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Thermal properties

Thermal properties. Y ou should be able to : - s tate the basic definitions of calorimetry , such as specific heat capacity and specific latent heats of fusion and vaporization ; - understand why temperature stays constant during a phase change ;

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Thermal properties

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  1. Thermalproperties Youshouldbeableto: -statethebasicdefinitions of calorimetry, such as specificheatcapacity and specificlatentheats of fusionand vaporization; -understandwhytemperaturestaysconstantduring a phasechange; -outlinemethodsfordeterminingspecific and latentheatsexperimentally; -solvecalorimetryproblemsusingQ=cmΔT and Q=mL; -statethefactorsthataffecttherate of evaporation and distinguishbetweenevaporationfromboiling; -appreciateBoltzmann’sequation, the fundamental relationshipbetweenabsolutetemperature and theaveragekineticenergy of themolecules.

  2. Specificheatcapacity Whenheatisprovidedto a body, thetemperature of a bodywill, in general, increase. Theamount of heatneededtoraisethetemperature of a mass of onekilogram of a substancebyone kelvin iscalledthespecificheatcapacity of the material. Toraisethetemperature of a massmbyΔTkelvins, theamount of heatrequiredistherefore Q = cm ΔT. Theunits of specificheatcapacity are J/kgK

  3. Heatcapacity Theproductof mass times thespecificheatcapacity defines de heatcapacityof a body C = mc, and therefore, Q = C ΔT. Heatcapacityistheamount of heatrequiredtochangethetemperature of a bodybyone kelvin. The concept of heatcapacityisusefulwhen a bodyconsists of a number of parts of differentspecificheatcapacities C = Mc + mc’

  4. Examplequestions When a car brakes, anamount of heatequalto 112,500 J isgenerated in thebrakedrums. Ifthemass of thebrakedrumsis 28 kg and theirspecificheatcapacityis 460.5 J/kgK, whatisthechange in theirtemperature? A radiatormadeout of iron has a mass of 45 kg and isfilledwith 23 kg of water. Whatistheheatcapacity of thewater-filledradiator? Ifheatisprovidedtotheradiator at therate of 450 W, howlongwillittaketothetemperaturetoincreaseby 20°C?

  5. Calorimetry Heatflowsfromhotbodiesintocoldbodies. Theamount of energy (heat) lostbythehotbodyisequaltotheamount of energy (heat) gainedbythecoldbody. Ifthereisinterchange of heatbetweentwoor more bodies, then Q1 + Q2 + Q3 +…+ QN = 0

  6. Examplequestion A piece of iron of mass 200 g and temperature 300°C isdroppedinto 1 kg of water at 20°C. Whatwillbethe eventual temperature of thewater? (Takecforiron as 470 J/kgK and forthewater as 4200 J/kgK)

  7. Phasestates • Kinetictheorybasicassumptions: • Allmatteriscomposed of extremelysmallparticles • Allparticles are in constantmotion • Ifparticlescollidewithneighbouringparticles, they conserve theirkineticenergy • A mutual attractiveforceexistsbetweenparticles. There are fourstates (phases) of matter: solids, liquids, gases and plasma.

  8. Macro and microscopicproperties Somemacroscopiccharacteristics of solids, liquids and gases Somemicroscopiccharacteristic of solids, liquids and gases

  9. Phasestates Solids.Theparticles are closelypacked and eachparticleisstronglybondedtoitsneighbour and isheldfairlyrigidly in a fixed position togiveitdefiniteshape in a crystallinelattice. Somepatterns are disordered as isthe case forceramics, rubber, plastics and glass. Thesesubstances are saidtobeamorphous. Theparticleshavevibrationalkineticenergy in theirfixed positions and theforce of attractionbetweentheparticlesgivesthempotentialenergy. Liquids.Theparticles are stillcloselypacked and thebondingbetweenparticlesisstill quite strong. However, they are notheld as rigidly in position and thebonds can break and reform. Thisinfersthattheparticles can slowly and randomlymoverelativetoeachotherto produce variable shape and slowdiffusion. Particles in a liquidhavevibrational, rotational and sometranslationalkineticenergyduetotheirhigher mean speeds. Thepotentialenergy of theparticles in a liquidissomewhathigherthanfor a solidbecausethespacingbetweentheparticlesislarge.

  10. Phasestates Gases. Theparticles are widelyspaced and theparticlesonlyinteractsignificantlyoncollisionorverycloseapproach. Because of therapidzig-zagmotion of theparticles, a gas willbecomedispersedthroughoutanycontainerintowhichitis placed. Diffussion can occurreadily. Gases are compressiblebecausetheparticles are widelyspaced at a distancemuchgreaterthanthesize of theparticles. Themuchhigger mean speeds are duetoanincreasedtranslationalkineticenergy of theparticles. Gases have a muchhigherpotentialenergythanliquidsbecausetheparticles are muchfurtherapart.

  11. Phasechanges A substance can undergochanges of stateorphasechanges at differenttemperatures. Puresubstanceshavedefinitemelting and boilingpointswhich are characteristic of the particular puresubstancebeingexamined. Whenthesolidisheatedthetemperaturebeginstorise. Whenthetemperaturereachesitsmeltingpoint, thesubstancebeginstomelt. Althoughheatingcontinuesthetemperature of thesolid-liquid mixture remainsconstantuntilallthesubstance has melted. Once allthesubstance has meltedthetemperaturestartstoriseuntiltheliquidbeginstoboil. Withcontinuedheatingthetemperatureremainsconstantuntilalltheliquid has beenconvertedtothegaseousstate.

