III MATTER9. Phases of Matter10.Deformation of solids AS11.Ideal gases 12.Temperature1.Thermal properties of MaterialsASA208/12/15 211. Ideal Gases11.2 Kinetic theory of gases11.1Equation of State11.3 Pressure of a gas11.4 Kinetic energy of a molecule! " n#$! " % & $ kT c m molecule perenergy kinetic Average2

221= > < =2

1PrcVNmpgas of essureANNn =08/12/15 3ReferenceTextbook Homework08/12/15 5T!E "AS #A$S'o( )o gases *eha+e if their ressure, +olume or temerature is change). -t is sensi*le to +ary t(o of the re+ious quantities (hile &eeing the other constant in three searate e.eriments/0i1 !ariation of ressure (ith +olume at a constant temerature0ii1 !ariation of ressure (ith temerature at a constant +olume0iii1 !ariation of +olume (ith temerature at a constant ressurehtt///(((.schoolhysics.co.u&/age12314/$hermal520hysics/6as520la(s/08/12/15 2Parameters! 3 +olume of container 3 ressure of gas in container$ 3 a*solute temerature of gas% 3 num*er of molecules of gas 7 " %mm " mass of a gas molecule total massof gas!,an) $ are calle) macroscoic roerties 0(hat (e can see an) measure1.08/12/15 8%ARIATI&' &( PRESS)RE $IT! %)ME$his can *e in+estigate) using the aaratus sho(n in the )iagram. $he air trae) in the glass tu*e is comresse) *y forcing in oil (ith the um an) ta&ing rea)ings of ressure an) +olume. 9fter each comression you shoul) (ait a fe( moments to allo( the temerature of the air to sta*ilise.$he relation *et(een ressure an) +olume (as first )isco+ere) *y #o*ert :oyle in 1220 an) is calle) Boyle's Law. -t states that/pV = constantPressure gauge08/12/15 8*o+le,s #a-9 grah of ressure against +olume is sho(n in the follo(ing )iagram for t(o )ifferent temeratures $1 an) $o 0$1 ;$o1. $he lines on it are isothermals, that is they a( can *e (ritten as/$oisothermals08/12/15 4%ARIATI&' &( PRESS)RE $IT! TEMPERAT)RE .Pressure #a-/$he (ater is heate) an) the ressure of the air in the seale) glass *ea&er is measure) (ith the ressure gauge. 0$he +olume of the air is effecti+ely constant1.#esults of this e.eriment sho( that for a fi.e) mass of gas at constant +olume/ ! an) 7 constant'eat?onstant +olume gas thermometerPressure gauge*ea&er(ater *ath08/12/15 10PRESS)RE #A$-f a fi.e) mass of gas (ith a ressure P1 an) a temerature $1 changes to a ressure P2 an) temerature $2 (ith no change of +olume this can *e (ritten as/ $he +ariation of the ressure of the air (ith temerature is sho(n in the grahs *elo(. @08/12/15 110!AR#ES, #A$$he caillary tu*e has a small lug of concentrate) sulhuric aci) lace) in it an) it is then seale) at the other en). 0-t is most imortant that aroriate safety recautions are ta&en (hen carrying out this e.eriment. Aour eyes must *e rotecte).1 $he (ater in the *ea&er is heate) an) the length of the trae) air column an) the temerature are *oth recor)e).#esults of this e.eriment sho( that for a fi.e) mass of gas at constant ressure. ?aillary tu*e08/12/15 12%ARIATI&' &( %)ME $IT! TEMPERAT)RE -f a fi.e) mass of gas (ith a +olume !1 an) a temerature $1 changes to a +olume !2 an) temerature $2 (ith no change of +olume this can *e (ritten/ an) 7 constant08/12/15 13"asBhen (or&ing (ith gases (e referre) to (or& (ith a quantity calle) the num*er of mole rather than mass of gas.9*solute temerature/ $/K " 0? C 283

