Inventing Temperature Read online

  As De Luc's doubts underscore, Cavendish's preference for steam rested on an extraordinary belief: that steam emerging from water boiling under a fixed pressure must always have the same temperature, whatever the temperature of the water itself may be. This claim required a defense.

  First of all, why would steam (or water vapor)30 emerging out of water be only at 100°C, if the water itself has a higher temperature? Cavendish's answer was the following: These bubbles [of steam] during their ascent through the water can hardly be hotter than the boiling point; for so much of the water which is in contact with them must instantly be turned into steam that by means of the production of cold thereby, the coat of water … in contact with the bubbles, is no hotter than the boiling point; so that the bubbles during their ascent are continually in contact with water heated only to the boiling point. (Cavendish [n.d.] 1921, 359)

  The fact that the formation of steam requires a great deal of heat was widely accepted since the work of the celebrated Scottish physician and chemist Joseph Black (1728-1799) on latent heat, and De Luc and Cavendish had each developed

  29. De Luc's letter has been published in Jungnickel and McCormmach 1999, 546-551, in the original French and in English translation; I quote from McCormmach's translation except as indicated in square brackets. The essay that De Luc was commenting on must have been an earlier version of Cavendish [n.d.] 1921.

  30. In De Luc's view, as in modern usage, there was no essential difference between steam and water vapor; they were simply different names for the gaseous state of water. Up to the end of the eighteenth century, however, many people saw steam produced by boiling as fundamentally different from vapor produced by evaporation at lower temperatures. A popular idea, which Cavendish favored, was that evaporation was a process in which water became dissolved in air. De Luc was one of those who criticized this idea strongly, for instance by pointing out that evaporation happens quite well into a vacuum where there is no air that can serve as a solvent. For further details, see Dyment 1937, esp. 471-473, and Middleton 1965.

  end p.26

  similar ideas, though they recognized Black's priority. However, for a convincing demonstration that the steam in the body of superheated boiling water would always be brought down to the "boiling point," one needed a quantitative estimate of the rate of cooling by evaporation in comparison with the amount of heat continually received by the steam from the surrounding water. Such an estimate was well beyond Cavendish's reach.

  De Luc also asked what would prevent the steam from cooling down below the boiling temperature, after emerging from the boiling water. Here Cavendish offered no theoretical account, except a dogmatically stated principle, which he considered empirically vindicated: "[S]team not mixed with air as soon as it is cooled ever so little below the [boiling temperature] is immediately turned back into water" ([n.d.] 1921, 354). De Luc's experience was to the contrary: "[W]hen in a little vessel, the mouth and its neck are open at the same time, the vapor, without condensing, becomes perceptibly cooler." (I will return to this point of argument in "A Dusty Epilogue.") He also doubted that steam could realistically be obtained completely free of air, which was necessary in order for Cavendish's principle to apply at all.31

  Judging from the final report of the Royal Society committee, it is clear that no firm consensus was reached on this matter. While the committee's chief recommendation for obtaining the upper fixed point was to adopt the steam-based procedure advocated by Cavendish, the report also approved two alternative methods, both using water rather than steam and one of them clearly identified as the procedure from De Luc's previous work.32 De Luc's acquiescence on the chief recommendation was due to the apparent fixedness of the steam temperature, not due to any perceived superiority in Cavendish's theoretical reasoning. In his February 1777 letter to Cavendish mentioned earlier, there were already a couple of indications of De Luc's surprise that the temperature of steam did seem more fixed than he would have expected. De Luc exhorted, agreeably: Let us then, Sir, proceed with immediate tests without dwelling on causes; this is our shortest and most certain path; and after having tried everything, we will retain what appears to us the best solution. I hope that we will finally find them, by all the pains that you wish to take. (De Luc, in Jungnickel and McCormmach 1999, 550)

  Thus, the use of steam enabled the Royal Society committee to obviate divisive and crippling disputes about theories of boiling. It gave a clear operational procedure that served well enough to define an empirically fixed point, though there was no agreed understanding of why steam coming off boiling water under a given pressure should have a fixed temperature.

  A more decisive experimental confirmation of the steadiness of the steam temperature had to wait for sixty-five years until Marcet's work, in which it was shown that the temperature of steam was nearly at the standard boiling point regardless of the temperature of the boiling water from which it emerged. Even when the water temperature was over 105°C, the steam temperature was only a few

  31. See De Luc, in Jungnickel and McCormmach 1999, 549-550.

  32. See Cavendish et al. 1777, 832, 850-853, for reference to De Luc's previous practice.

  end p.27

  tenths of a degree over 100°C (Marcet 1842, 404-405). That is still not negligible, but it was a reassuring result given that it was obtained with serious superheating in the boiling water. The situation was much ameliorated by the employment of all the various means of converting superheated boiling into common boiling. If these techniques could bring the water temperature down fairly close to 100°C, then the steam temperature would be reliably fixed at 100°C or very near it. Marcet's work closed a chapter in the history of superheating in which it posed a real threat to the fixity of the boiling point, although it did not address the question of whether steam could cool down below the boiling point.

