHrsicAu PROPERTx  Blas THERMOMETER Bbosevnds GASES ar row T BEnAvE 1DeALLY Th vcrives OO units BETWEEN Ice Ard STFA Points y @ M.. USE FirrteR corstaer PRESssuRE Pon corsra-r vorvné 400 | wee Pre ssuas a i= lvelaavinne V. a S\= $7 £Acs= Pez too Be veuune a TEE pee Pe ieee rele Males Oo |= 6K 3 - 293 18% poe MrteT: TheW- 27545 Araime Tor oF HzO ie UMIQvE Por? AT Wier Sourd, LiQuid, AP GAS PrHAsES cobxit7 Bx. thazs.46 k © 10 lot °o a Pep Sand Na a ICE toler = 273.15K = 0.0°C me te Pome = 37315 k = 1900.0 °C * 3 poe (Or Werle eal re reed las Tin Vs 1293196. +) ee eC ca a 1 Lom poo CPV Yep Havana OF Stare Aree STATE oF A S7STEM Ar F@uniBRivm 1S Furry DETERM web By oust a FE _hacROScoPre VARLABLES. 4 STATE. FuNerionw a FuveTIOm THAT DEPENDS onty ow THE srare OF a System (vor om 17S HIS7eRY) Actes’ Pease RULE “Al ror A HOMOGENEOUS, OVE-comPorEn7 3xSTEM AT EQUILIBRIVA, oney Two s7are @ VARIABLES ARE REQUIRED TO PescriPE THE STATE Aa Ard REAL Gases MB joc. cas Law| Ek Pvt a RT Hel =\s. 344 2/ mol-k at $s | DER WAALS a (p+ eV elalhy dR we Dehavee w Ee@uriBRiun SsTaTes j Ar PROCESS 15 A TRAWSITIOM PROM THE LWITIAL STATE TP THE FUvar STATE “dtp PROCESS 15 DESCR\RED AS A PATH ET ISoBARic PRocEssS = CONS TAw7 — PRESSURE Bicocrore PRocess a COWMSTAKT ~— VOLUME Ab isortermac Process = SYSTED AT A ComSraw? TEMPERATURE Civead_cas| Pw %) NO HEAT rRAMSFER BETWEEN SYSTEM AMD SU FROUAPIN OS AbIABATICc PRoc  Benn (~ IRREVERSIBLE PROCESS Theanvor BE sotvem BY SAME METHODS oF REVERSI DLE PRocEss @ WORK By Aw ELECTRic FIELD eee een A PARALLEL PLraTE CAPACITOR a A = PLATES AREA ‘4 bt SEPARAtion H V2 vours or covecé o> = EvreetRic DISPLACEMEns a P = Porapiearion =_PERMEZTIvIT7 OF VAcVU Be Recanve PeRmitrivity Tax, = EreeTRic SuseE P71Bie ITY Ap > OVERALL. ELECTRIC piPOrE nomenr WR el ec hetaie pe Mp-c, €,E MBrizte) xe 98 A, S/Vv|P “tw = Edp- BA mond bh pola ewe mecerere Bute BY aA _maceéric Filip Me ce A MAGNETIC MATERIAL BECOMING MAGMETIZED wirtin Soceworh We = _LEWGTH a = CRoss - seetionar AREA fs = NAGAE7IC [nbueTiow a Bo = imduerien tm ApsewcE oF MATERIAL 7] = _APPLiED FIELD “an MAGRETIZATION Mh. = _PERMFABILITY OF Vacuum i an = MAGHET IC SuUScEPrIBIUTY ww. = OVE RAw MR nar af + = 2 3. waslH+M) = BL + men 2 Cins x H Mp = we. Gx JH mart P= Vin fe t “dtw- Betis Ba vcen REQUIRED TO Pela a MAcrEric MATERIAL ThE CER ARA EL ei 3 Ere woRk REQUIRED To CHArGE Ar AblABAz Ic s¥S7F FROM ovE SPECI