08/12/15 14Definition1 mole 0or mol1 is the amount of su*stance, (hich contains as many elementary units or entities as there are atoms in 12g of 12?.e.g. 1 mole " 2 g of '2" 32 g of o.ygen gas.0entities many *e atoms, molecules, ions, electrons or other articles1.Avogadro constant 0>, %91 is the num*er of atoms in 0.012 &g of car*on312.%9 " 2.02 . 1023 mol31-f there are % molecules in a container, then the num*er of mole of the su*stance isANNn =08/12/15 15Molar mass$he molar mass 07r1 is )efine) as the mass of one mole of the su*stance unit / g mol31 e.g. molecular mass of 12? " 12 g mol31Dor 7 &g of a su*stance of molar mass 7r, the num*er of mole,rMMn=E1ample 11.112g of car*on312 contains 2.02 . 1023 atoms. ?alculate 0a1 the mass of one car*on 3 12 atom an) 0*1 the a+erage mass of a nucleon 0$his is the atomic mass unit1. 09 nucleonis a article foun) in the nucleus namely roton or neutron1. 09ns. 1.44 . 10322 &g, 1.22 . 10328&g1a1 2.02 . 1023 atoms has a mass of 12 gmass of one atom*1 there are 12 nucleons in the nucleus.mass of nucleon08/12/15 12kg xxg2210 02 . 21210 99 . 12= =kg xx231210 99 . 110 22 . 122= =ANNn =Example 11.2?alculate a1 the num*er of atoms in 0.3 g of lithium 0 8>i1, an)*1 the num*er of moles of lithium. 09ns. 2.58 . 1022 atoms, 0.043 mole1 a1 8 g of >ithium contains 2.02 . 1023 atoms.0.3 g contains*1 no. of moles " 0.3/8 " 0.04308/12/15 18atoms xx22210 45 . 23/. 0 . 10 02 . 2==rMMn=08/12/15 18E6uation of state .Ideal gas e6uation /p% 7 nRT?om*ining the equations P! " constant, P/ $ " constant an) !/ $ " constant gi+es/ Dor 1 mole of gas the constant is &no(n as the molar gas constant (R) %o( the +olume of one mole of an i)eal gas at Standard Temperature and Pressure (STP) 01.014.105 Pa an) 283.15 K1 is 0.0224m3 an) so1.014.105 . 0.0224 " 1 . # . 283.15 an) therefore # " 8.314 EK31mol31.Fgi+en in GH9$9 S'EE$IJconstantTpV=! " #$08/12/15 14Ideal gas e6uation .alternati8e/! " % & $ & " :oltKmannIs constant " #/%9 " 8.31/2.02.1023

" 1.38.10323 E K31% " num*er of moleculesF!alues gi+en in GH9$9 S'EE$IJHeri+ation! " n#$ " ! " % & $ 22 211 1TV pTV p=RTNNpVA=$hat is an ideal gas99n ideal gas is one that o*eys the gas la(s, an) equation of state for i)eal gas, at all temerature, ressure an) +olume.E.amles are o.ygen an) nitrogen near room temerature, car*on )io.i)e gas can *e liquefy near room temerature, thus )oes not o*ey :oyleIs la(.Many gases at room temperature and moderate pressure behave as ideal gas.08/12/15 20$hat is an ideal gas9$he internal energy 0L1 is entirely &inetic energy, an) )een)s on its a*solute temerature. L " 3/2 %&$ $he *eha+iour of real gas 0an) unsaturate) +aour1 can *e )escri*e) *y ! " n#$ if they are at lo( temerature (hich are (ell a*o+e those at (hich they liquefy.08/12/15 2108/12/15 22Example 11.39 +olume 250 cm3 of gas is trae) in a cylin)er close) *y a smooth iston, at a ressure of 1.2 . 105 Pa. $he iston is ushe) in slo(ly until the +olume of gas is 150 cm3, (hat is the ne( ressure.09ns. 2.0 . 105 Pa1SolutionPushe) in slo(ly means the temerature is constant.V = pV1.2 . 10502501 " p 150p = 2.0 . 105 Pa08/12/15 23Example 11.4 9 uniform caillary tu*e is close) at one en) *y a threa) of mercury of length 4.0 cm Bhen the tu*e is lace) horiKontally the column of air has a length of 12 cm. $a&e the atmosheric ressure to *e 82 cm'g.$he tu*e has a cross3sectional area of20 cm2.a1Bhat is the ressure of the trae) airMSolution' " atmosheric ressure " 82 cm'g9 " 20 cmV= 12A cma1 = pressure of trapped air = 76 cmHg to t!e rig!t e"uals t!e atmosp!eric pressure to t!e left#4.0 cm 12 cmtrae) airthrea) of mercury'08/12/15 24Example 11.4 *1 Bhen the tu*e is hel) +ertically,i1 (ith the oen en) u(ar)s, (hat is the length of the column of trae) airM 9 " cross3sectional area of tu*e!= A$p = H % & # = '( cmHgp supports t!e mercur) t!read a*d atmosp!eric pressure#V = pV7612A# = '(A$$ = 11.& cm4.0 cm'>08/12/15 25Example 11.4 ii1 Bith oen en) )o(n(ar)sMp+ % & = Hp+ = 76 , & = 72 cmHgatmosp!eric pressure supports t!e mercur) t!read a*d trapped gas#V = p+V+7612A# = 72A $+#$+ = 12.7 cmc1 -f the temerature of the gas is 280?, calculate the num*er of mole of gas enclose). +'>+. 10 95 . 9/ 23 23 . 1 . 5/ 10 . 20 / 12 . 0 . 10 01 . 1