  The Understanding of Boiling

  The "steam point" proved its robustness. After the challenge of superheating was overcome in the middle of the nineteenth century, the fixity (or rather, the fixability) of the steam point did not come into any serious doubt.33 The remaining difficulty now was in making sense of the empirically demonstrated fixability of the steam point. This task of understanding was a challenge that interested all but the most positivistic physicists. From my incomplete presentation in the last two sections, the theoretical situation regarding the boiling point would appear to be discordant and chaotic. However, a more careful look reveals a distinct course of advancement on the theoretical side that dovetailed neatly with the practical use of the steam point. Whether this advancement was quite sufficient for an adequate understanding of the phenomenon of boiling and the fixability of the steam point is the question that I will attempt to answer in this section.

  Let us start with a very basic question. For anything deserving the name of "boiling" to take place, vapor should form within the body of the liquid water and move out through the liquid. But why should this happen at anything like a fixed temperature? The crucial factor is the relation between the pressure and the temperature of water vapor. Suppose we let a body of water evaporate into an enclosed space as much as possible. In the setup shown in figure 1.4 (left), a small amount of water rests on a column of mercury in a barometer-like inverted glass tube and evaporates into the vacuum above the mercury until it cannot evaporate any more. Then the space is said to be "saturated" with vapor; similarly, if such a maximum evaporation would occur into an enclosed space containing air, the air is said to be saturated. Perhaps more confusingly, it is also said that the vapor itself is saturated, under those circumstances.

  It was observed already in the mid-eighteenth century that the density of saturated vapor is such that the pressure exerted by it has a definite value determined by temperature, and temperature only. If one allows more space after saturation is obtained (for instance by lifting the inverted test tube a bit higher), then just enough additional vapor is produced to maintain the same pressure as before; if one reduces the spac
e, enough vapor turns back into water so that the Figure 1.4. Experiments illustrating the pressure of saturated vapor (Preston 1904, 395).

  33. Marcet already stated in 1842 that the steam point was "universally" accepted, and the same assessment can be found at the end of the century, for example in Preston 1904, 105.

  end p.28

  vapor pressure again remains the same (see fig. 1.4 [right]). But if the temperature is raised, more vapor per available space is produced, resulting in a higher vapor pressure. It was in fact Lord Charles Cavendish (1704-1783), Henry's father, who first designed the simple mercury-based equipment to show and measure vapor pressures, and the son fully endorsed the father's results and assigned much theoretical significance to them as well.34 Cavendish's discovery of the exclusive dependence of vapor pressure on temperature was later confirmed by numerous illustrious observers including James Watt (1736-1819), John Dalton (1766-1844), and Victor Regnault (1810-1878). Table 1.2 shows some of the vapor-pressure data obtained by various observers.

  As seen in the table, the pressure of saturated vapor ("vapor pressure" from now on, for convenience) is equal to the normal atmospheric pressure when the temperature is 100°C. That observation provided the basic theoretical idea for a causal understanding of boiling: boiling takes place when the water produces vapor with sufficient pressure to overcome the resistance of the external atmosphere.35 This view gave a natural explanation for the pressure-dependence of the boiling point. It also provided perfect justification for the use of steam temperature to define the boiling point, since the key relation underlying the fixity of that point is the one between the temperature and pressure of saturated steam.

  This view, which I will call the pressure-balance theory of boiling, was a powerful and attractive theoretical framework. Still, there was a lot of "mopping up" or "anomaly busting" left to do (to borrow liberally from Thomas Kuhn's description of "normal science"). The first great anomaly for the pressure-balance theory of boiling was the fact that the boiling temperature was plainly not fixed even when the external pressure was fixed. The typical and reasonable thing to do was to

  34. See Cavendish [n.d.] 1921, 355, and also Jungnickel and McCormmach 1999, 127.

  35. This idea was also harmonious with Antoine Lavoisier's view that a liquid was only prevented from flying off into a gaseous state by the force of the surrounding atmosphere. See Lavoisier [1789] 1965, 7-8.

  end p.29

  Table 1.2. A comparative table of vapor-pressure measurements for water

  C. Cavendish (c.1757)a

  Dalton (1802)b

  Biot (1816)c

  Regnault (1847)d

  Temperature

  Vapor pressuree

  Vapor pressure

  Vapor pressure

  Vapor pressure

  35°F (1.67°C)

  0.20in. Hg

  0.221

  0.20

  40

  0.24

  0.263

  0.25

  45

  0.28

  0.316

  0.30

  50 (10°C)

  0.33

  0.375

  0.3608

  55

  0.41

  0.443

  0.43

  60

  0.49

  0.524

  0.52

  65

  0.58

  0.616

  0.62

  70

  0.70

  0.721

  0.73

  75

  0.84

  0.851

  0.87

  86 (30°C)

  1.21

  1.2064

  1.2420

  104 (40°C)

  2.11

  2.0865

  2.1617

  122 (50°C)