FeuLIiBRIun stare To Avprien Rains Beiue srAre lis THE SAME HOWEVER THE WORK Ss DOME, a AU =U, = U4 = War noarie er a lebepay ae SYSTEN 15 pOT THERMALLY 1SOLATED “Bau sur -v, = wre Ho: near 3 Pee E~TERS $78TEN a4 Qze ir we ee LEAVES SyS7EN a Qi -.E 4 Naess 16 THE EXCHANGE OF Er ERGY BETWEEN THE SYSTEM And THE SURRovmdin es THAT - -cenwet BE 1PE~7)FiEbD AS wolle  a EMERGY OF THE SYSTER can GE IMC REASED iTmER RY ADDING HEAT wre THE SrsTeR maa eRe Nau: wee Bios sesrw | Bu = nat Hear @ Bear CAPACITY Weel darted (at Ar lo bp eae | atnchidha Vad cchsihae) redial eb teslnmtar veel pice mw. MPa doe lier Meise ae reamed phate y hs che trlad Vouulne Mic.. Miso oda Bil: -pdv Au = vlz,v) Bio=-4du+ pdv dui: (3) at ef p ely Mre-i(i)l a7. Ee (3), Jay S. Comstanr V SS. aVizlo @ Mio=(3)ar edu Mola (S)e Miu = fos a7 4 nor constanr V PROCESS Bove (Cea Mi dvijtclan 4 Sal | the) a Bi hk: vw eel Wivear GAS Wo =| VIG) mt) BL WA ic dtl acy ar @ Bitar capscary ar ComsTa nh? PRESSURE i ae ae ‘BouzuG.p) meee My =e) rs (320 1, Mite) ies (aa, do = dur piv har ccm: p ba ict ts Wra: (ea) drislpitz ] dir Mico irra tied, Beeruarey Me eps leer ee ets View Coy Ado Mas lcd °@ Mu susp Mdn-dus,pdv +vdp = datvd, Mi dui vosl=lclar io re o 4 Eo  (=). dT + (el dp Bi MOT comTsTanT p | dh = Ceo dT + (2), dp ci en Foran 4 du eu Gas an Bye (ora ° Mduzcar Mausic har Bc arn Cp iw iDdpAL GASES me IE ak Bol Mo e: pulse). 4 Cp > Cv t+ mR Bue CAPACITY OF A SYSTEM (assecere) @ Mase: cur [an] a SPEQ\FI€ MovAR PEAT cAPAciTy Mit@ieles dn ilk! ja HEAT caPaci77Y PER Ke (Hee pede vapadiey) BM dalle aes ke gd iron A MOWwATOMIE cas aR * ‘ fp ssa t a Mc: 2 pea Move. icp = 2 pee move Qc, RYE CeY Be abiapene EXPArSi0~n OF \DEAL GAS 2 [Bto-o0 Milage lo clit till ° =) évdT + mlRtoe =o fic Ba 4 deel 20 az. (cea Bhima kh vl: od | Me: F Mirvac ay isch a, Werle lek saws he IDEAL Gas a Ys PA pisronie IDPAL GAs rth Weew 3 |THE LAW OF TD lata ENTROPy eo SEcovs LAW oF THERMobyNAMICS Mr iest raw (du: dal+ dw A FIRST LAw FOR C¥ctie process Mavic } ‘42 ow ier = lw  = Mw za} a! By) =)4/- |S B.. ErGive OPERATING BE TWEE. (Two | RESERVOIRS Caw RE More EPFici Rr? —THAN~ A CARM OF Freire OPERAN rr 6 ow FE sAME RESERVOIRS =) A roe A REAL ENGINE a m-< ne a THER MODY KAA IC TE PERATURE Q at Pi beats Th i [ a | ee 7} aS | Me =| ot Qs Tr a EFFic.ewery n= a = ee gEeicipely | |= |t-) er FF 2) Wy pt raickndron Or Qz a5 - 2 . et + Wel = lag Fa >: ze - 4 MEAT