Müller I. A history of thermodynamics. The doctrine of energy and entropy (1185104), страница 41
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132.1726 Third Law of ThermodynamicsThis is the modern version of the law and it is amply confirmed in experiments by comparing the entropies calculated from measurements of specificheats with the known value of entropy in the ideal gas phase of a substance,see below.Planck’s form of the third law goes far beyond Nernst’s, because it is notrestricted to chemical reactions, or phase transitions. It allows us tocalculate the absolute value of the entropy of any single body. Thehandbooks used by physicists and chemists provide these values as parts oftheir tables of constitutive properties.Note that this is more than the chemists need, because in their formulae itis only the entropy of reaction that is needed, that is to say a combination ofthe entropy constants of the reactants and resultants, see Chap.
5.This is just like with energy: Chemists need only the heat of reaction, but Einstein’s2formula E = mc furnishes the absolute value of energy for all reacting constituentsin terms of their mass. This, however, is not useful knowledge for the chemist.Indeed, the mass defect of chemical compounds is too small to be measured byweighing (say). Yet, in summary it may be said that the first decade of the 20thcentury furnished both: the theoretical possibility for the determination of theabsolute values of energy and entropy.Liquefying GasesIt is not easy to lower temperatures and the creation of lower and lowertemperatures is in itself a fascinating chapter in the history ofthermodynamics which we shall now proceed to consider. The chapter isnot closed, because low-temperature physics is at present an active field ofresearch.
Currently the world record for the lowest temperature in theuniverse16 stands at 1.5 µK, which was reached at the University ofBayreuth in the early 1990’s. Naturally the cold spot was maintained onlyfor some hours. Such a value was, of course, far below the scope of thepioneers in the 19th century who set themselves the task of liquefying thegases available to them and then, perhaps, reach the solid phase.The easiest manner to cool a gas is by bringing it in contact with a coldbody and let a heat exchange take place. But that requires the cold body tobegin with, and such a body may not be available.
No gas – apart fromwater vapour – could be liquefied in this manner in the temperate zones ofEurope where most of the research was done.Since liquids occupy only a small portion of the volume of gases at thesame pressure, it stands to reason that a high pressure may be conducive toliquefaction, just as a low temperature is. Both together should be even16The universe, through its background radiation, imparts a temperature of 3K to bodies thatare not otherwise heated or cooled.Liquefying Gases173better.
That idea occurred to Michael Faraday – a pioneer of both electromagnetism and cryogenics, the physics of low-temperature-generation – in1823. He combined high pressure and low temperature in an ingeniousmanner by using a glass tube formed like a boomerang, cf.
Fig. 6.3. Somemanganese di-oxide with hydrochloric acid was placed at one end. The tubewas then sealed and gentle heating liberated the gas chlorine which mixedwith the air of the tube and, of course, raised the pressure. The other endwas put into ice water and it turned out that chlorine condensed at that endand formed a puddle at 0°C and high pressure.Fig. 6.3. Michael Faraday (1791–1867) Liquefaction of chlorineWhen the pressure is slowly released, some of the liquid chlorineevaporates and, if this is done adiabatically, the heat of evaporation comesin part from the liquid, which therefore cools. In this manner Faraday wasable to determine the boiling point of chlorine at 1atm as being –34.5°C.
Afurther decrease of pressure will cool the liquid chlorine beyond that point,provided of course, that any is left.Other scientists joined the campaign for low temperatures, notablyCharles Saint Ange Thilorier (1771–1833), a chemist, who liquefied carbondioxide in a strong metallic boomerang under high pressures and thenlowered the pressure – hence, by evaporation, the temperature – far enoughto make it solid. When enough solid was accumulated to experiment with, itturned out that carbon dioxide at 1atm goes immediately from the solidphase into vapour and vice-versa – at –78.5°C – in a process calledsublimation, or de-sublimation respectively.
That makes solid carbon dioxide popular as dry ice. It cools an article without soaking it upon melting;after all, it does not melt, it sublimates.1746 Third Law of ThermodynamicsThilorier invented another trick as well. He mixed the strongly volatileether17 with solid carbon di-oxide. The ether evaporated and thus producedtemperatures as low as –110°C, or 163 K. Having enough of this coldmixture available, Faraday and Thilorier could now liquefy other gases bysimple heat exchange, although for some of them they needed high pressureto help in the process.And yet, there are eight gases which cannot be liquefied at 163 K evenunder high pressure.