: 4mol xxRTpVn=+==Example 11.59 mass of car*on )io.i)e occuies 15.00 m3 at 100? an) 101.48 &Pa.a1 Bhat (ill *e its +olume at 40.00? an) 102.23 &PaM?alculate*1the num*er of mole of gas,c1 the num*er of molecules of gas an) )1 the mass of gas if the molar mass of ?@2 is 44 g.09ns. a1 15.4m3, *1251,c1 3.45 . 1022 molecules,)1 2.82 . 104 g1Solutiona1!2 "15.4m3 *1" 251 moles 08/12/15 22/ 10 23 ./ 14 . 93 . 101/ :0 23 .2 . 102211 122 2+=+=VTV pTV p/ 10 23 . 1 . 5/ 14 . 10 93 . 101

+==xnRTpVExample 11.5c1 1 moles contains 2.02 . 1023 molecules 251 moles contains 251.2.02 . 1023 " 3.42 . 1022 molecules)1 mass of gas" 2510441 " 2.82 . 104 gANNn =rMMn=Example 11.6$(o flas&s ha+ing equal +olumes are connecte) *y a narro( tu*e (ith a ta (hich is close). $he ressure of air in one flas& is )ou*le the other. 9fter the ta is oene) the common ressure in the flas&s is 120.0 &Pa. Din) a1 the num*er of moles of gas use) if +olume of each flas& is 5.2 m3 at temerature 200? an)*1 the original ressure in the flas&s.09ns.a1 552 mol. *180.0&Pa,120.0&Pa108/12/15 28;al;ulationsa1 total num*er of moles " 552 mol*1 conser+ation of mass or num*er of moles

