Inventing Temperature Read online

  3215 [L]

  Source code:

  B: Bergman 1783, 71, 94

  C: Chaldecott 1979, 84

  C/D: Clément and Desormes

  Da: Daniell 1821, 317-318, by platinum

  Db: Daniell 1830, 279, by platinum, corrected for non-linearity

  Di: Daniell 1830, 279, by iron

  Dr: Draper 1847, 346

  G: Guyton 1811b, 90, table 3; 117, table 5; and 120, table 7

  L: Lide and Kehiaian 1994, 26-31

  N: Newton [1701] 1935, 125-126; data converted assuming the highest boiling heat of water at 212° F.

  Pa: Pouillet 1827-29, 1:317

  Pb: Pouillet 1836, 789

  Pc: Pouillet 1856, 1:265

  Pr: Prinsep 1828, 94

  R: Rostoker and Rostoker 1989, 170

  W: Wedgwood 1784, 370

  a All degrees are on the Fahrenheit scale, except in the first column of data, which gives Wedgwood degrees. The last column gives the currently accepted values, for comparison. The code in parentheses indicates the authorities cited, and the code in square brackets indicates my sources of information, if they are not the original sources.

  b Bergman's 1783 text does not generally indicate how his melting points were determined. But on p. 94 he notes that the number for the melting point of iron was based on Mortimer's work on the expansion of metals, so I have put all of his values above the boiling point of mercury into the "metal" column. I assume that he used the mercury thermometer for lower temperatures, but that is only a conjecture.

  c This point is described as fonte de fer prête à couler by Guyton.

  d This is described as fusion de fer doux, sans cément.

  Source: Adapted from the second series of data given in Regnault 1847, 188.

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  in research and teaching.41 Apparently unaware of Guyton's work, Daniell (1821, 309-310) asserted that in pyrometry "but one attempt has ever been made, with any degree of success," which was Wedgwood's. He lamented the fact that Wedgwood's measurements were still the only ones available, although the Wedgwood pyrometer had "long fallen into disuse" for good reasons (he cited the difficulty of making clay pieces of uniform composition, and the observation that the amount of their contraction depended on exposure time as well as temperature).

  Daniell (1821, 313-314) graduated his instrument on two fixed points, on the model of the standard thermometers. He put the zero of his pyrometer where the mercury thermometer gave 56°F, and then set 85° of his scale at the boiling point of mercury, which he took as 656°F. Simple comparison gave about 7°F per each Daniell degree. That was an estimate made assuming the linearity of the thermal expansion of both mercury and platinum, but Daniell did test that assumption to some extent by comparing the two thermometers at various other points. The result was reasonably reassuring, as the differences were well within about 3 Daniell degrees through the range up to the boiling point of mercury. However, on the most crucial epistemic point regarding the validity of extending that observed trend beyond the boiling point of mercury, he made no progress beyond Guyton. The following non-argument was all that Daniell (1821, 319) provided for trusting the expansion of platinum to remain linear up to its melting point: "[T]he equal expansion of platinum, with equal increments of heat, is one of the best established facts of natural philosophy, while the equal contraction of clay, is an assumption which has been disputed, if not disproved." After taking our lessons from Regnault in chapter 2, we may be pardoned if we cannot help pointing out that the "equal expansion of platinum" was an "established fact" only in the temperature range below the boiling point of mercury, and even then only if one assumes that mercury itself expands linearly with temperature.

  By 1830 Daniell had discovered Guyton's work, and he had some interesting comments to make. All in all, Daniell's work did constitute several advances on Guyton's. Practically, he devised a way of monitoring the expansion of the platinum bar more reliably.42 In terms of principles, Daniell chastised Guyton for going along with Wedgwood's assumption of linearity in the contraction of clay (1830, 260): "Guyton, however, although he abundantly proves the incorrectness of Mr. Wedgwood's estimate of the higher degrees of temperature, is very far indeed from establishing the point at which he so earnestly laboured, namely, the regularity of the contraction of the clay pieces." Daniell made much more detailed comparisons between temperature readings produced by the various methods in question (1830, 260-262). His general conclusion regarding Guyton's correction of the Wedgwood scale was that he had not shrunk it sufficiently, while his lowering of the zero point (red heat visible in daylight) went too far. In Daniell's view, the best correction of the Wedgwood scale was obtained by actually raising Wedgwood's

  41. See the Dictionary of National Biography, 14 (1888), 33.

  42. See Daniell 1821, 310-311, for his basic design, and Daniell 1830, 259, for a critique of Guyton's design.

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  estimate of the zero point a little bit, and shrinking each Wedgwood degree drastically down to about 20°F. However, he thought that no simple rescaling of the Wedgwood scale would bring one to true temperatures, since the contraction of clay was not regular.