  3.50

  3.4938

  3.6213

  140 (60°C)

  5.74

  5.6593

  5.8579

  158 (70°C)

  9.02

  9.0185

  8.81508

  176 (80°C)

  13.92

  13.861

  13.9623

  194 (90°C)

  20.77

  20.680

  20.6870

  212 (100°C)

  30.00

  29.921

  29.9213

  302 (150°C)

  114.15

  140.993

  392 (200°C)

  460.1953

  446 (230°C)

  823.8740

  a These data are taken from Cavendish [n.d.] 1921, 355, editor's footnote.

  b Dalton 1802a, 559-563. The last point (for 302° F or 150° C) was obtained by extrapolation.

  c Biot 1816, 1:531. The French data (Biot's and Regnault's) were in centigrade temperatures and millimeters of mercury. I have converted the pressure data into English inches at the rate of 25.4 mm per inch.

  d Regnault 1847, 624-626. The entries for Regnault in the 35°-75° F range are approximate conversions (except at 50° F), since his data were taken at each centigrade, not Fahrenheit, degree.

  e All of the vapor pressure data in this table indicate the height (in English inches) of a column of mercury balanced by the vapor.

  postulate, and then try to identify the existence of interfering factors preventing the "normal" operation of the pressure-balance mechanism. An alternate viewpoint was that the matching of the vapor pressure with the external pressure was a necessary, but not sufficient condition for boiling, so other facilitating factors had to be present in order for boiling to occur. The two points of view were in fact quite compatible with each other, and they were used interchangeably sometimes even by a single author: saying that factor x was necessary to enable boiling came to the same thing in practice as saying that the absence of x prevented boiling. There were various competing ideas about the operation of these facilitating or preventative factors. Let us see if any of these auxiliary ideas were truly successful in defending the pressure-balance theory of boiling, thereby providing a theoretical justification for the use of the steam point.

  Gay-Lussac (1818, 130) theorized that boiling would be retarded by the adhesion of water to the vessel in which it is heated and also by the cohesion of water within itself. The "adhesion of the fluid to the vessel may be considered as analogous to its viscidity. … The cohesion or viscosity of a fluid must have a considerable

  end p.30

  effect for its boiling point, for the vapor which is formed in the interior of a fluid has two forces to overcome; the pressure upon its surface, and the cohesion of the particles." Therefore "the interior portions may acquire a greater degree of heat than the real boiling point," and the extra degree of heat acquired will also be greater if the vessel has stronger surface adhesion for water. Gay-Lussac inferred that the reason water boiled "with more difficulty" in a glass vessel than in a metallic one must be because there were stronger adhesive forces between glass and water than between metal and water. Boiling was now seen as a thoroughly sticky phenomenon. The stickiness is easier to visualize if we think of the boiling of a thick sauce and allow that water also has some degree of viscosity within itself and adhesiveness to certain solid surfaces.

  Twenty-five years later Marcet (1842, 388-390) tested the adhesion hypothesis more rigorously. First he predicted that throwing in bits of metal into a glass vessel of boiling water would lower the boiling temperature, but not as far down as 100°C, which is where water boils when the vessel is entirely made of metal. This prediction was borne out in his tests, since the lowest boiling temperature he could ever obtain with the insertion of metal pieces was 100.2°C, contrary to Gay-Lussac's earlier claim that it went down to 100°C exactly. More significantly, Marcet predicted that if the inside of the vessel could be coated with a material that has even less adhesion to water than metals do, the boiling temperature would go down below 100°C. Again as predicted, Marcet achieved boiling at 99.85°C in a glass vessel scattered with drops of
sulphur. When the bottom and sides of the vessel were covered with a thin layer of gomme laque, boiling took place at 99.7°C. Although 0.3° is not a huge amount, Marcet felt that he had detected a definite error in previous thermometry, which had fixed the boiling point at the temperature of water boiling in a metallic vessel: It is apparent that previous investigators have been mistaken in assuming that under given atmospheric pressure, water boiling in a metallic vessel had the lowest possible temperatures, because in some cases the temperature could be lowered for a further 0.3 degrees. It is, however, on the basis of that fact, generally assumed to be exactly true, that physicists made a choice of the temperature of water boiling in a metallic vessel as one of the fixed points of the thermometric scale. (Marcet 1842, 391)

  Finally, it seemed, theoretical understanding had reached a point where it could lead to a refinement in existing practices, going beyond their retrospective justification.

  Marcet's beautiful confirmations seemed to show beyond any reasonable doubt the correctness of the pressure-balance theory modified by the adhesion hypothesis. However, two decades later Dufour (1861, 254-255) voiced strong dissent on the role of adhesion. Since he observed extreme superheating of water drops removed from solid surfaces by suspension in other liquids, he argued that simple adhesion to solid surfaces could not be the main cause of superheating. Instead Dufour stressed the importance of the ill-understood molecular actions at the point of contact between water and other substances: For example, if water is completely isolated from solids, it always exceeds 100°C before turning into vapor. It seems to me beyond doubt that heat alone, acting on