Sketching the History of Statistical Mechanics and Thermodynamics

8/13/2019 Sketching the History of Statistical Mechanics and Thermodynamics

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Sketching the History of Statistical Mechanics andThermodynamics(From about 1575 to 198!

" 199#$%8 Hy&er'eff et)ork

History*+hilo* +hysics*,log

- Sources. /inks. otes 0

Anti-

quitydeas of atomism. that heat is a mode of motion)ithin bodies and that &ressure is the result ofsuch motion. are all floating around2

1st

cent

AD

Hero of 3le4andria(see alsohere! )ritesPneumatics. an inestigation on atmos&heric air.summari6ing a great deal of )hat )as kno)n atthe time on sy&hons. &um&s. the effects of heaton liuids. and engine designs2

The aeoli&ile of Hero

9th

cent

3l$,ailani(d 11! said to hae introducedatomism to the Muslim alam(&erha&sinfluencing /eibni6!2

11thcent

The loss of &ermanent magnetism )henmaterials are sub:ected to high tem&eratureskno)n in ;hina2

13th

cent

/ei ben 3braham(1%alilei(15#


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acuum2

1644

BenC @escartes= (159#$1#5! treatisePrincipaPhilosophiae&ublished in 3msterdam2 The)ork e4tends effords to formulate a fullymathematico$mechanical model of the )orld.

including conce&ts of nonlocality. the absence ofany acuum and his orte4 model of atoms2

1647

>illes +ersonne de Boberal(1#%$1#75!&erformed an oft$uoted e4&eriment on air&ressure )hereby a car&=s s)im$bladder is&artially remoed. suee6ed of almost all air andtied shut2 The car& is then &laced in aTorricellian acuum and the bladder is obseredto e4&and2

1648

Florin +erriere4&erimentally sho)s that theheight achieed by mercury in a barometer

decreased as one scaled a mountain. a theoretical&rediction of his brother$in$la).,laise +ascal.and also kno)n as the +uy de @Dme e4&eriment2

ca

1650

(Coffee begins to be important to and catch on

in Europe.)

1651

'ean +ecuet=s (1#%%$1#7

1654

Etto on >uericke=s (1#%$8#! e4&eriment )itht)o iron hemis&heres held together by a strong&artial acuum being strong enough to resist the&ull of a train of horses on either side2

Ferdinand inents the sealed thermometer2

1660

Bobert ,oyle(1#%7$91! &ublishesNewEperiments Physio!"echanicall# touching the$pring of the %ir# and its Effects2 Enee4&eriment clearly sho)s the de&endency onTorricelli=s acuum on ambient air &ressure23lso &resented are discussions of both +ecuet=sidea of air modelled by coiled$u& )ool$like ors&ring$like atoms ()hich )as &referred by,oyle! and of@escartes=idea of )hirling&articles )hich re&ell one another at shortdistances2

Bobert ,oyle
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Descartes.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Roberval.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Pascal.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Pascal.htmlhttp://www.funkandwagnalls.com/encyclopedia/low/articles/g/g010001146f.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Boyle.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Descartes.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Descartes.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Descartes.htmlhttp://www-history.mcs.st-and.ac.uk/history/Biographies/Boyle.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Descartes.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Roberval.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Pascal.htmlhttp://www.funkandwagnalls.com/encyclopedia/low/articles/g/g010001146f.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Boyle.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Descartes.html


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n res&onse to ,oyle=s ideas. Franciscus /inus(1595$1#75! &ro&oses a theory )hereby aacuum is e4&lained by the creation of aninisible collection of thread$like ?funiculus.?)hich strie to hold nearby ob:ects together2

Bichard To)nley(1#%8$177! and Henry+o)er=s (1#%$1##8! e4&eriments establishingthe + la) for e4&ansion (the so$called ?,oyle=s/a)? or ?Marriotte=s /a)?!2

1661

,oyleadds an a&&endi4 to his 1## )ork.res&onding to the criticisms of /inusandThomas Hobbes. &resenting im&roede4&erimental results and giing a ersion of)hat is no) kno)n as ?,oyle=s /a)? for thecase of com&ression2

1662 ,oyle=s ?@efense of the @octrine touching theS&ring and Geight of the 3ir2?

1663

,laise +ascal(1#%$1##%! )rites &n theE'uilibrium of Li'uids(&ublished&osthumously! suggesting that &ressure istransmitted eually in all directions in a fluid(later kno)n as ?+ascal=s la)?!. &robablydiscoered around 1#


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else)here2!