Pump 3 B a) - Bee CYCLE Sole dk ae Le eet eee _ a PSS Se icoh Fe Igual 1Qer 2 halls los ele clol | Fiat = 1Qel + Iywt_ a ke air et a LQ Ty Bu ee —t ee i ae pS C4 fais |= Vag te Pr eed dR I as YL TN, a Mysto eS eee 2 Beas Gureodadia) | eh 3 as : pees Le P : pee es Be te eee ah ic ea Awl cLosED everk $ = \</o wine | THE BQvALiry NECESSAR My Hobs e ze FoR A REVERSI PLE cy eR _ ies ca etme sorte et ere ba z AW ear EXCAIANGE tH 3 RBobiks ee eee fete acy a 2! wer | ponies! (Ts, Te!) doup bory |CTe)| A. caRvoT peFRiertarons (A, 8), 4 prerre CE) Bao), eee ele NASI eee We eee eI HEAT Flowire TO AND sehees cod reser Qoa + Qop Bw wor Ww > (%, 4 Wp) 8 Avzo Bio.) + Oo,)-Q. > Ww - (wy + Wp) Uw < : 4 @ nt My Wi ol lzlol eo  Ora Qon Te Qry av Be a> Fe S10 qo g. @ BS sce Te Te S001 51 Ma,, 0) | PAU Wwe auAUTy ale v ~ fake mp \F_ srBPs OF B ADEN AAR SMALL Awd Maw y Pett ot FoR REvERS: Bie Crees tou Boas |. Pe THEOREM We eo ladsletatads bbe da @ i \RREVERSIGLE PROCESS § f toe ree REVERSIBLE PRocEss =o “Ferory a Wide = 3@e Abo pees > REVERSIBLE process Bas [7s “AD proverries OF Er7Roly w S2-S1 i (7 1s A STATE FUKerionw ™” Umi Query DEFi rE FoR EVERY $7476 OF A sySTEN =D a AS 1s PATH In~DEPEWDENT (Bop A REVERSIDUE cy CLE DB eteory IX A CARWOT CYCLE all ISOTHERMAL ExPAXS 10x Aube dealer ay AdIABATIC ExPansionw Alsii= 1 Bese (Aso rurenar| comberssiow AS dE tory OR pamaparie Con Pressi ow ZV) Sa @ rt Sy oe WE ier levee JAS a Te | eo a) To Ruder (We rropy 1 A REVERS\OLE PROCESS e@ Mien ¢plar rr TF us - paeaes 1 c {las pha. i cy as mlep sdb tl Bhai Mais: bp ] Wheel Al peokess = HAT AbsoRBeD /RELRAStA BY S7STEN rROCESS “Tevrnopy (WM \anB VE RSIBLE CHAMGES Bt tio Ww: i = af | tel do Ay inr 8 mei se ‘Ae Ayrey 7 a eae {| 2a mi! IZ IAS = Sale Sa \4 Min S AS. dQ (Alas > = Bf plreopy lv Am 1SOLATED S7*7En iy. Ar (SevarEd s7stem , $ carror | pECREASE (wer EXTRoPy cHan~oeE zo) as 70° 8 IWcREASE iv 1RREVERSIBLE PROCESS AS =0 a COMSTAAT IN REVEASIDLD PROcESS [a As <¢o a InPOssiBLE , PROCESS Witt co te OPPOsiTE DikREcTION De abel OF _En7ROPY cup~r~ Ge Mol ete sate Gieinh Qu Mas te Se Berto CHAMGE (7 FREE EXPArsLor ff ag eis! ts, 2 fe L a REVERSIBLE |SOTHERRAL ExPArsio~ (vz = 2¥2) de = du + pay Mast & . 