Müller I. A history of thermodynamics. The doctrine of energy and entropy (1185104), страница 40
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Therefore the usual manner for decreasingtemperature, – namely isothermal compression followed by reversibleadiabatic expansion – indeed decreases the temperature, but never to zero,since the graphs become ever closer for T ĺ 0.Fig. 6.1. (a) Isothermal compression (Ļ) and adiabatic expansion (ĸ) (b) Equilibriumpressure for the transition graphiteļdiamondHaving presented that argument, Nernst summarizes the three laws ofthermodynamics thus:7It is impossible to build an engine that produces heat or work fromnothing.It is impossible to build an engine that produces work from nothingelse than the heat of the environment.It is impossible to take all heat from a body.This accumulation of negatives appealed to Nernst and it has appealed tophysicists ever since.Diamond and GraphiteOne of the more unlikely cases of coexisting phases occurs in solid carbonand they are known as graphite and diamond.
Both are crystalline indifferent ways: Graphite consists of plane layers of benzene rings tightlybound – inside the layer – in a hexagonal tessellation. And each layer is7W. Nernst: “Die theoretischen und experimentellen Grundlagen des neuen Wärmesatzes.”[Theoretical and experimental basis for the new heat theorem] Verlag W. Knapp, Halle(1917), p. 77.Diamond and Graphite169loosely bound to the neighbouring ones.
If one rubs graphite against a sheetof paper (say), the uppermost layers are scraped off and leave a mark on thepaper. That is why graphite can be used for writing. Hence the name:graphos = to write in Greek. The lead inside our pencils consists of graphitemixed with clay. It has the gloss of lead.And then there is diamond, the hardest material of all; it cannot bescratched or ground except by use of other diamonds and it is unaffected bymost chemicals. The Greek word was “adamas” = untameable and that iswhere, after some distortion, the name diamond comes from. In diamondsthe carbon atoms sit in the centre of tetrahedra and are quite tightly bound,although not as tightly as the in-plane atoms in the graphite layers.
Atnormal pressure and temperature graphite is stable and diamond is metastable.All this, of course, was unknown until modern times and, naturally, sincediamond was rare and beautiful, and therefore valuable, it was of muchinterest to chemists and alchemists alike. To investigate its properties,however, it needed a rich patron. Cosimo III, Grand Duke of Tuscany – trueto the Medici tradition of patronizing the arts and sciences – provided agood-size sample for scientific investigation. For security he entrusted it toa group of three scientists who could not – try as they might – affect it inany way.
Eventually they brought a burning glass to bear, in order to heatthe stone. It developed a halo and then – it was gone! Naturally the reportwas met with some scepticism,8 but nobody was much tempted to repeat theexperiment until Lavoisier did so 80 years later. Lavoisier, living up to hisreputation, controlled his experimental conditions by using a closed jar. Hefound that, after the diamond had been burned, the air inside the jarcontained an appropriate amount of carbon di-oxide and so he couldconclude that diamond is pure carbon.After the inevitable sceptics had been convinced, there arose a strongdesire to reverse the process and make diamond from graphite.
Sinceǻg(T,p) = gdia(T,p)-ggraph(T,p) is the affinity of the process and since( wwIR )6 v holds, we haveR'I (6 , R )'I (6 ,0) ³ 'v(6 , S )FS .0Diamond is a lot denser than graphite –3.5g/cm3 as compared to 2g/cm3 – andtherefore we have ǻv < 0 so that ǻg(T,p) decreases with increasing p.
Forphase equilibrium ǻg(T,p) must vanish and thus we obtain an equation forthe requisite p as a function of T8According to I. Asimov: “The unlikely twins” in: “The tragedy of the moon” DellPublishing Co. New York (1972).1706 Third Law of ThermodynamicsR³ 'v(6 , S )FS'I (6 ,0) .0By the third law ǻg(T,0) is known – without any unknown constants –from measurements of the latent heat of the transition for p = 0 and frommeasurements of the specific heats cp(T,0) of both phases starting at T = 0,or as low as possible.