1685Mariotte=s *he "otion of +ater and &therluids&ublished (&osthumously!2

1690@enis +a&in(1#eorg Arnts Stahlintroduces the idea of&hlogiston as the agent of burning and rusting2

1702

>uillaume 3montonse4tra&olates the idea ofabsolute 6ero from the obseration that eualdro&s in tem&erature &roduce eual dro&s in&ressure. and since &ressure cannot becomenegatie. there must be a lo)er limit totem&erature2

Ele ;hristensen BImerdeises a tem&eraturescale based on the t)o &henomena of the boiling

&oint of )ater and the tem&erature at )hichsno) begins to form2

1705Francis Hauksbeesho)s that sound needs air for&ro&agation2

1712 Thomas e)comen=s steam engine2

1714>abriel Fahrenheit=s mercury thermometerintroducing his tem&erature scale2 (seenotes!

1716

'akob Hermann(1#78$17! &ro&oses the firstdefinite measure of the heat of molecular motionin his )ork on rational mechanics.Phoronomia2He &ostulates that (in modern lingo! &ressure is&ro&ortional to density and to the suare of theaerage elocity of the &articles of motion2

'akob Hermann1723

Stahl=soundations of ,ogmatic andEperimental Chemistry&o&ulari6es &hlogistonand the ideas of 'ohann ,echer2

1724Hermann ,oerhaae&ro&oses that heat is a fluidof some sort2

1729

/eonhard Auler(177$178!. e4tending 'ohann,ernoulli=s )ork on @escartes=orte4cosmology. models air )ith tightly$s&aced.s&inning s&heres2 He formulate an euation ofstate relating humidity. &ressure. density andelocity. finding the To)nley$+o)er$,oyle la)as an a&&ro4imation2 He calculates air moleculesto be about


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1733

@aniel ,ernoulli(17$178%!. in a treatise onhydrodynamics )orked out in the &eriod from17%8 to 17. gies a deriation of the gas la)sfrom a billiard ball model. deries the ,oyle$Mariotte relation and used conseration of

mechanical energy to sho) that as tem&eraturechanges the &ressure )ill change &ro&ortionallyto the suare of the &article elocities2 This te4tmarks the first truly statistical treatment ofkinetic theory2 3 significantly u&dated edition ofthe te4t is &ublished in 1782 The &a&er is all butforgotten until 18592

@aniel ,ernoulli1739>eorge Martineestablishes that the olume ofan ob:ect is not &ro&ortional to the amount ofheat it has2

1742

3nders ;elsius(171$17?Ebserations on t)o &ersistent degrees on athermometer.? basing his scale on the free6ing&oint (1 degrees! and boiling &oints (degrees! of )ater2 (The system is reoriented in17


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changing tem&erature2

1765'ames Gattinents his steam engine. )hich isoer si4 times more effectie thane)comen=s2

1772'ohan ;arl Gilckecalculates the latent heat ofice2

+hlogiston Theory (1##=s to 179=s!inetic Heat Theory (171# to 17#=s!

(then 181# to &resent!;aloric Heat Theory (178=s to 18#=s!Gae Theory of Heat (18=s to 18#=s!Statistical Mechanics (185=s to &resent! (,ernoulli e4ce&ted!Kuantum Statistics (19=s to &resent!

1781Gilckecomes u& )ith the conce&t of s&ecificheats2

1782

/aoisierestablishes an early ersion of theconseration of matter through his finding ofconstancy of )eight before and after chemicalreactions2

1783

/aoisier=s )ork.-eflections on Phlogiston. onthe )eaknesses of &hlogiston theory )ith res&ectto combustion2

1786 /aoisierand /a&lace=s )ork"emoir on Heat2

1787

'ackues$3le4andre ;harlesdetermines that at a

gien tem&erature change. different gasese4&and the same amount (kno)n as ?;harles=sla)?!2

1789

/aoisier=s bookElementary *reatise onChemistry. containing the la) of massconseration2

1791

Bichard ir)an(17$181%!. &reiously astaunch defender of &hlogiston theory. concedesthat the e4&erimental eidence says other)ise2

+ierre +rCost=s theory of heat and radiatione4change. stating that cold is the absence ofheat. hot bodies radiate continually and that alack of radiation indicates euilibrium )ithsurroundings tem&erature2

'eremias Bichter(17#%$187! foundsstoichiometry. the &rinci&le of fi4ed chemicalreactions2

1798

;annon$boring e4&eriments of ,en:aminThom&son (;ount Bumford!(175$181


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()hereas caloric theory seerely limits itsaailable amount!2