4) -slav 4 Misia Pe ete ie) vw = ZR = : | | DW isemone PROcE £3 Be vind iole ADA BAT IC Ghs =|0 i: = ConstTaneT WEEK a - Tbe Beeb a yataml PoreuriAls | Avd ue Maxweve RELATIoxs CEv7RAr Fevarionw OF} Tu eRH6 syvanie Ss BR elroy caw BE USE To Revisit 1" Law oF Tb Bi rieteiva oF ye du- dQi dw Tih coe REVERSIBLE CHArGES Maw: - pay Aso: tds WA diul-| tas + Pav Milras adult poy a FOUNDANExTAL Eavario~w oF TD  bel tO dsl hal cledade | reese Bdo-tis -pav + rda 9 Mide= va, -sdt + eda Bit Constant p = | dGlzl=S$ dr it eda w- (4), = GE), M, tons rawr TT Blac ¢ Vdpl+ eda a(S), = GP), Feddsbebe ComDITIONS a PECHAMICS STABLE FQvieiBun 1s wee EQ = mini at TD Sysrenc Ted TO EOuunRiwn @ Mesias DEPEXPS or PourbARy combiner’ ees) alee Pe tee meeting (to ls peseabinpel a SIMCLE S¥Sren THERE 15 comPLET THERMO DIVAMIC EQVILIBRI vn See obs laa alacta ” 1S wor iwinAciy Ww A~ EQULIBRIUM STATE 4 1S Compurx @.. IRREVERS Pie PROCESS witn @ TAA-SFER USUALLY OCeURS WHF SySri TExDS Fo EQULIRRIUN Deeds SYSTEMS ExamPres 3 A, MULTI — PHASE SYSTEM Pee eal ek woe A SYSTEM AT CorsrarT Vi Coerberes wire a RESERVO.R ar To Beh ue IsoL are» Bae VY, To Ber eur oF Faun BRivm (commer) TW ecevore Te = Censrart a SysTEA T, V = cosracs BF avebeo a when) T= TS. Ge. ISOLATED COMBINED SYSTEM Q g Ba: 7O B DSc + ASnss % O a Ades ree, MHo- Tas, <0 a Av -T.e AS £@ Bo w-alzs) ¢o MPalu-ts) <0 [4 Ar, = OF <0  Jar co ma. CHarck Towarbt EQuiuintiun ner REDUCE Foye | Febs_1$ Eauivareer ye! mactmizinie | $1 4 Sines a. Mueri- conPoneer s7eTEn 4 CorcinER a SYSTEM AT comSTAn? Pin Con7ae7r wirh a RESERVOIR Ar To elas ror ar Eauiidaiun pe and Te MotrAsislo a AU = Q@- pe AV A nua pav- Tas £6 Pau + alpv) atts) £0 AY Alot py-ts) co [A aago Bacicio Ma, CHANGE TewaRrS Four iBRiun usr RERYCE Gs Mae a. Gry 18 | BOvivaceer po paximzire 1Ssy5 + Sass 4 MP atrdicladrolwe TO CHEnICA REACTIONS _ ee tee BR pad pot wit. PROCEED sPo~TanFausry iF AG <O Be Oubariow C lO. 14 16 O, | = 1G CO|+ CHO x | Bo : | Fe 2554) Pac == 2900 K) mel "| (sromtanrous) BP eho deletal | lected, eleho) | ld bl ol beol B este Se de 4 #0| KS bel" (Yer cpokbaeaie IS BF dg alul-ts tipv SW Ts | Ft pv bo ! s Pha = AH! = TAS x Bac = lan 4 Alpv) : Biehl ch hs BP aval bile Furero~ | =P Vas + as. > 0 Mas. sl | ale pile Bas. 2 ple Belt dslelo Wale h- ee aus o- pray a DU + po AV - To AS £0 ale AVAL CABIEITY A(S,Y, Po, Te) = V+ p¥-TeS Wala <o (spot Tale lut CHAMGES Iw A. ARE noe) Bas AT £Quict BRium «HERE SYSTEM Ard SURROUADIMGS APE AT EQviu BRUM i Pot pare Te = T @ DA-AG LO B- constant V ay 46 = AF ¢<o BTL de  Week 5 - Hea CAPACITIES, JOULE An Joule Kevin ExPawsiow Hear CAPACITIES