1 CHAPTER 3 TEMPERATURE

Transcription

1 1 CHAPTER 3 TEMPERATURE 3.1 Inrducin During ur sudies f hea and hermdynamics, we shall cme acrss a number f simple, easy-undersand erms such as enrpy, enhalpy, Gibbs free energy, chemical penial and fugaciy, and we expec have n difficuly wih hese. There is, hwever, ne cncep ha is really quie difficul grasp, and ha is emperaure. We shall d ur bes undersand i in his chaper. 3.2 Zerh Law f Thermdynamics Perhaps he simples cncep f emperaure is regard i as a penial funcin whse gradien deermines he direcin and rae f flw f hea. If hea flws frm ne bdy anher, he firs is a a higher emperaure han he secnd. If here is n ne flw f hea frm ne bdy anher, he w bdies are in hermal equilibrium, and heir emperaures are equal. We can g furher and asser ha If w bdies are separaely in hermal equilibrium wih a hird bdy, hen hey are als in hermal equilibrium wih each her. Accrding ase, yu may regard his as a ruism f he ums rivialiy r as a fundamenal law f he ms prfund significance. Thse wh see i as he laer will refer i as he Zerh Law f Thermdynamics (alhugh he "zerh" des sund a lile like an admissin ha i was added as an aferhugh he her "real" laws f hermdynamics). We migh imagine ha he hird bdy is a hermmeer f sme sr. In fac i need n even be an accuraely calibraed hermmeer. We inser he hermmeer in ne f ur w bdies (we are n hinking paricularly f human bdies here), and i indicaes sme emperaure. Then we inser i in he secnd bdy. If i indicaes he same emperaure as indicaed fr he firs bdy, hen he Zerh Law assers ha, if we nw place ur w bdies in cnac wih each her, here will be n ne flw f hea frm ne he her. There exiss sme measure which all hree bdies have in cmmn and which dicaes ha here is n ne flw f hea frm any ne any her, and he hree bdies are in hermal equilibrium. Tha measure is wha we call heir emperaure. T sme, his will sund like saying :"if A and C are a he same emperaure, and if B and C are a he same emperaure, hen A and B are a he same emperaure". Ohers, f philsphical ben, may wan pursue he cncep greaer rigur. In any case, a whaever level f rigur is used, wha he Zerh Law esablishes is he exisence f sme quaniy called emperaure, bu i desn' really ell us hw define a emperaure scale quaniaively. I is as if we have esablished he exisence f smehing called "lengh" r "mass", bu we haven' really specified ye hw measure i r wha unis express i in. We culd, fr example, discuss he cnceps f "lengh" r f "mass" by describing a es shw wheher w lenghs, r w masses, were equal, bu wihu

2 2 develping any unis fr expressing such cnceps qualiaively. Tha, I hink, is where he Zerh Law leaves us. 3.3 Temperaure Scales (1) In everyday pracice, we use eiher he Celsius r he Fahrenhei emperaure scales, depending n wha we are used, r he fashin f he day, r wha ur Gvernmen ells us we shuld be using. In he Fahrenhei scale, he freezing pin f waer is 32 F and he biling pin is 212 F, s ha here are 18 F beween he w fixed pins. In he Celsius scale, he freezing pin f waer is Cand he biling pin is C, s ha here are C beween he w fixed pins. (When Celsius riginally inrduced his scale, he se he emperaure f biling waer as, and he emperaure f meling ice as. Tha was reversed wihin a few years!) The Celsius scale was frmerly called "he" cenigrade scale, bu presumably any scale wih degrees beween w fixed pins culd be called a cenigrade scale, s we nw call i (r are suppsed call i) he Celsius scale. Cnversin is bviusly by F = 18. C and C = F = ( F 32) Ne ha "a emperaure f s many degrees n he Fahrenhei scale" is wrien F and "a emperaure f s many degrees n he Celsius scale" is wrien C; whereas "a emperaure inerval f s many Fahrenhei degrees" is wrien F and "a emperaure inerval f s many Celsius degrees" is wrien C. In eiher case, he degrees symbl ( ) is mandary. In scienific wrk, we generally use he Kelvin emperaure scale. The w fixed pins n he Kelvin scale are he abslue zer f emperaure, which is assigned he emperaure K, and he riple pin f he waer-ice-seam sysem, which is assigned he emperaure K. Thus i culd reasnably be said ha he Kelvin scale is n a cenigrade scale, since i desn' have degrees beween is w fixed pins. Hwever, he size f he degree n he Kelvin scale is alms exacly he same as he size f he Celsius degree, because he abslue zer f emperaure is abu C and he emperaure f he riple pin is abu.1 The definiin f he Kelvin scale, hwever, des n menin he Celsius scale, and herefre, alhugh he size f he degrees is abu he same n bh scales, his is n inheren in he definiin. One migh speculae abu wha migh happen in he far disan fuure if peple n lnger use he Celsius scale and i is ally frgen. Peple hen will wnder wha pssessed us divide he Kelvin scale in divisins beween is w fixed pins! I wuld n be gd enugh define he upper fixed pin f he kelvin scale as he emperaure f "meling ice", because his depends n he pressure. The riple pin is he emperaure a which ice, waer and seam are in equilibrium, and i ccurs a a emperaure f abu.1 C and exacly K, and a pressure f abu 61.6 Pa.