'ose&h$/ouis +roustformulates that elements ina com&ound al)ays combine in definite mass

ratios (?+roust=s /a)?!2

1800

Gilliam Herschel(179%$1871! &ublishes ?3ninestigation of the &o)ers of &rismatic coloursto heat and illuminate ob:ects? inestigating theeffects of different )aelengths of light on athermometer. finding light :ust beyond the red tobe the hottest2

1801

'ohann Bitterdiscoers ultraiolet radiation)hile doing )ork )ith siler chloride2

'ohn @alton(17##$18the same region &roduce the same &ressure as ifthey occu&ied the region alone. kno)n as thela) of &artial &ressures2

1802

'ose&h$/ouis >ay$/ussac(1778$185! findsthat. at a gien &ressure. the change in olume is&ro&ortional to the change in tem&erature2

1803

@altonformulates his atomic theory of matter.stating that chemicals are formed by integernumbers of atoms. by studying the )eights ofchemicals and reactants2

;laude$/ouis ,ertholletdemonstrates thatreaction rates de&end on both the amount ofsubstances &resent as )ell as their affinities inhis )orkEssay on $tatic Chemistry2

Gilliam Henryfinds that a gas=s mass )hendissoled in a liuid is &ro&ortional to the&ressure (later kno)n as ?Henry=s la)?!2

1804

'ohn /eslie(17##$18%! )rites%nEperimental n'uiry into the Nature and

Propagation of Heat. sho)ing that light andradiated heat hae similar &ro&erties2

1805

+ierre$Simon /a&lace(17


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Loung=s $ystem of Chemistrycontains the first&ublished account of @alton=s ideas on atomictheory2

1807

'ean ,a&tiste 'ose&h Fourier(17#8$18!

com&letes his &n the Propagation of Heat in$olid 0odies. introducing many mathematicalnoelties. including his series e4&ansiontechniues2

'ean Fourier

1808

(@ec 1st! >ay$/ussacstates that gaseschemically combine in e4act &ro&ortions ofolume2

1811

SimCon$@enis +oisson(1781$18


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constant &ressure for metals oer )ide range oftem&eratures. finding that the &roduct of thes&ecific heat and the atomic mass remainsconstant (kno)n as the ?/a) of @ulong and+etit?!2

1821

Hera&ath&ublishes. ?3 mathematicalinestigation into the causes. la)s. and &rinci&al&haenomena of heat. gases. graitation. etc.? inthe%nnals of Philos.He e4&lained in outlineho) kinetic theory could gie accounts of sound&ro&agation. &hase changes and diffusion2 The&a&er is all but ignored due to re:ection by theBoyal Society of /ondon. and Hum&hry @ay in&articular2

Thomas 'ohann Seebeckdiscoers a &rocess by

)hich heat is conerted into electricity in the:unction of some metals. kno)n astheormoelectricity2

1822

Fourier=s essay%nalytic *heory of Heatis&ublished. furthering his techniues of analysis2

;harles ;agniard de la Tour. in liuificatione4&eriments. finds that both tem&erature and&ressure must be a&&ro&riately controlled. anddiscoers )hat is no) kno) as the critical &ointof a substance2

1824

Sadi ;arnot(179#$18%! &ublishes ?Beflectionson the Motie +o)er of Fire.? introducing theideal gas cycle analysis. sho)ing that )hen heat&asses bet)een t)o bodies theormodynamic)ork ()hich he defines! is done. and &ro&osesan idea for an internal combustion engine2

+ierre$Simon /a&lace(17ustae$>as&ard ;oriolisdefines the term?kinetic energy? in his studies &ublished as &n
http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Fourier.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Carnot_Sadi.htmlhttp://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Laplace.htmlhttp://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Newton.htmlhttp://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Newton.htmlhttp://www-history.mcs.st-and.ac.uk/history/Biographies/Carnot_Sadi.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Fourier.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Carnot_Sadi.htmlhttp://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Laplace.htmlhttp://turnbull.dcs.st-and.ac.uk/~history/Mathematicians/Newton.html


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the Calculation of "echanical %ction2

Thomas >raham(185$18#9! e4&erimentallyuncoers the la) of gas diffusion. by )hich therate of a gas=s diffusion. suared. is &ro&ortional

to its density21833

Heinrich Friedrich Amil /en6determines thatresistence in metals increases )ith tem&erature2

Gilliam Thomson

1834

;la&eyronformulates the first ersion of thesecond la) of thermodynimcs. based on studiesof steam engines2

