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The Thermodynamics of Systems at Negative Absolute Temperatures

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The Thermodynamics of Systems at Negative Absolute Temperatures Articles Ilidiall Journal ofChclllical Tcc hn ology Vol. tJ, S.:plclllbcr 2002, pp, 402-406 , , I The thermodynamics of systems at negative absolute temperatures Jaime Wisniak'" I kparlmclli or Chcmic" En gi nceri ng, Ikn-C/urion Uni \ c r ~ il y or Ihe Negc\', Beer-She\',:. Israel X4 10) Ueceil'cd 27 Jill.'" 2001 : IIIH'fI/('d II MOl' 2002 The application of the laws of thermodynamics is a nalyzed fOl' the case that a system exists in the domain of ncgatiyc ahsolute tcmpcrature, It is shown thaI irreversible proccsses arc accompanied by an increase in cntropy, but that it is possihlc to l'onvcrt heat totally into work. In addition, it is impossihlc to convert work totaHy int o heat and work llIust hc added to the S)'stCIll to transfer thermal energy frolll a cold source to a hot one. ' Thc possihility of the cx istence of ncgative absolutc AllyIH)\\ . it i <; o f intcres t to di,>cuss hO\\ th c L aws 0" tcmpcraturcs has bccn discussed In a prc\ IOU'> th crlllodynamic'. appl) to the'.c si tuations an d ir the publicati on I, It ha s bccn shown that for ordinary propn ti cs or thc,c sy <.,[c ms bcha vc in thc salllL' '>\ ~ t CIll thc ahsol utc tcmpcraturc lllU <., t hc pos itive IllallIlL'1 as to thc (lIlC, Ihat h:l \'C pos iti vc tem peraturc, bccausc It ha'> an UPP C! hllUI1l! tll cllcrgy, II()\\L'\ n. 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'. - I 00 ... - \( I..... - I . -() I, arl' ahout 10 ' S, \\ hill' CI') stal "pill-Ja1licc rcia.\atidll It must hc ulltkrqll()d thai the Zerotll and thl' Fil"-l tllllC arc at least ~()() s, II \\ ill ta\... ' hct \\ CL'1l ri \ L' to I ,a\\ or tl1L'rmlld) n:lmic'> apply ~quall) tt' hoth thin) millutcs ulltil thc Spill '.uh'.) "kill \\ ill rctllrII to tcmpc raturc dClmai n\ hcc,l lI '>e th ey are indepelldcnt 01 the rmal cqu ilibriu m with th e maill '.y'>tcm'l th c sign or thc te mperat urc, The Zcroth L I\\ It Gill be said that the Ilcgati vc tcmpcralLlrc CO llCL'p t d e tcrmin e~ that t\\ () sv ... tcm ,> are In thermal lllay bc applicd to thc cspeci al ca-; c ,> wherc thc equ ilibrium w hen th cy ha ve thc sa me temperaturL'. addition of cllerg) rrom Il 'illuml crcatl'S a pse udo­ and the First Law represents the encrgy halanee shcct cCJuilih riulll subsystem or illvcrtcd Icvek Whether it or the change, is appropriate to u <; e the term negati vc temperature or Now {'oliowing three statcments of thc Second L I\\ pscudo-temperaturc is a question of terminology, ot sha ll be investigated: olll) that, Ilowadays masers ane! lasers are best (a) Heat flows spontaneously from a hot s()urce to a approximated as thermodYIlamic systems that ex ist at cold one (Clausius) or, it is impo sible to const ruct an llegative absolute temperalLlres 5 A lso. at negati e engine th at operat es in a reversible manner and the ahso lutc temperatures most res ista nces are negati ve . so le effect or its operation is th e transfer of hea t from thu s an elec tro magnetic wave wi ll be amplified a cold to a hot source, instead o f being absorbed, (b) It is imposs ible to con. truct an engine that withdraws heat from a th ermal so urce and converts it ", For corrc;. poncl l:ncc: (E-mail : wi slliak @hglllllail. bg u.ac.il) completel y into work, Wi sniak: TherlllUllynalllic~ of systems at negati ve absolute temperatures Articles (c) Any irreversible cha nge in an iso lated sys tem has been added) it must be that dSi,rel' > 0, th e same as res ults in an increase in th e entropy of the system. in the domain of positive absolute tem perat ures. It can Ba se d on th e definition or heat given above, clea rl y th en be generally sa id that entropy will always th e fi rst part or statement (a) is also rul fi lied in th e Increase during a process that takes place in an nega ti ve temperature domai n if the hotter source is iso lated sys tem, independen t of th e sign of th e defined as the one having the highest o"solilte va lue absolute temperature. Hence. in th e domain of or th e tem pera ture. Alternatively, as shown in th e negati ve temperatures the corres pondi ng expression previous publication. if two bodies arc brought into for Eq. ( I ) w ill be, thermal contact. the hotter is th e one that releases heat. The fi rst definition will be appropriate for TdS ~ dU +8W ... (6) phenomena occu rring in onl y one domain of th e temperature; the second, fo r phenomena that take A n immediate co nseq uence is that if a heat engine place between the two domain s. is con nected that w ithdraws an amount of heat Q I'rom Statement (c) will be first anal yzed and th en used to a so urce at temperature -T, th e so urce wi ll experiment investigate the other two. a positive change in entropy (Qln and hence there is In ordinary systems th e joint expression I'or the no impediment for transforming completely heat into First and Second laws is, work, a res ult that negates the Kelvin-Planck statement of th e Second Law. But now the reverse TdS ? dU +8w .. ( I ) process of converting work co mplete ly into heat becomes i mposs i ble because it is accompanied by a and decreose in entropy. In oth er word s, in th e domain of negati ve temperatures th e Kel vi n-Planck statement dS>O ... (2) reverses itse l f: (a) hea t w ithdrawn from a source can be complete ly converted into work and , (b) it is for an ad iabatic sys tem. The sy mbol 8 is used to impossible to co nstruct an engine that rece ives work indica te th at th e differential is not exact. and co nverts it completely into heat. ow, two equilibrium stat es of a sys tem are Let now two sys tem s A and B be considered, very considered, very close one to the olher, and each at a close to each oth er, at temperatures T,1 and TIJ. We Il egative absolute temperature. Appropriate amount of assume th at system A is hotter th an system B and that thermal energy, 8Q , is now added to ca use the sys tem it tran sfers to B th e amount of hea t 8QJ\ by mea ns of a to evolve from one state to th e oth er, once by a qULl sistati c irrel'ersible process . T he total change in reversible change and th en by an irreversible one. entropy w ill be, Since th e internal energy is a state property, thus In the absence of kinetic and potential effects one has, .. (7) For th e amount of heat 8QJ\ transferred from A to B it d U = r8Q - 8W J" 'I = r8Q - 8W Jill 1'1 ' (3) mu st be that, 8Qill'('I' - 8Q"'I' = 8Wirrel .
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