Müller I. A history of thermodynamics. The doctrine of energy and entropy (Müller I. A history of thermodynamics. The doctrine of energy and entropy.pdf), страница 3

Fig. 1.26. It is clear what Sagredomeans: If you bring water up in summer from a deep well and you stickyour hand into it, it feels cool, while, if you do that in wintertime, the waterfeels warm.GIOVANFRANCESCO SAGREDO a GALILEOin FirenzeVenezia, 7 febbraio 1615Molto Ill.re S.r Ecc.mo… Con questi istrumenti ho chiaramente veduto,esser molto più freda l’aqua de’ nostri pozzi ilverno che l’estate; e per me credo che l’istessoavenga delle fontane vive et luochi soteranei,anchorchè il senso nostro giudichi diversamente.Et per fine li baccio la manoIn Venetia, a 7 Febraro 1615Di V.S. Ecc.maTutto suo Il Sag.Fig.

1.2. Galileo Galilei. A cut from a letter of Sagredo to Galilei with the remarkablesentence: I have clearly seen that well-water is colder in winter than in summer …, althoughour senses tell differentlyMisconceptions due to the subjective feeling of hot and cold were slowlyeliminated during the course of the 17th century. A serious obstacle wasthat no two thermometers were quite alike so that, even when there were56Middleton. loc.cit.

p. 7.“Le Opere di Galileo Galilei”, Vol. XII, Firenze, Tipografia di G. Barbera (1902) p.139.The letter, and other letters by Sagredo to Galilei are replete with flattering, even sycophantic remarks which the older man seems to have appreciated. Part of that may beattributed, perhaps, to the etiquette of the time. But, in fact, it may generally be observed –even in our time – that, the more eminent a scientist already is, the more he demandspraise; and a diplomat knows that.41 Temperaturescales on them, it was difficult to communicate objective information fromone place to another.Scales were just as likely to run upwards as downwards at that time.Middleton7 lists the scale on a surviving thermometer built by John Patrickin or around the year 1700; it runs downward with increasing heat from 90°to 0°, thus maintaining remnants of Galen’s scale of 9 degrees, perhaps.90°85°75°65°Extream ColdGreat FrostHard FrostFrost55°45°35°25°Cold AirTemperate AirWarm AirHott15° Sultry5° Very Hott0° Extream HottFix-points were needed to make readings on different thermometers comparable.

From the beginning, melting ice played a certain role – either inwater or in a water-salt-solution – and boiling water, of course. But alternatives were also proposed:the temperature of melting butter,the temperature in the cellar of the Paris observatory,the temperature in the armpit of a healthy man.The surviving Celsius scale uses melting ice and boiling water, and onehundred equal steps in-between. However, since Anders Celsius (1701–1744) wished to avoid negative numbers, he set the boiling water to 0°Cand melting ice to 100°C, – for a pressure of 1atm.

Thus he too counteddownwards. That order was reversed after Celsius’s death, and it is in thatinverted form that we now know the Celsius scale, or centigrade scale.Gabriel Daniel Fahrenheit (1686–1736) somehow thought that three fixpoints were better than two. He pickeda freezing mixture of water and sea-salt (0°F),melting ice in water alone (32°F),human body temperature (96°F).Later he adjusted that scale slightly, so as to have boiling water at 212°F,exactly 180 degrees above melting ice.

One cannot help thinking that 180°is a neat number, at least when the degrees are degrees of arc. HoweverMiddleton, who describes the development of the Fahrenheit scale in somedetail, does not mention that analogy so that it is probably fortuitous.Anyway, after the readjustment, the body temperature came to 98.6°F. Thatis where the body temperature stands today in those countries, where theFahrenheit scale is still in use, notably in the United States of America.From the above it is easy to calculate the transition formula between theCelsius and the Fahrenheit scales: C = 5/9(F – 32).7 Middleton:loc.cit.

p. 61.1 Temperature5There were numerous other scales, advertised at different times, indifferent places, and by different people. It was not uncommon in the 18thand early 19th century to place the thermometric tube in front of a wideboard with several different scales, – up to eighteen of them. Middleton8exhibits a list of scales shown on a thermometer of 1841:Old FlorentineNew FlorentineHalesFowlerParisH. M.PoleniDelisleFahrenheitRéaumurBellaniChristinMichaellyAmontonsNewtonSociété RoyaleDe la HireEdinburgCruquiusAll of these scales were arbitrary and entirely subjective but, of course,perfectly usable, if only people could have agreed to use one of them, –which they could not.A new objective aspect appeared in the field with the idea that theremight be a lowest temperature, an absolute minimum.