'ean$;harles$3thanase +eltiersho)s that heatcan be absorbed or gien off )hen current is&assed one )ay or the other across a :unctionbet)een t)o different metals (kno)s as the

+eltier effect!2

1837

on Suerman=s e4&eriments on air at reduced&ressures erifying ;la&&eyron=s ersion of;arnot=s formulas2

The 18


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1847

'oule&ublishes ?En Matter. /iing Force. andHeat? in the"anchester Courier. stating the&rinci&le of the conseration of energy andgiing the conersion from heat to kineticenergy2

Hermann /ud)ig Ferdinand on Helmholt6(18%1$9

begin to glo) around 5%5O;. starting in the redand eentually becoming )hite2'ames 'oule

1848

'oulereads a &a&er using Hera&ath=s kinetictheory2 The &a&er contains the first numericalresults from the kinetic theory2 (ot &ublisheduntil 1851. and not )ell kno)n until;lausius=sreference to it in 18572!

Gilliam 'ohn Macuorn Bankine=s (18%$187%!researches into mechanics and heat (mainlythrough 1855!2

elindeelo&=s a scale of absolute tem&erature(no) kno)n as the ?elin? scale! based on thetheory of ;arnot2

1849

'ames Thomson(18%%$189%!. using ;arnot=stheories. &redicts the lo)er of the free6ing &ointof )ater under high &ressures2

elin.in s&eaking of ;arnot=s theory. coins theterm ?thermodynamics2?

1850

'ohn Herschel(179%$1871! &ublishes(anonymously. though generally kno)n! anarticle on Kuetelet=s )ork in statistics.introducing much of the continental )ork onstatistics to ,ritish scientists2

Budolf ;lausius(18%%$88! gies a erbalformulation of the second la). for )hich there isno mechanism )hose only function is the

Hermann on Helmholt6
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transfer of heat2

1851

elininde&endently rediscoers the idea ofabsolute 6ero (1


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1859

'ames ;lerk Ma4)ell(181$79! reads a &a&eron kinetic theory. &rinted in 18# as?llustrations of the @ynamical Theory of>ases.? using random elocity distributions forgases. and sho)ing iscosity to be inde&endent

of tem&erature2 The &a&er is originally intendedto sho) internal inconsistencies in the kinetictheory. but through its rigor it greatly refined thetheory and &roided ne) insights2

>usta Bobert irchhoff(18%


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aboe a substance=s critical &oint it may becontinuous changed from gas to liuid and iceersa through ariations of tem&erature and&ressure2

1864

;lausius&ublishes"echanical *heory of Heat.

the first treatise on thermodynamics2 ol %&ublish in =#9. dealing )ith a&&lications toelectricity2 3 second edition. &ublished as ate4tbook. )as finished in =752 Anglish translationin 18#7 (ol 1 only!. and French in 18#8 (botholumes!2

1865

;lausiususes;arnot=s techniues to derie?entro&y? (and sho)s the t)o la)s ofthermodynamics e4&ressible in the same )ays asthe older caloric theory!. a term coined for theuantity defined early by him. dKJT2 n a &ublic

s&eech entitled ?The entro&y of the uniersetends to a ma4imum.? he sho)s ho)thermodynamics seem to im&ly an eentual heatdeath for the unierse2

'osef /oschmidt=s (18%1$95! &oints out thatMa4)ell=s conclusion that the &ro&ortionality ofthe mean free &ath to Jd%could be used toestimate the si6e of an atom2 Gith furtherconsiderations. he estimates the si6e of an airmolecule to be about 1$7cm. about < times toolarge. but the best estimate to date2

1866

Ma4)ellmodels interatomic forces by a inersefifth$&o)er la). though only as an interimsolution2

1867

Ma4)ell&ublishes his ma:or )ork on kinetictheory. &n the ,ynamical *heory of Gases.

elin=s &n 3orte!%toms.

(S&urred on by Ma4)ell=s )ork. serious debateson the statistical inter&retation of irreersibilitybegin2!

1868

/ud)ig ,olt6mann=s (18


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u& )ith his &arabol of the daemon toconce&tually e4&lain heat statistics2

,olt6mannsuggests that one may derie the&robabilistic &icture from the kinetic one by

heuristically assuming that all microstates mustbe reali6ed in a system before returning to as&ecific microstate. and thus measured aluesshould aerage the effects of such states2(no)n as the ?ergodic theorem.? and so namedby Ahrenfest in 19112!