Also v(T,p) is known for all T as a function ofpressure. Of course, it takes a protracted experimental campaign to measureall these values, but the end might justify the means: For every fixedtemperature we obtain the pressure that should convert graphite intodiamond.
Fig. 6.1.b shows the graph.9Inspection of the graph shows that, at room temperature, it should takeapproximately 15 kbar to obtain diamond, if indeed the transition occurredin equilibrium. However, in both directions the transition is hampered byenergetic barriers: In the interesting direction the planar benzeneconfiguration must first be destroyed before diamond can be formed, and inthe other direction the tetragonal diamond structure must be weakenedbefore diamond turns to graphite. For both it needs high temperature andtherefore the equilibrium graph of Fig. 6.1.b is really relevant only in theupper part. When diamonds were eventually synthesized in 1955, byscientists of the General Electric Company in the USA, it occurred at 2800K and at a pressure of about 100 kbar.10There had been several false alarms before that time.
But the reportedresults turned out to be either fakes or hoaxes. It is believed that the chemistHenri Moisseau had been hoodwinked by one of his assistants when – in1893 – he presented a diamond which he believed he had created in hislaboratory. Certainly he could never repeat the feat.Hermann Walter Nernst (1864–1941)It is difficult to say much in praise of Nernst which was not already saidbetter by Nernst himself, cf. Fig. 6.2.
He was a bon-vivant, as much as thatis possible for a hard-working professor, operator and administrator. Hehunted in the stylised European manner, was a connoisseur of wine andwomen, an early gentleman automobilist and, quite generally, a personendowed with a healthy self-regard. That by itself is one way to get aheadin the world and Nernst was good at that.9J. Wilks: “Der dritte Hauptsatz der Thermodynamik” [The third law of thermodynamics]Vieweg, Braunschweig (1963)10 Or 700 tons per square inch in the cute American units.Hermann Walter Nernst (1864–1941)171Nernst reassures us concerning theemergence of further thermodynamiclaws:The 1st law had three discoverers:Mayer, Joule and Helmholtz.The 2nd law had two discoverers:Carnot and Clausius.The 3rd law has only one discoverer,namely himself: Nernst.The 4th law … (?)Fig.
6.2. Hermann Walter NernstHe had obtained the patent for an essentially useless electric lamp – theNernst pin – which nevertheless, to Edison’s amazement,11,12 he sold toindustry for a million marks, a very sizable amount of money indeed at thetime. Nernst suggested to Röntgen that he should patent X-rays so as tomake money, an idea that had never occurred to Röntgen; nor was hetempted.Nernst’s law, or theorem stood on uncertain grounds at first. It is nowrecognized that, at the beginning,13 it was a daring proposition with little orno evidence to back it up.14 To be sure, the theorem was not presentedcautiously, but rather with some fanfare.
A somewhat irrelevant differentialequation was solved and one solution was preferred arbitrarily over allothers, because a priori that seemed to Nernst to be the easiest solution.15However, at the end, just like with his pin, Nernst was lucky. Otherscollected the evidence, which he had failed to present. By and large,Nernst’s proposition was confirmed through painstaking work lasting manyyears. To be sure, amorphous solids had to be excluded somewhere alongthe way, but that was a secondary qualification, perhaps.Despite Nernst’s proud statement, cf.
Fig. 6.2, about being the sole discoverer of the third law, there were really two discoverers. Indeed, Planckstrengthened the law on the grounds of statistical thermodynamics bydemanding that the entropy of all crystalline bodies tend to zero for Tĺ0.11Thomas Alva Edison (1847–1931), the greatest inventor of all times, owned 1300 patentsat the end of his career, among them one for the electric light bulb. He held a poor opinionof the practical skills of professors like Nernst.12 I. Asimov: “Biographies …” loc.cit.13 W. Nernst: “Über die Berechnung ....” loc.cit. (1906).14 See: A. Hermann (ed.): “Deutsche Nobelpreisträger” [German winners of the Nobel prize]Heinz Moos Verlag, München (1969) p. 131–132.15 Ibidem, p.
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