Cocept o Iteral Eergy, U Iteral eergy s the sum o the ketc ad potetal eerges o the partcles that make up the system. Frst Law o Thermodyamcs Chapter Coservato o Eergy At molecular level, cotrbutors to the teral eergy, U are; traslatoal eergy o the molecules. eergy the orm o molecular vbratos ad rotatos. potetal eergy o the costtuets o the system due to the evrometal eects (tra). eergy stored the orm o chemcal bods that ca be released through a chemcal reacto. potetal eergy o teracto betwee molecules (ter). Traslatoal whole atom or molecule chages ts locato three dmesoal space Rotatoal whole molecule sps aroud a axs three dmesoal space Moto o whole molecule All types o eergy o molecules, except traslatoal eergy are quatzed. 1 KE m v bratoal Moto wth molecule moto that chages the shape o the molecule stretchg, bedg, ad rotato o bods
The rst law o thermodyamcs The rst law o thermodyamcs states that eergy ca be ether created or be destroyed, the eerges o both the system ad the surroudgs are take to accout. U U U Total sys Surr U sys U The teral eergy U o a solated system s costat,.e. U sys = 0. Surr Chagg U; I a closed system whch o chemcal reactos or phase chages occur; heat, work, or a combato o both s the meas to chage U. I such a system the low o heat, q, ad/or work, w, across the boudary betwee the system ad surroudgs durg a process whch chage U o the system ; Heat to the system, q > 0 Work doe o the system, w > 0 Smple processes: The smplest processes; oe o, or T remas costat. A costat temperature process s reerred to as sothermal. A costat pressure process s reerred to as sobarc. A costat temperature process s reerred to as sochorc. Work: mechacal work (-) w : - work s the eergy traser across the boudary betwee the system ad the surroudgs due to a orce actg through a dstace (rom expasos (-ve) ad cotractos (+ve) o system volume). Work s perormed by other ways too, e.g. electrcal, soar,.. Work: w (sothermal process) o the system (+ve): w x x x x 1 d w RT w Adx d w F dx w RT RT d w x x x=0 d w 0, o system-cotracto w 0, by system-expaso
Heat: Heat s the eergy traser across the boudary betwee the system ad the surroudgs (lows rom hgh temperature to low temperature) due the temperature derece betwee them. Surroudgs: Everythg other tha the system s surroudgs. As a practcal matter or a gve stuato oly the mmedate rego that ca teract wth the system s the (eectve) surroudg. Molecular Level erspectve; I the al aalyss matter has to be vewed terms o ther exstece o ettes as atoms, molecules, macromolecules At molecular level the eergy a etty ca acqure s quatzed. Allowed eerges o ettes are well deed, 1,, 3, 4, All the molecules a system do ot have the same eergy. There s a dstrbuto o eerges amog them at a gve temperature. The relatve probablty o a molecule allowed eergy states 1 ad (> 1 ) s gve by; > 1 () 1 b e k T as (), 1 1 1 ( - 1 )=Cost. () 1 k b T e as T, 1 1 T = cost. Smaller eergy gaps Bgger eergy gaps Low T Hgh T
Heat Capacty, C Flow o heat /out o matter (system) results a temperature chage o the matter the system. The amout o heat (strctly speakg eergy) requred C, to chage the temperature s deed as the heat capacty q C lm T T dq C dt T 0 C depeds o the materal - SI ut; J K -1. per mole o materal, C m - SI ut; J K -1 mol -1. Heat capacty depeds o the expermetal codtos as well. Costat heat capacty, C, s deret rom costat heat capacty, C. Molecular vew o C Heat exchagg wth matter chages the temperature, ad thereore the populatos the eergy levels chage. The eergy levels a molecule geeral s the sum o deret (eergetc degrees o reedom) types o eerges; E tot = E tr + E rot + E vb + E elec + Molecules ca ga/lose eergy rom.to other molecules va molecular collsos. Eergy levels comparso Equpartto Theorem The law o equpartto o eergy states: that each quadratc term the classcal expresso or the eergy cotrbutes ½RT (J mol -1 K -1 ) the average eergy. For stace, the traslatoal moto o a atom or molecule has three degrees o reedom (umber o ways o absorbg eergy), correspodg to the x, y ad z compoets o ts mometum. # degrees o reedom or each eergy types: or a etty wth atoms, Tr = 3, Rot. = 3 or, b. = (3-6) or (3 5). Each degree o reedom has ts ow eergy levels. Sce these compoets o mometa appear quadratcally the ketc eergy, every atom has a average ketc eergy o (3/) RT thermal equlbrum. http://chemwk.ucdavs.edu/hyscal_chemstry/statstcal_mechacs/equpartto_theorem