'ames Thomsonsuggests that een belo) thecritical &oint. a substance may smoothlytransition bet)een gas and liuid fromconsiderations of e4&erimental data on &ressure

and olume2

1872

n a 1$&age &a&er entitled. ?Further Studies ofthe Thermal Auilibrium of >as Molecules.?,olt6mann=s deries his trans&ort euation (P$Theorem!. sho)ing e4&licitly that isolatedsystems must al)ays eole in such a )ay thatentro&y increases2 He introduces a number ofmathematical innoations. including a techniueof discreti6ing the allo)ed energy leels for amolecule. and allo)ing this energy bin to go to6ero2 /ittle read at first. the &a&er later meets)ith )ide$s&read o&&osition2

1873

'osiah Gillard >ibbs(189$19! &ublishesGraphical "ethods in the *hermodynimcs of

luidsand% "ethod of Geometrical-epresentation of the *hermodynamicProperties of $ubstances by "eans of $urfaces.introducing many ne) gra&hical techniues2From 187 to 1878 he &ublishes a series ofim&ortant articles in the *ransactions of theConnecticut %cademy of %rts and $ciences#)idely influencing scientists in the QS and inAuro&e2

'ohannes @iderik an der Gaals(187$19%!. indoctoral dissertation. gies the first correcta&&ro4imation for the effects of a non$anishingratio of molecule diameter to aerage distanceby assuming long$range attractie and short$range re&ulsie forces. a&&lying this to the case

'osiah >ibbs
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of gases at high densities2 Qsing his ?euation ofstate.? he gies the first successful attem&t toe4&lain a (gas$liuid! &hase transition2 Thetheory both accounted for 3ndre)s=s critical&oint &henomena and confirmed 'ames

Thomson=s hy&othesis2

1874

elin&oints out that the irreersibility of,olt6mann=s kinetic theory seems to contradictthe underlying classical la)s of &hysicsremaining time$inariant (the so$called?reersibility &arado4.? sometimes attributed to/oschmidt!2

1876

>ibbs&ublishes the first &art of &n theE'uilibrium of Heterogeneous $ubstances(the%nd &art in 1878!2 The )orks deal )ith chemicalreactions. &hase euilibrium and the use of free

energy2

(arl +aul >ottfried on /indebuilds the first&ractical refrigerator using liuid ammonia2!

1877

,olt6mannformulates a statistical mechanicalersion of the second la) of thermodynamics inthe &a&er. ?En the Belation ,et)een the Second/a) of the Mechanical Theory of Heat and the+robability ;alculus )ith Bes&ect to theTheorems on Thermal Auilibrium?2 There heformulates that the entro&y of a system is&ro&ortional to the log of the &hase s&aceolume occu&ied by the macrostate of thesystem. $ 4 2 ln 5. making use of hismathematical innoation of using finite areas of&hase s&ace2

/iuification of o4ygen achieed. after nearlyone hundred years of trying. by /ouis +aul;ailletet(18%$191! (on @ec %nd! and Baoul+ierre +ictet(18


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radiation in order to satistfy the second la)2

>ibbscoins the term ?statistical mechanics? forthe kinetic theory=s treatment of thermodynamicissues2

1885

/odge&romotes the idea that mechanical energycan be locali6ed and flo). as ins&ired by the)ork a year earlier by +oyntinginelectromagnetic theory2

'ohann 'akob ,almer(18%5$1898! finds aformula for describing the four s&ectral)aelengths then kno)n for hydrogren as foundby Rngstrom2

1889

'ules Henri +oincarC(185ibbs=last )ork.Elementary Principles in$tatistical "echanics2

1890

Ad)ard +arnell ;uler)ell(1855$191! &ointsout the a&&arent contradiction bet)een,olt6mann=s H$theorem and the irreersibility ofthe micromechanical &rocesses on )hich it isbased. suggesting that some kind of irreersible&rocess takes &lace at this micro leel. &erha&sin connection )ith the ether2

1893

Gilhelm ;arl Gerner Etto Frit6 Fran6 Gien(18#


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1895

+ierre ;urie(1859$19#!. in his doctoraldissertation. defined both ferro$. dia$. and&aramagnetism. sho)ing that ferromagnets losetheir magnetic &ro&erties as their tem&erature isincreased. eentually losing it com&letely aboe

a certain tem&erature s&ecific to that material(the ?;urie &oint?!2 He suggests thatdiamagnetism is an atomic &ro&erty. )hile theother t)o are &ro&erties of bulk matter2

Gilhelm Bntgen(18


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Ma4 arl Arnst /ud)ig +lanck(1858$19


20/31

1906

Galther ernst(18#


21/31

+lanck=s first &a&er e4&licitly uanti6ing theallo)ed radiation of oscillators in a blackbody2