3 3 The Kelvin scale sars a zer a he lwes cnceivable emperaure. The kelvin (K) is herefre regarded as a uni f emperaure, much as a mere is regarded as a uni f lengh, r a kilgram as a uni f mass. One herefre des n alk abu a emperaure f s many "degrees Kelvin", any mre han ne wuld alk abu a lengh f s many "degrees mere" r a mass f s many "degrees kilgram". When using he Kelvin scale, herefre, we alk simply f a emperaure f "28 kelvins" r "28 K". We d n use he wrd "degree", nr d we use he symbl. In he Briish Engineering Sysem f unis, which is used exclusively in he Unied Saes and has never been used in Briain, he Rankine scale is used. The lwer fixed pin is he abslue zer f emperaure, and i is assigned he emperaure R, and he size f he rankine is equal he size f he Fahrenhei degree. Meling ice a C has a emperaure f R, and he riple pin has a emperaure f R. I dub wheher he Réaumur scale has been used anywhere in he las 5 years, bu i has prbably been used in he las. This had meling ice a R and seam a 8 R. I menin his nly pin u ha if yu see a emperaure given as s many R, yu migh n knw wheher he Rankine r Réaumur scale is inended! (Sricly, R wuld dene degrees Réaumur, while R wuld dene rankines bu can yu rus ha?) In hese nes, he Kelvin scale will be he scale ha is nrmally used. There may be ccasinal use f he Celsius scale, bu we shall n use he Fahrenhei, Rankine r Réaumur scales. 3.4 Temperaure Scales (2) We nw knw by definiin he emperaures a he w fixed pins n he Celsius and Kelvin scales. Bu wha abu emperaures beween he fixed pins? We culd say ha he emperaure halfway beween he meling pin f ice and he biling pin f waer is 5 ºC, r we culd divide he emperaure beween he w fixed pins in equal inervals. Bu: Wha d we mean by halfway r by equal inervals in such a prpsal? This leaves us raher sumped. Here is ne suggesin. We culd cnsruc a glass capillary ube wih a bulb a he bm cnaining mercury, which als exends a shr way up he capillary. We culd ne he lengh f he mercury clumn when he ube was immersed in meling ice and call he emperaure ºC, and again when i is in biling waer ( ºC). We culd hen divide he lengh f he ube beween hese w marks in equal inervals f lengh, and use ha define ur emperaure scale. Bu yu may ask: Hw d we knw ha mercury expands (relaive glass) unifrmly wih emperaure? Well, i expands unifrmly, by definiin, wih emperaure n he mercury-in-glass emperaure scale. Indeed, we can define he emperaure in he mercury-in-glass scale by l l = l l

4 4 (I am ging use he symbl T in hese nes fr emperaure in kelvin. Here I am using fr emperaure n he Celsius scale.) If we place he hermmeer (fr such i is) in a bwl f warm waer, and he lengh f he mercury clumn is halfway beween l and l, we culd say ha he emperaure f he waer in he bwl is, by definiin, 5 ºC n he mercury-in-glass scale. Nw le us repea he experimen wih anher ype f hermmeer, using sme differen prpery f maer which is als knwn vary wih emperaure. We migh chse, fr example, use he elecrical resisance R f a lengh f plainum wire; r he hermelecric penial difference V ha appears when we hea he juncin f w differen meals; r he pressure P f sme gas when i is heaed up bu kep a cnsan vlume. We culd ry immersing each f hese hermmeers in meling ice and biling waer and we culd inerplae linearly fr inermediae emperaures. Thus, using he resisance f he plainum wire, we culd define a plainum resisance emperaure scale by R R = R R Or we culd define a hermelecric emperaure scale by V V = V V Or we culd define a cnsan vlume gas emperaure scale by P P = P P Bu wha assurance d we have ha all f hese emperaure scales are he same? Wha assurance d we have ha he resisance f plainum increases linearly n he emperaure scale defined by he mercury-in-glass hermmeer? Wha assurance d we have ha, when we immerse all f hese hermmeers in he waer ha regisered 5 ºC fr he mercury-in-glass hermmeer, hey will all regiser 5 ºC? The answer is ha we have n such assurance. Wha we need d is eiher chse ne paricular phenmenn quie arbirarily use fr ur sandard emperaure scale, r smehw define an abslue emperaure scale which is abslue in he sense ha i is defined independenly f he prperies f any paricular subsance. I urns u ha i is pssible d he laer, and define a emperaure scale ha is abslue and independen f he prperies if any paricular subsance by means f an idealized hereical cncep called a Carn Hea Engine. This imaginary engine uses as is peraing medium an equally imaginary subsance called an ideal gas, and indeed he emperaure indicaed by a cnsan vlume gas hermmeer is idenical he abslue emperaure defined by a Carn engine prvided ha he

5 5 gas used is an ideal gas! The bes ha can be said fr real gases is ha, a lw pressures, hey behave very much like an ideal gas; and indeed if yu smehw exraplae he behaviur r a gas is behaviur a zer pressure (when here isn any gas a all!), i wuld behave exacly like a real gas. Unil we have discussed wha are mean by a real gas and by a Carn engine, all his has served d is underline wha we said in he Inrducin his chaper namely ha here are a number f relaively easy cnceps in hermdynamics, bu emperaure is n ne f hem. If we d evenually undersand wha a Carn engine is and we can cnsruc in ur minds a definiin f wha is mean by an abslue emperaure scale, here will remain he prblem f reprducing such a scale in pracice. Tha is he purpse f he Inernainal Temperaure Scale 199 (ITS9). On his scale a number f fixed pins, such as he riple pin f hydrgen he riple pin f nen he riple pin f waer he freezing pin f zinc he freezing pin f silver he freezing pin f gld ec., are assigned cerain values. In he cases f he six pins lised, hese values are kelvin respecively. A number f sandard insrumens are be used in differen emperaure ranges, wih defined inerplain frmulas fr emperaures beween he fixed pins. A cmplee descripin f ITS9 wuld be raher lenghy (see, fr example, hp:// bu is purpse is reprduce as precisely as pracically pssible he abslue emperaure scale as defined by he Carn engine.