e* USEFUL MATH RE LATIONSHIPS Bie ACs. %, %) Owe aety 2 vaRABLRS ARB IAD EP DEAT Mx] kG 2) dy syle) Me = 2 (sy) Boy - ner: le p= /p(v,7) WW = vly7) Ar- rp, V) Wx: 2 (See MW ear Lenaclnes|. desarionsees ll wp ane ea spake @ Bc eee MS Woe Ey Mich cpa (oes as!) Ma ely gus Tas a... eR orem Pr a inoeraisl| Bete Bea (Sy Ms s(t Vv). Bogs: (ey dint (yay Wc, = cv +7 (3), (%), BCG: Ce) > cy +r (3%), (3) @ “ IsoPARic ExParSiiry as +) a He -comPerssipieity K=-Y¥ (%), a a aots estat 1 MW tocar lcs) CAPE SUS Ae e Pp Be ANd Cp VARIATIO~S wiTH Vv amd P 2s t aC Ea ees * ae BGS): Taal Solel x4) 3 ocx | awe/r = O FoR 4m Idea. cas Uc, sg: (ar A CW s karen S it =a) a 2p Dy SIOMEF OR Als hEALLGAS rane OF HEar CAPACITIES \ , Cote (arate = (Ap), CPAr). = (ov/ap), Bie ly sya st (assy ie Ca¥ 7 a7), QQv/ap)s a (= 8 Die rose nd ComPRESS pity Ky =~ Vv lip ie at (5) Wa asses COMPRESSIBILITY Ki Ss TV Mo ase Spake Cy - Ks  Wri Pow? Typ 5 FAT wetien Au THREE Plases coex!sT Michi TEMPERATURE Tp, = APOVE \r, 1s0THERMAL Con PRESsion pRabucES wo SHAAP Ligvib- VaPovR TRAW Si TIOw eer Fuurp 9 Bre raic DREAM Ie ehonecl le METALLIC HYDROGEW Puasel | TRAMSiziows | 2 Be rou helud Te Wess AT Thee tHASES EL .t SYSTER COMTAIPING Two PHASES (5 KEPT A? core%anT P= Par And T= arenes BP eb tulad, ve wen G18 Ar fininun Ain sy |t Ma ‘4n = TetTac pass ; | cl: Magi tM ge Wicls|toral © lor me ssren © | Weise SYSTEN B dn Elder + dm lalo 4 dn, = - dz ~ = | War pet a dG = 02 9,dM,+ 4, dn, ed 41=g2 Weekes OF Two PHaSeS ww Fahad 1s THAT THEIR SPECPI€ GIBDS FuncTio~w ARE Eauay Me ae ot leaded a EQuarto~ Me ded G1 =-G2— Swoued DE_SarisriEh Fok 6VERY PotwT Op THE coExisTivce CURVE We elite Ak [nb |e ee lal BP rib lah rly May a) 4. (radr| psdp) = gel THdr, prde) 8 114.0) 2 5. )tdgs MO let ta dg Ws ay ia : = et Bor (eo Cel Gp et @( (202: ee WB dclelvas dor mes 4 MG, - 5.) 37 = (=v) de mie te | Dentrory CHAMYGE \¥ PHASE TRAYS ITION ) tQmy Godt Grey BL Con STAMT pp Tidhs A Te Gas: Ea Ban = au +pav = oH  ff FUSiOw = f Chew ahi alie VAHL, AS pus = Mire. 4 Qapvaaele pet AH an a3 Side Bienes = Lawes e 4 Se asta Tete tai a EtAapsl= TAS nas 2P L L aw Bala SL ie(ve = V0) fs TA a Crausius ~ CLAPEYROX~ Favariow Be slece OF PHASE BouwbaRy 4 WIEGRATIOn OF CLAUSIUS - CLAPEYROr EQvATIOW Bon. A LLQUIB= VAPOUR TRAPSITION, ASSUME VAPOUR BEHAVES Ad Aw IDEAL GAS Wasa. THAT Var 2? Vira Baye Vee ee Ase: aan Diplelebsar une. a 42 (4): S bear (= - t) PHASE