3rnold Sommerfeld(18#8$1951! notes that

elementary regions of &hase s&ace should berelated to +lanck=s constant2

Etto Sackur(188$191

/adisla) atanson&ro&oses that +lanck=s la) isthe result of the indistinguishability of states of

light uanta2

iels Henrik @aid ,ohr(1885$19#%! defendshis dissertation and begins constructing atomicmodels )hich try to forge a connection )ith+lanck=s constant as a fundamental constant ofuanti6ation2

Heike amerlingh Ennes(185$19%#!e4&erimentally finds that mercury )ill becomesu&erconductie )hen cooled ery close toabsolute 6ero and also discoers su&erfluidity2

+aul(188$19! and Tatiana 3fanass:e)aAhrenfest(187#$19#

ernst=s e4&eriments )ith many substances.sho)s s&ecific heats going to 6ero at absolute6ero in general. &roiding strong su&&ort for thene) uantum theories2

1912

+oincarC&roes that one can inert the +lanckdistribution ia a Fourier transform and deducethat black$body radiation im&lies a uanti6ationof energy states2

Sackurand H Tetrodeinde&endently sole,olt6mann=s /a) to obtainS V k ln-(%UmkT!(J%!Jh0 ] (5J%!k
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22/31

sho)ing a need for uanti6ation in classical gasla)s2

1913

3rtur Bosenthal(1887$1959! and Michel+lancherel(1885$19#7! &roe that the ergodichy&othesis is not iable for any dynamical

system (o&ening the )ay to the uasi$ergodichy&othesis and certain theorems in ergodictheory!2

+aul Ahrenfestsho)s ho) to estimate rotationaleffects of a diatomic gas on s&ecific heat byre&lacing integrals )ith sums oer discretecontributions from uanti6ed states2 The )ork islater refined by A Holm(191! and by +lanck(1915!2

,ohr=s article. ?En the ;onstitution of 3tomsand Molecules2?

1916

Bobert 3ndre)s Millikan(18#8$195!. ine4&eriments )ith the &hotoelectric effect. bothconfirms the theoretical )ork of Ainsteinandconfirms the alue of +lanck=s constantinde&endent of )ork done )ith blackbodies2

Ainstein&roduces a deriation of the black$bodyradiation distribution )ith the assum&tion ofboth s&ontaneous as )ell as stimulated emissionof radiation by matter2

ernst&redicts a state of degeneration can bereached for any gas at a lo) enoughtem&erature. through e4tensions of histhermodynamic theory2

Sydney ;ha&man(1888$197! and @aidAnskog(188http://www-history.mcs.st-and.ac.uk/history/Mathematicians/Bohr_Niels.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Bohr_Niels.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Einstein.htmlhttp://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Planck.htmlhttp://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Planck.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Einstein.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Chapman.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Enskog.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Enskog.htmlhttp://www.woodrow.org/teachers/ci/1992/Lewis.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Eddington.htmlhttp://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Planck.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Bohr_Niels.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Einstein.htmlhttp://www-groups.dcs.st-and.ac.uk/history/Mathematicians/Planck.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Einstein.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Chapman.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Enskog.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Enskog.htmlhttp://www.woodrow.org/teachers/ci/1992/Lewis.htmlhttp://www-history.mcs.st-and.ac.uk/history/Mathematicians/Eddington.html


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&ublishes a &a&er on radiatie euilibrium.suggesting that the ioni6ation of atoms in stars2

1920

Meghnad Saha(189$195#! )rites. ?oni6ationin the solar chromos&here.? analy6ing s&ectrallines of stars as atomic dissociation in the

chromos&here. )here lo)er &ressures oerridethe lo)er tem&eratures of a star. also (in asecond &a&er! &redicting that lo)er$tem&eraturesun$s&ots )ill sho) lines of rubidium andcesium (an effect detected in 19%% by H Bussell!2

Gilhelm /en6(1888$1957! models crystals by alattice of di&olar atoms )hich feel nearest$neighbor interactions. obtaining the ;urie la)for magneti6ation and suggestions its

a&&lications to ferromagnetism2

1922

/ouis ictor +ierre Baymond duc de ,roglie(189%$1987! a&&lies Sackur=s techniue ofuanti6ing &hase s&ace to derie the Giendistribution la) for energy density^du V (8UhJc! e4&($hXJkT! XdX

;harles @ar)in(1887$19#%! and Bal&h Ho)ardFo)ler(1889$191923

/e)is=s *hermodynamics and the ree Energyof Chemical $ubstances. bringingthermodynamics in closer contact )ithchemistry2