  12. Molecular behaviour Whenthesolidisheatedtheparticles of thesolidvibrate at anincreasingrate as thetemperatureisincreased. Thevibrationalkineticenergy of theparticleincreases. At themeltingpoint a temperatureisreached at whichtheparticlesvibratewithsufficientkineticenergyto break fromtheirfixed positions and beginto slip overeachother. As thesolidcontinuestomelt, more and more particlesgainsufficientenergytoovercometheforcesbeweenparticles and over time allthesolidparticleschangeto a liquid. Thepotentialenergy of thesystemincreases. As heatingcontinuesthetemperature of theliquidrisesduetoanincrease in thevibrational, rotational and parttranslationalkineticenergy of theparticles. At theboilingpoint a temperatureisreached at whichtheparticlesgainsufficientenergytoovercometheinterparticleforcespresent in theliquid and scapeintothegaseousstate. Continuedheating at theboilingpointprovidesthepotentialenergyneededforallthemoleculestobeconvertedfrom a liquidto a gas. Withfurtherheatingthetemperatureincreasesduetoanincrease in thekineticenergy of thegaseousmoleculesduetothelargertranslationalmotion.

  13. Latentheat Theheatrequiredtomeltonekilogram of substance at itsmeltingpointiscalledthelatentheat of fusion, Lf.Theheatrequiredtovaporiseonekilogramof substance at itsboilingpointiscalledthelatentheat of vaporisation, Lv. Thustomeltorvaporisea quantity of mass m, werequire a quantity of heat Q = mLf and Q = mLv, respectively. Thelatentheatunitis J/kg

  14. Examplequestion An ice cube of mass 25 g and temperature -10°C isdroppedinto a glass of water of mass 300 g and temperature 20°C. Whatisthetemperatureeventually? (Specificheatcapacity of ice = 2200 J/kgK; latentheat of fusion of water = 334 kJ/kg.)

  15. Evaporation and boiling A substance at a particular temperature has a range of kineticenergies. So in a liquid at any particular instant, a smallfraction of themoleculeswillhavekineticenergiesconsiderablygreaterthantheaveragevalue. Iftheseparticles are nearthesurface of theliquid, theymayhaveenoughkineticenergytoovercometheattractiveforces of neighbouringparticles and escape fromtheliquid as a vapour. Theprocess of evaporationis a changefromtheliquidstatetothegaseousstatethatoccurs at a temperaturebelowtheboilingpoint.

  16. Evaporation and boiling Whenthe more energeticparticleshaveescaped, theaveragekineticenergy of theremainingparticles in theliquid has beenlowered, whichimplies a lowertemperature. Thisphenomenoniscalledevaporativecooling. A substancethatevaporatesrapidlyissaidtobe a volatileliquid. A liquid’svolatilityiscontrolledby a factor known as itsequilibrium vapor pressure. Differentliquidsexertdifferentvapourpressuresthatdependontherelativestrengths of the intermolecular forcespresent in theliquids.

  17. Kineticmodel of an ideal gas Theproperties of gases can beunderstood in terms of a simple buteffectivemechanicalmodel. The gas consists of a verylargenumber of moleculesmovingrandomlyaboutwith a range of speeds and collidingwitheachother and thecontainerwalls. We can make a model of thisbymakingcertainassumptions: A gas consists of a largenumber of molecules. Moleculesmovewith a range of speeds. Thevolume of themoleculesisnegligiblecomparedwiththevolume of the gas itself. Thecollisions of themoleculeswitheachother and thecontainerwalls are elastic. Moleculesexert no forcesoneachotherorthecontainerexceptwhen in contact. Theduration of collisionsisverysmallcomparedwiththe time betweencollisions. ThemoleculesobeyNewton’slaws of mechanics.

  18. BoltzmannLaw Usingthisassumptions: Wecallvtheroot mean squarespeed o rmsspeed. Itisnottheaveragespeed of themolecules. Wherethespeedvisdefinedby k iscalledtheBoltzmannconstant and has a value of 1.38 x 10-23 J/K Theabsolutetemperatureis a measure of theaveragekineticenergy of themolecules of a substance.

  19. Molecular explanation of pressure Thepressure of a gas originatesfromthecollisions of themoleculeswiththewalls of itscontainer. At everycollision, eachmolecule has itsmomentumchanged and so a forceactsfromthewallontothemolecule. ByNewton’sthirdlaw, themoleculeexertsanequal and oppositeforceonthewall. The total forceduetoallthecollidingmoleculesdividedbytheareaoverwhichtheforceactsgivesthepressure of the gas.

  20. Boyle-Mariottelaw TheparametersP, V, T and n are relatedtoeachother. Theequationrelatingthemiscalledtheequation of state. At constanttemperature and with a constantquantity of gas, pressureisinverselyproportionaltovolume, thatis PV = constant.

  21. Charles law At constantpressure, itisfoundthatthevolumeincreasesuniformlywithtemperature V/T = constant

  22. Gay-Lussaclaw At constantvolume, itisfoundthatthevolumeincreasesuniformlywithtemperature P/T = constant

  23. Theequation of state Ifwe combine thesethreelaws, weseethat PV/T = constant Itwasalsodiscoveredthat PV/T = n x constant Itwasfoundthatthisconstant has thesamevalueforall gases R = 8.31 JK-1mol-1 Then, PV = nRTorPV = NkT k = R/NA

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