By the midnineteenth century, two hundred years of experimental research on idealgases had jelled into the result that the pressure p and the volume V of gaseswere linear functions of the Celsius temperature (say), such thatkpV m (273.15’C t )µm is the mass of the gas.9 Therefore, upon lowering the temperature tot = – 273.15°C at constant p, the volume had to decrease and eventuallyvanish, and surely further cooling was then absurd. At first people wereunimpressed and unconvinced of the minimal temperature. After all, eventhen they suspected that all gases turn into liquids and solids at low temperatures, and the argument did not apply to either.However, in the 19th century it was slowly – painfully slowly –recognized that matter consisted of atoms and molecules, and thattemperature was a measure for the mean kinetic energy of those particles.This notion afforded an understanding of the minimal temperature, because89Middleton: loc.cit.

p. 66.In much of the 19th century literature this equation is called the law of Mariotte and GayLussac. Nowadays we call it the thermal equation of state for an ideal gas. The pioneersof the equation were Robert Boyle (1627–1691), Edmé Mariotte (1620–1684), GuillaumeAmontons (1663–1705), Jacques Alexandre César Charles (1746–1823), and Joseph LouisGay-Lussac (1778–1850). Their work is now a favourite subject of high-school physicscourses. Therefore I skip over its motivation and derivation. I only emphasize that thevalue 273.15 is the same for all gases. That value was established by Gay-Lussac whenhe measured the relative volume expansion by heating a gas of 0°C by 1°C.

[The value273.15 is the modern one; in fact it is 273.15 r 0.02. Gay-Lussac and others at the timewere up to 5% off.] [The factor k/µ is also modern. k is the Boltzmann constant and µ isthe molecular mass. Both are quite anachronistic in the present context. However, I wishto avoid the ideal gas constant and the molar mass in this book.]61 Temperaturewhen temperature dropped, so did the kinetic energy of the particles – ofgases, liquids, and solids – and finally, when all were at rest, there was noway to lower the temperature further.Therefore William Thomson (1824–1907) (Lord Kelvin since 1892)suggested – in 1848 – to call the lowest temperature absolute zero, and tomove upward from that point by the steps or degrees of Celsius. This newscale became known as the absolute scale or Kelvin scale, on which meltingice and boiling water at 1atm have the temperature values 273.15°K and373.15°K respectively.

K stands for Kelvin. It became common practice todenote temperature values on the Kelvin scale by T, so that we havet ØÈT = É 273.15 Ù °K .ʒC ÚKelvin’s absolute scale was quickly adopted and it is now used byscientists all over the world. However, the scale has subtly changed since itsintroduction.

In 1954, by international agreement the temperatures ofmelting ice and boiling water were abolished as fix-points. They werereplaced by a single fix-point:Ttr = 273.16°Kfor the triple point of water.The triple point of water occurs when ice, liquid water and water vapourcan coexist; its pressure is ptr = 6.1mbar, and its temperature is ttr = 0.01°Con the Celsius scale. The modern degree is defined by choosing 1°K asTtr/273.16.

This unit step on the Kelvin scale was internationally agreed onin 1954 so as to coincide with the familiar 1°C. The 13th InternationalConference on Measures and Weights of 1967/68 even robbed temperatureof its little decorative adornment ‘‘°” for degree. Ever since then we speakand write of temperature values prosaically as so many ‘‘K” instead of‘‘degrees K”, or ‘‘°K”.10The lowest temperatures reached in laboratories are a few µK – a fewmillionth of one Kelvin –, the highest may be 10MK – ten million Kelvin –,and we believe that the temperature in the centre of some stars are as highas 100 million K, cf.

Chaps. 6 and 7.For the early researchers there was no need to define temperature. Theyknew, or thought they knew, what temperature was when they stuck theirthermometer into well-water, or into the armpit of a healthy man. Theywere unaware of the implicit assumption, – or considered it unimportant, orself-evident – that the temperature of the thermometric substance, gas ormercury, or alcohol, was equal to the temperature of the measured object.10Temperature measurements at extremely low temperatures are still a problem.

Theinterested reader is referred to the publication ‘‘Die SI-Basiseinheiten. Definition,Entwicklung, Realisierung.’’ [The SI basic units. Definition, development and realization]Physikalisch Technische Bundesanstalt, Braunschweig & Berlin (1997) p. 31–35.1 Temperature7This in fact is the defining property of temperature: That the temperaturefield is continuous at the surface of the thermometer; hence temperature ismeasurable. Axiomatists call this the zeroth law of thermodynamicsbecause, by the time when they recognized the need for a definition oftemperature, the first and second laws were already firmly labelled.2 EnergyThe word energy is a technical term invented by Thomas Young (1773–1829) in 1807. Its origin is the Greek word ȑȞİȡȖİȚĮ which means efficacyor effective force. Young used it as a convenient abbreviation for the sum ofkinetic energy and gravitational potential energy of a mass and the elasticenergy of a spring to which the mass may be attached.