They are oxygen, argon, fluorine, carbon monoxide,nitrogen, neon, hydrogen and helium of which Faraday knew five; he didnot know the noble gases. So he called those five gases permanent. Andthat is where the further development was stuck for a while. Until ThomasAndrews (1813–1885) found out about the critical point or, in particular,the critical temperature.Andrews worked with carbon dioxide CO2, a gas that can be liquefied atroom temperature under pressure. He took a sample of liquid CO2 underhigh pressure – 60–70atm (say) – and watched the liquid evaporate at somefixed temperature upon heating. Then he raised the pressure and startedagain, and again.
He observed that the phase separation became lesspronounced for higher pressure and vanished altogether at p = 73atm andT = 31°C. That point was called the critical point by Andrews. For higherpressures the liquid did not evaporate upon heating nor did the vapourliquefy upon cooling; the vapour just became ever denser without anyevidence of a separation between liquid and vapour.Andrews conjectured that all substances have critical points and thatthese points had escaped the attention of thermodynamicists only, becausethey were far out of the usual and easily accessible ranges of pressure andtemperature.
Therefore he concluded that the permanent gases can also beliquefied, if only we start raising the pressure on a sample that is colder, oreven considerably colder than 163 K, which at that time was the recordminimum.Eventually this proved to be the case. But there was the problem ofreaching lower temperatures. This problem was solved by Louis PaulCailletet (1832–1913) in 1877. He compressed oxygen to a pressure ofpH = 66atm (say) in a compressor and then cooled the compressed gas back toroom temperature TH = 298K.
Afterwards he subjected the gas to anadiabatic expansion to pL= 1atm through a turbine, regaining some of thecompressor work. For the expansion the adiabatic equation of state may bepTused in the form pHL ( THL ) z 1 , and for z = 5/2 – appropriate for a twoatomic ideal gas – it follows that the oxygen leaves the turbine with TL § 90 K,very close to the condensation point and far below the previous recordminimum of 163 K. Actually Cailletet observed a fog of liquid droplets17Diethyl ether, not the luminiferous variety of Chap. 2, of course; that would have beensomething!Liquefying Gases175behind the turbine.
Thus he had successfully liquefied oxygen although, ofcourse, the droplets quickly evaporated. The same could be done forfluorine, carbon monoxide and nitrogen and – after the noble gases hadbeen isolated – for argon and neon.18Effective isolation eventually produced liquids of the permanent gases inquantities sizable enough to study their properties, e.g. the boiling points.Even hydrogen was eventually liquefied in 1898 by James Dewar(1842–1923) and its boiling point turned out to be 20.3 K; solidificationhappens at 14K. For isolation Dewar invented the Dewar flask, a kind ofthermos bottle, in which cold liquids could be stored for a long time,because the flasks had a vacuum-filled double wall, whose surface wassilvered, so that even radiation losses were kept at a minimum.Dewar was a man of many interests and talents: He erred, however, whenhe saw a connection between the blue of the sky and the blue colour ofliquid oxygen.
He invented cordite, a smokeless gun powder, and thatbrought him into a bitter fight about an alleged patent infringement withAlfred Bernhard Nobel (1833–1896). So, understandably, there was noNobel prize for Dewar, although the road to absolute zero was otherwisepaved with those prizes. However, Dewar was knighted and became SirJames. After his work only helium remained a gas.
It deserves its ownsection, see below.Despite effective isolation, until 1895 the cold liquids remained alaboratory curiosity. But then Carl Ritter von Linde (1842–1934) invented acontinuous process of successive adiabatic throttling which producedliquids of oxygen and nitrogen in quantity, to be filled into high-pressurebottles and put to industrial use.19 Throttling occurs when a vapour or aliquid are pushed or sucked through a narrow opening so that the pressuredecreases and so does the temperature in most substances. The coolingeffect is known as the Joule-Thomson effect – or Joule-Kelvin effect.
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