1 " 80.0&Pa

2 " 120 &Pa5.2 m35.2 m3200?200?Dinal ressure "120.0 &Pa

121/ 20 23 . 1 . 52 . 4 / 10 120 . 2 2

+= =xRTpV442/ 20 23 . 1 . 5/ 42 . 2/ 20 23 . 1 . 5/ 42 .1 1=+++p p08/12/15 30Real gases .info./$he i)eal gas *eha+iour an) the relationshi *et(een , ! an) $ are *ase) on e.erimental o*ser+ations of gases such as air, helium, nitrogen at temeratures an) ressures aroun) room temerature.-n ractice, if (e change to more e.treme con)itions, such as lo( temeratures an) high ressures, gases start to )e+iate from these la(s as gas atoms e.ert significant intermolecular forces on each other.08/12/15 31'itrogen .info./Bhat haen (hen nitrogen is coole) )o(n to(ar)s a*solute KeroMDirst a follo( a goo) straight line at high temerature.9s it aroaches the temerature at (hich it con)enses it )e+iates from i)eal *eha+iour, an) at 88 K it con)enses to *ecome liqui) nitrogen.!olume$/K100 200 300 8808/12/15 32The ecture04.htm ressure+olume08/12/15 35Real gases VERY RARELY BEHAVE LIKE IDEAL GASES sin;e $here IS an attraction *et(een article 0+an )er Baals forces1 $he +olume of articles are !T negligi*le, es. at lo( tems N high3ressure since atoms/molecules are close together "#$R!%& an) "&LI'( are the most I$&)L gases.9lso, Hiatomic molecules an) nonsymmetrical molecules N no*le gases act the most i)eal. $'E S79>>E# $'EA 9#E $'E 7@#E -HE9> $'EA :E'9!E. 08/12/15 32Summar+ 08/12/15 38Intermole;ular for;es-n a soli), the molecules are *on) together as if they are connecte) *y srings. $he molecules are in ran)om +i*ration an) the temerature of the soli) is a measure of the a+erage &inetic energy of the molecules. 08/12/15 38#ud-ig *olt=mann(as *orn in 1844 09ustria1. :oltKmann (as a(ar)e) a )octorate from the Lni+ersity of !ienna in 1822 for a thesis on the &inetic theory of gases suer+ise) *y Eosef Stefan. 9fter o*taining his )octorate, he *ecame an assistant to his teacher Eosef Stefan. :oltKmann taught at 6raK, mo+e) to 'ei)el*erg an) then to :erlin. -n these laces he stu)ie) un)er :unsen, Kirchhoff an) 'elmholtK. O.9ttac&s on his (or& continue) an) he *egan to feel that his life=s (or& (as a*out to collase )esite his )efence of his theories. Heresse) an) in *a) health, :oltKmann committe) suici)e , containing % articles 0monatomic1 each of mass m.chsfc5.chem.ncsu.e)u/.../lecture/--/--.html > < =2

1cVNmp.yK>>>08/12/15 480hange in momentumDor a molecule, ?hange in momentum, " m 0- P u1 " 3 2mu$he time for the article to imact the same face of the (all ist " 2>/u 0as see) " )ist./time1Dorce on article, mass " mu " u- " 3 u(all of container+ectorLmuu LmutpF2A 22 = ==08/12/15 48Pressure9ssumtions11 9ll the molecules ha+e the same +elocity.21 9ll molecules mo+e in the .3)irectionDorce on (all *y % moleculesDorce on (all " 3 force on article 0%$>@71.Pressure on (all " D$/9 " %mu-$p = .mu-V/!ere V = $0orrecti*g for assumptio*s 1# i* ge*eral t!e molecules ca* !a1e a*) 1elocit) i* a*) directio*22# 34+ of t!e molecules mo1e i* a*) of t!e t!ree directio*spV = 34+ .m5c6LNmuNF FT2= =08/12/15 44Pressure e1erted < =2

1cVNmp41 State the *asic assumtions of the &inetic theory of gases.51 State the meaning of each of the sym*ols in the equation.Bhat is the significant of T m Qc6>6# 0a* /e sa) t!at si*ce )esterda) t!e temperature /as 1(?0 a*d toda) t!e temperature is 2(?02 t!e* toda) is t/ice as !ot>51 m" mass of article, Qc6= mea* s"uare speed@ A = BoltCma** co*sta*t@ < =2

1cVNmp9ns. 908/12/15 22P?P 11.2 $he simle &inetic theory of gases may *e use) to )eri+e the e.ression relating the ressureto the )ensity of gas.-n this e.ression, (hat )oes Qc6 represe*t>A. t!e a1erage of t!e s"uares of t!e speeds of t!e gas moleculesB. t!e rootEmea*Es"uare speed of t!e gas molecules0. t!e s"uare of t!e a1erage speed of t!e gas moleculesF. t!e sum of t!e s"uares of t!e speeds of t!e gas molecules. > < =2

1c p 9ns. 9> < =2c crmsQc;Sc S C c S C c S C OO c +nS08/12/15 23P?P 11. $he molecules of an i)eal gas at thermo)ynamics 0a*solute1 temerature $ ha+e a root3mean3square see) cr.$he gas is heate) to temerature 2$.Bhat is the ne( root3mean3square see) of the moleculesMSolutionm an) & are constant>et the ne( root3mean3square see) *e .Qc6-< = co*sta*tcr-< = G-2 < =2

1cVNmpt u v mF=/ .kT c m2

221= >