TRANSITION, 3 eee OF GIBBS Fuweriow in 1°" oRDER TRarSiTIoKs My (oD Sada ss clit : ‘ Bw. COrsSTarT p ake ” (52), =\=/5 ‘i a. 2 ° Pens g a) HAs weearive Stohr sf (3), ETS). = me <o° ie | Cp 20 Aways a gt) berds town 10 T Ams | THAT 15. STABLE a3 HiGHER T. HAS GkeareR S 2 a. constant T a =) V1 210 a a (p) LAS A POSTIVE SLOPE (33), = (le <o 4 gl) pews down Te rahe ibs 4 have Via Vel = pe = Beinsx ORDER PHASE TRArSITIONS A. CluanGE IM sheewrie GIBBS Furcrio~ r (colezmvers) | 1X SPECIFIC Volume V Bc nc tw srEeiFle ExTRopy § or ORDER. PHASE TRarsirions 2 Wc,': Plse lh m2 tl my 2-2 (3). “| AI< — >  af eheee) (ur Te B eevreer CLASS\ FicATIOM OF PUASE TRArSITIO~S Gu. ORDER Sl DERIWATIVES of g WITH RESPECT TO Tard p me biscontmvous 2°? opPER PHASE 7TRersiT1Ons BB ieonees FRUATIO~“~S FOR moO sys 6G. : Tey eo cikvl Mier) = av Maes cls iat dr Cp2-- Cer av > Tv (ee -Bs) a PIRST EHREY FEST FavaTion a 2 - Ay mS r mats Ss SEco~p EMRE FEST EQvarionw Wee 2 - Twits raw of Ib Amd Kiwirie THEORY of GASES ABso. TE ENTROPY AND | 3" Law oF | THERMObY NAMICS FD iwreopy OF tbEAL Gas iE Mirds sau tpdv = Cvdt-+ pdy > Cvdt + ~ydyv Mas. co B+ Mav Ms 2 eek a nk bn v4 8 DB bsh eure eumory wire venrowe coms rane BD eariow OF ErtRoPy with TEMPERATURE S.- CowstT Aart p Wde, = dH d d d Mais |=| Ses Se ir fey May th earl Sin pA; Ab yap Mi Asielce C=) ae Ber rropy AnD PHASE CHANGES la S Uresxt Es Ab tews QS tows > Trrars Trans - — (Wevreory INCREASES AS Sorib — Liauib ™ GAs Baiscrare INCREASES with EMrROPy (PHASE SrADLE AT HIGHER T HAS HIGHER EX7RoPY) @ osscavarions FoR DIFFEREYT PHASES i Ran MOMATOMIC GASES SHowd DE EQ@varry DISORDERED AT SANE a EXCEPTIOw a TROVUTOM’S RULE |: HAVE SAME ~ DS var FOR MOBLE GASES AT THEIR Bowe Ports (85 tkmel? on 10.5R)  | Caan DISTRIBUTION OF NorEcULAR SPEEDS f iy) BF eon Fim TESimAtcry SMALL iv TRRVALS amy? aT 34, @ Mya): ae Ga av: Os Wb atalirarwe, Comenepations dmlv) a Qi SS OF asl EB Sol lan | als | =. 00. (ea) We ie fle) + decemswo fle) WP eialid Sim FuKeTions 7? anf WeREASIMG Ar smart E. oy Oo Ie a dn(v) BE | DEcREASwe Ar raRee E ay eos daxtvs Sep aE : av. = AE @ = goat | daly? r -BY a t 2 epi et v7 le MAXWELL DISTRIBU rion vz00 va. per ith eek er NUMBER oF mMocscutes N = sl dn(v) = ), #v*e dv = avd 7 3 a = iia Wa = 4nn (Ge 2 Azizi dnlyy (= my? 4 sq SON 2 or i Ter ft Bovténanr Factor = Sc te Poisranurion Or MoOrEcuL AR SPEEDS Biassune WE CAr~ DEFINE SOME CrHAkAcTERIST