Satyendranath ,ose

1924

('une!Satyendranath ,ose(189


24/31

rendusof the +aris 3cademy elaborating on afundamental &rinci&le of )ae$&article duality2The )orks mature into his 19%5 doctoral thesis2

1925

Ma4 ,orn(188%$197!.Gerner arlHeisenberg(191$197#!. and +ascual 'ordan

formulate uantum mechanics based on themathematics of matri4 algebra2

Ainstein. citing )orks by,oseand de ,roglie.suggests that the analogy bet)een uantumgases and molecular gases are com&lete. and thatboth &hotons and molecules hae both &articleand )ae characteristics2 He also &oints out thatmolecules at lo) tem&eratures cannot beconsidered inde&endent entities. een in theabsence of intermolecular forces. and )ill form

a uantum condensate2

Samuel 3 >oudsmit=s (19%$1979! hy&othesisan e4tra degree of freedom to electrons termed?s&in? due to the mathematical similarity toclassical s&in2 /ater. )ith >eorge AugeneQhlenbeck(19$1988!. half$integer uantumnumbers are introduced in the theory of thehydrogen atom2

Golfgang +auli(19$1958! formulates thee4clusion &rinci&le for the electron. accountingfor a number of chemical &ro&erties in atomsand molecules2

+lanckdeises a ne) deriation ofthermodynamic formulas for ,olt6mann gasesusing the formulations.6 V e4&($_JkT!. V 6J `

Arnst sing(19$!. follo)ing the inestigationsof /en6. &ublishes a &a&er dealing )ithmagnetic models ia di&olar atomic interactions2

1926

,ornintroduces into uantum mechanics his&robability inter&retation of interactions2

Anrico Fermi(191$195

+aul @irac
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25/31

Ar)in Budolf 'osef 3le4ander Schrdinger(1887$19#1! deelo&es a second formulation ofuantum theory in terms of )ae mechanicsinde&endently2

+aul 3drien Maurice @irac(19%$198

Addington=s *he nternal Constitution of the$tars. relating the radiation &ressure of stars totheir luminosity2

Fo)lersho)s that some of the &ro&erties of

)hite d)arf stars could be accounted for bytreating them as (Fermi! uantum degenerategases. being an early e4am&le of uantumstatistics e4&laining the &ro&erties of largemacrosco&ic ob:ects2

Bobert Hutchings >oddardlaunches the firstrocket. using liuid fuel and reaching a height of18< feet and # miles &er hour2

1927

'ohn on eumann(19$1957! formulates afully uantum mechanical generali6ation ofstatistical mechanics2

,ohr&ronounces his notion of com&limentarityin uantum theory2

Heisenbergformulates the uncertainty &rinci&leof uantum mechanics2

@iracand+auliinde&endently &ro&ose to modelmetals )ith molecules obeying Fermi$@iracstatistics2

+aulie4&lains the &aramagnetic susce&tibility ofmetals using electron s&in and the e4clusion&rinci&le2

Gillem Hendrik eesom(187#$195#! and MGolfkefind discontinuities in seeral &ro&ertiesof helium at ery lo) tem&eratures and suggest
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that it may be due to a &hase change. callingthem helium and 2

Galter Heitler(19the coalent molecular bond bet)een t)ohydrogen atoms. sho)ing stability to a functionof electron s&ins. and arguing against thestability of such helium bonds2

1928

Sommerfeldtreats electrons in metals as adegenerate Fermi gas using the ne) techniuesof uantum theory2

@iraccomes u& )ith a relatiistic uantummechanical )ae euation for the electron2

Feli4 ,loch(195$! suggests a theory of metalsbased on electrons layered &eriodic &ositie&otentials )hich can sustain small dis&lacements)hich lead to resistance ia scattering ofelectrons by the lattice ibrations2

'ohn ;larke Slater(19$197#! is the first tostudy the uantum mechanical treatment of themolecular formation of rare gases (helium!2

/inus +auling(191$! a&&lies the Heitler$/ondon treatment to chemical bonds2

1929

Admund ;lifton Stoner(1899$19#8!. using(s&ecial! relatiistic formulas for electronenergies. suggests that beyond a certain densityin stars the out)ard degenerate gas &ressure)ould no longer sustain itself against the in)ardgraitational attraction (though he did nots&eculate about )hat )ould then ha&&en!2

Slaterformulates a multi$electron )ae function)hich can generally satisfy the +auli e4clusion&rinci&le2