The cotrbuto to heat capacty C m or a gas at a temperature o T ot much lower tha 300 K s R/ or each traslato ad rotatoal degree o reedom, where R s the deal gas costat. Each vbratoal degree o reedom or whch the relato E/kT < 0.1 (s actve) cotrbutes R to C m. I E/kT > 10 (s actve) such degree o reedom does ot cotrbute to C m. For 10 > E/kT > 0.1, the degree o reedom cotrbutes partally to C m. Each actve degree o reedom cotrbute to the heat capacty. C m or gases : Mooatomc gases: E tot = E tr C m = 3(R/) J mol -1 K -1 olyatomc gases wth rotatos actve: E tot = E tr + E rot C m = 3(R/)+(R/) - ear C m = 3(R/)+3(R/) - o ear olyatomc gases wth rotatos ad vbratos actve (upper lmt): E tot = E tr + E rot +E vb quadratcs terms!! C m = 3(R/)+(R/)+(3-5)(R/) - ear C m = 3(R/)+3(R/)+ (3-6)(R/) - o ear 300K Calculato o q ; Tsys, dq dt Tsys, C q C dt Heat or costat pressure processes (gases):.78 + 4 ormal modes.78 + 1 ormal mode 1.47 Uder costat pressure chagg temperature would chage volume o the gas. Ths volves pushg or pulg o surroudg, thus volves mechacal work. The eergy (heat) requred to chage the temperature, C m, or costat pressure processes are deret rom C m. Tsys, Tsur, sys sur Tsys, Tsur, q C dt C dt
For gases C > C because eergy s eeded to eect volume chages. C C R.e. C C R m m Tsys, Tsys, sys :Borrowed Chapter 3 Tsur, q C dt C dt Tsur, sur State uctos ad path uctos: U q w du q w state path Ay quatty that does ot deped o the path t takes to move rom stage 1 to stage s a state ucto. All thermodyamc quattes are state uctos. State o a sgle phase o xed composto s characterzed by ay two o, ad T. Ay quatty that deped o the path t takes to move rom stage 1 to stage s a path ucto; q ad w are path uctos. A state ucto descrbes the curret state o a system. How the system came to be that partcular state s o o cosequece. The ollowg are state uctos: ressure, olume, Temperature, T Mass, m Quatty, Iteral Eergy, U Ethalpy, H Etropy, S Gbbs Eergy, G The overall chage or a cyclc process o a state ucto s zero. U du U du 0 :cyclc path U
Thermodyamcs apples to systems teral equlbrum. It mples ay chage doe must be perormed gvg sucet tme to acheve equlbrum terally ad wth the surroudgs; rate o chage - slow very slow; quas-statc process. We deal wth quas-statc processes whch are reversble. Reversble process: A reversble process s a process where the eects o ollowg a thermodyamc path ca be udoe be exactly reversg the path. It s a process that s always at equlbrum eve whe udergog a chage. Ideally the composto throughout the system must be homogeeous. Reversble process: Thereore the o gradets, currets or Eddys exst. To prevet all -homogeetes, a reversble process must be carred out tely slowly. A truly reversble processes s o-exstet. However, may systems are approxmately reversble. Assumg reversble processes acltates calculatos o varous thermodyamc state uctos. Fact: Maxmum work s acheved rom the system durg a reversble expaso ad vce versa.,,t,,t RT - sotherms do ot cross. : sothermal process All pots o the surace correspod to all possble, ad T values (equlbrum state) o 1mol o a deal gas.
Reversble - chages o a deal gas (sothermal);,,t RT costat :sothermal process Reversble - chages o a deal gas (sothermal);,,t RT costat :sothermal process,,t,,t w w RT w expaso RT d d RT 1 dcator dagram Maxmum work s volved durg a reversble expaso (or compresso). dcator dagram w dcator dagram plot area For the cyclc reversble process(sothermal); 1, 1,T RT costat :sothermal process For the rreversble process, - work 1, 1,T w w plot area w total,,t 0; q 0 total Reversble process ollows the IGE. RT 1 w ex td d RT d w RT w expaso RT 1 w 1 w,,t w w w1 0 steps w () 1 w dcator dagram plot area
For the cyclc rreversble process, - work 1, 1,T w1 0 w3 0,,T w w w plot area w w 4 cycle For - work w rrev < w rev. U q w 0 :U ucto o state total total q w ; q 0 :because w 0 total total total total Example roblem.4 p.3
4.50L, 5.0bar Use Boyle s Law!! 11.5L, 4.5bar 5.0L, 4.5bar Use Boyle s Law, easer!! The magtude o the work s greater or the two-step process tha or the sgle-step process, but less tha that or the reversble process. For - work w rrev < w rev. Expaso Compresso 5 10 Smaller steps (slower) process closer to reversble. 5 10 Smaller steps (slow) process closer to reversble. Maxmum work s volved durg a reversble expaso (or compresso).
Determato o U U q w q d eral d 0; U q q U q erorm the process uder costat volume, ad measure the heat low, q assocated. Ethalpy: rocesses perormed uder costat pressure du would be; du dq d eral du q d q d U U q () a d q U U H U Ethalpy q H H H H q Calculato o q, w, U ad H or deal gases: Needed: equato o state, tal state, al state ad the path take. U q C dt v H U ()()()() T U T RT q C T U ucto o T H ucto o T Note: Isothermal process; H U 0 Adabatc process: q = 0 deto - work, costat volume: w = 0 H q C T RT w erald d
Reversble Adabatc Expaso/Compresso: Ideal Gas Cosder the adabatc expaso o a deal gas. Because q = 0. the rst law takes the orm; U w d C dt eral d C dt RT dt d C R T T C R T T C T R T C () C C T T () C C T C ( 1) C where C T T T T (1) (1) (1) T T 1 (1) cost cost :sothermal Two systems cotag 1 mol o N have the same ad values at 1 atm. Isothermal: >1 q < 0 to keep T cost. <1 q > 0 Adabatc: q = 0 >1 T crease, ad > so <1 T decrease, ad < so