Ie SPEED Vans @ PS Ale noveeues Wourd MevE witig Vans Aeoor Pear SsavaRE SPERD { By elie ee ee BR alecrct SPEED | vie ete) 2 | Wa: I. v a = Sep Wp 2 eae yer. [err Bivo = lim = Aer os; TRoDA pie sherD as Peerol ec 4 Pave ted RELAT LOM PeLrWwEE AM | Vin} of YP. mcd Vams BR vb: vn. Sl patel Sala S42 -4.13-5-1.22  Ve aL Grok al mpd i fhe ell del abe pa eto bede be tel | | | Kinetic MOLECULAR THEeRY OF GASES 2 BB ete Uae BY AN IDEAL GAS W,- $ p<v*? 3 Mv: tNm vi? > KT (ileal asl (al nicdoabapel blenune) Baka! FREE PATH >» Mi lect DISTAWEE TRAVELLED By A molBeutE fErwher 2 CowsBcurivE corrisians rear FREE mn Pea cleshe TIME BETWEEN Covvisions a As hyp Ble _ FREE Pate! kT i: Az dp a: DIAM AZER OF GAS MerecuLR e a 4 % AT Constant p AX~ > x GB. pie At 8,.-+ 8 a DULKIER NMorecure LEADS TO SuerTER DISTArCE BETWEEN Corrl Sio~s Beds. VAwWES oF Are bance e y = ae 3e +10 &.. Ts2e%c | awd Belt, ER > ite ae EG) te ey Faiernsront PRePERTIES OF GASES : Bi ceveic. Be raac lon fase (coerFiciexr Db) mL. TRAMSFER 4 TRarsporr OF Kiwerie Ewe RGY (coerricierr «) = BAe coche) a TRArSPORT OF birEAR MomEnrTUM eles nee 7 ) = | EAT CAPACITIES OF GASES We eerste gs Wc. .% Mic, = a | a, = ae = > 142 Ms 4 Mic) | Bc BS seal ee cuieaati mn oe OF ErEray ab a. Some = fi + my? dn(y)= = an v <v*> ZNwr |. A eles Mewerey EQuUIPARTITIOo~ THEOAEN st ra cu DEGREE or) FRaston! (V. Vv, \ve|,.|)-|-Polss bam comrAlbume Skt” yo (ue reac enERGy cr AS¥srEM G Way ee Rs x ‘4 Be Fa fll Bh m1 = DEGREES OF PREEDOM  Pose ee Ne dad abemcbalel q — leet la 2 2 2) {4 EVERGY OF AW WwDIVIDYAL ATOM E=ymvt =z mlvitvi+vi e@ ie 3M DEGREES OF FREEDOR Pa rdral. yeimEric EXERGY oF N Arons 4 Biatomie MovEcuLe Me Ce lk + hoy ) aa Me el ket Pes Sm vit dk (eren) Wi visceelodal Morton BECOMES SiGwIFICEAMT OnLy Ar VERY HioH T a Porry Atomie nore cures (w ATons 1% A horecutc) @ ‘4 LIMEAR Orecuens = | By 7 5 vieranons ae LIMEAR MoLvecuL ES oy 3M > 6 vignarions \ Weex @ - Rear Gaees avs Iwrobucriow To Smristiae Mecrames REAL GASES Bo GAS el p= a RT Pe A CompRESs:o~ FACTOR Z = mk : p Von | By zl: 45 WA Vi rl laals sod arate “Aven WRAL GaASES., 2 = 1 Arwarys REAL GASES ‘a 23 a= raed “a Bact ff: As atpt 0 4 Tye Lal FOR HIGHER vatvct of 2 (Vn LARGER Tun. ik dss) 4 Zig FoR INTERMEDIATE (Von SraLeE A THEM BAL Gases) Wvievae EQuatior OF STATE Be sa Bie + Cpt... PY v2 nar (tse p scp...) Me, C, ++. 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