'ohn on eumann

1930

@iscoery of the lambda &oint of helium at)hich it becomes a su&erfluid (so$named in19eorge @aid ,irkhoff(188
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&roing the stability of such bonds2

1932

3leksandr Lakoleich hinchin(189

1934

Gilliam /a)rence ,ragg(189$1971! andGilliamsformulates an sing model for&aramagnetic to ferromagnetic transitions2

;ornelius 'acobus >orter(197$198! andHendrik ,ruygt >erhard ;asimir(199$! forman analysis of the e4&ulsion of magnetic fields in

su&erconducting metals in a magnetic field2

1935

Gilliam Francis >iauueachiees a tem&eratureof only 21O for helium using a magnetic tra&to slo) the motion of the molecules2

/e @aidoich /andau(198$19#8! &ublisheshis &henomenological mean$field treatment for&hase transitions2

Subrahmanyan ;handrasekhar(191$1995!deries the ma4imum mass formula for adegenerate Fermi gas2

Frit6 Golfgang /ondon(19$195

Hans ,ethe(19#$! im&roes on ,ragg$Gilliams theory by adding short$range atomicinteractions2

Ad)ard 3rmand >uggenhaim(191$! deelo&sa theory of liuid solutions using nearest$neighbor rules. into )hat is no) callod the?uasi$chemical? (K;! method2

/e /andau

1936

'ose&h Ad)ard Mayer(19oe&&ert$Mayer(19#$197%!. initiate the
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modern theory of gas condensation. in )orkthrough 198. by use of ?cluster integrals?re&resenting the interactions of many moleculesto find the irial coefficients of intermolecularforces2

1937

+eter /eonidoich a&it6a(189


29/31

inariant /iouille euation. further clarifyingthe internal structure of statistical mechanics2

hinchinrefines ,olt6mann=s theorem to readthat. as a function of the si6e of an ensembles.

the time aerage of a system becomes arbitraryclose to the canonical aerage2

Bichard 3 Egg. 'rsuggests that &airs ofelectrons behae as bosons. and thatsu&erconductiity may be thought of as a ,ose$Ainstein condensate2 (The idea is ignored untilabout 195


30/31

the hard$s&here &hase transition2

1961

>eorge 3llen ,aker. 'r(19%$! found a methodof determining the singularities at the critical&oint ia series e4&ansions of /en6$singmodels2

1965 ,en:amin Gidom=s (19%7$! )ork on surfacetension theory using a modified an der Gaalstheory2

19683lderand Gain)rightdiscoer orte4 diffusionin liuids2

1971

enneth Gilson(19#$!. e4tending earlier )orkby /eo adanoff(in 19##!. a&&lies thetechniue of the renormali6ation grou& to studyof scaling la)s for &hase transition theory2

1972

Michel Allis Fisher(191$! and Gidomsho)that the /en6$sing model generali6ed to

arbitrary dimensions dis&lay a continuoustransition bet)een classical and non$classicalla)s. )here correlation lengths tend to)ardinfinity at critical &oints2

1980

Heinrich Bohrerand >erd ,innigdeelo& thescanning tunnelling microsco&e. allo)ing forimaging of atoms embedded on surfaces2

Sources: ,rush. Ste&hen >. Statistical +hysics and the 3tomic Theory of Matter From ,oyle ande)ton to /andau and Ensager(out of &rint!,unch. ,ryan Hellemans. 3le4ander. The Timetables of ScienceAisberg. B and Besnick. B. Kuantum +hysics. %nd ed. 1985

Flamm. @ieter. ?History and outlook of statistical &hysics.?&hysicsJ985. < March.1998Flamm. @ieter. ?/ud)ig ,olt6mann $ 3 +ioneer of Modern +hysics.?&hysicsJ9717.7 Ectober. 1997uhn. Thomas S. ,lack$,ody Theory and the Kuantum @iscontinuity. 189ases.? Physics *oday.March 19#1Mendelssohn. . The Kuest for 3bsolute ero(out of &rint!Moore. Galter. Schrdinger^ /ife and ThoughtTruesdell. ;. Assays in the History of Mechanics(out of &rint!

3nd the great MacTutor History of Mathematics 3rchieLinks: The +neumaticsof Hero of 3le4andria

+aul ;harles)orth=sHistory of Science&ages;hris Hillman=s Antro&y in the +hysical Sciences,iogra&hies of chemists and some &hysicists aailable at the History of ;hemistry&age3bout Tem&eratureby +ro:ect Skymath
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Fahrenheit=s +a&er of 17%

Sketching the History of Statistical Mechanics and Thermodynamics

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