  Not regular when judged by the platinum pyrometer, that is. Daniell (1830, 284-285) admitted that the expansion of platinum was also unlikely to be linear and took Dulong and Petit to have shown that "the dilatability of solids, referred to an air-thermometer, increases with the heat." Extrapolating Dulong and Petit's results, Daniell arrived at some corrections to his pyrometer readings obtained with the assumption of linearity. (Daniell's corrected results are labeled Db in table 3.2, which summarizes various pyrometric measurements.) These corrections were nontrivial. Dulong and Petit had indicated that a thermometer of iron graduated between 0°C and 100°C assuming linearity would read 372.6°C when the air thermometer gave 300°C; the deviation from linearity was not so dire for platinum, but even a platinum thermometer would give 311.6°C when the air thermometer gave 300°C (1817, 141; 1816, 263). Daniell deserves credit for applying this knowledge of nonlinearity to correct metallic thermometers, but there were two problems with his procedure. First of all, Dulong and Petit's observations went up to only 300°C (572°F), probably since that was the technical limit of their air thermometer. So, even in making corrections to his linear extrapolation, Daniell had to extrapolate an empirical law far beyond the domain in which it was established by observation. Daniell carried that extrapolation to about 1600°C, covering several times as much as Dulong and Petit's entire range. Second, Daniell's correction of the platinum pyrometer made sense only if there was assurance that the air thermometer was a correct instrument in the first place; I will return to that issue later.

  Ice Calorimetry

  Given the futility of relying on unverifiable expansion laws for various substances at the pyrometric range, it seems a sensible move to bring the measurements to the easily observable domains. The chief methods for doing so were calorimetric: the initial temperature of a hot object can be deduced from the amount of ice it can melt, or the amount of temperature rise it can produce in a body of cold water. The latent and specific heats of water being so great, a reasonable amount of ice or water sufficed to cool small objects from very high temperatures down to sensible temperatures. Different calorimetric techniques rested on different assumptions, but all methods were founded on the assumption of conservation of heat: the amount of heat lost by the hot body is equal to the amount of heat gained by the colder body, if they reach equilibrium in thermal isolation from the external environment. In addition, inferring the unknown initial temperature of a body also requires further assumptions about the specific heat of that body, a more problematic matter on which I will comment further shortly.

  Calorimetry by means of melting ice was a well-publicized technique ever since Lavoisier and Laplace's use of it, described in their 1783 memoir on heat. Wedgwood (1784, 371-372) read a summary o
f the Lavoisier-Laplace article after his initial publication on the pyrometer, with excitement: "The application of this important

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  discovery, as an intermediate standard measure between Fahrenheit's thermometer and mine, could not escape me." However, Wedgwood (1784, 372-384) was greatly disappointed in his attempt to use the ice calorimeter to test the soundness of his pyrometer. Ice calorimetry rested on the assumption that all the melted water would drip down from the ice so that it could be collected and weighed up accurately. Wedgwood noted that even a solid block of ice imbibed and retained a considerable amount of melted water, and the problem was much worse for pounded ice, used by Lavoisier and Laplace. Wedgwood's confidence in the ice calorimeter was further shaken by his observation that even while the melting of ice was proceeding as designed, there was also fresh ice forming in the instrument, which led him to conclude that the melting point of ice and the freezing point of water, or water vapor at any rate, were probably not the same.

  The French savants, however, were not going to give up the invention of their national heroes so easily. Claude-Louis Berthollet, Laplace's close associate and the dean of French chemistry since Lavoisier's demise at the guillotine in 1794, defended the ice calorimeter against Wedgwood's doubts in his 1803 textbook of chemistry. The problem of ice retaining the melted water could be avoided by using ice that had already imbibed as much water as it could. As Lodwig and Smeaton (1974, 5) point out, if Wedgwood had read Lavoisier and Laplace's memoir in full he would have realized that they had considered this factor but thought that their crushed ice was already saturated with water to begin with.43 As for the refreezing of ice that takes place simultaneously with melting, it did not in itself interfere with the functioning of the instrument. Citing Berthollet, Guyton (1811b, 102-103) argued that the calorimeter was "the instrument best suited for verifying or correcting Wedgwood's pyrometric observations."

  Guyton never had the opportunity to carry out this test of the Wedgwood pyrometer by the ice calorimeter, not having met with the right weather conditions (low and steady temperatures). But he cited some relevant results that had been obtained by two able experimenters, Nicolas Clément (1778/9-1841) and his father-in-law Charles-Bernard Desormes (1777-1862), both industrial chemists; Desormes was for a time an assistant in Guyton's lab at the École Polytechnique.44 Their data showed that temperatures measured by ice calorimetry were generally much lower than those obtained with the Wedgwood pyrometer (not only by Wedgwood but also by Clément and Desormes themselves). All of their results cited by Guyton are included in table 3.2. As one can see there, Clément and Desormes measured four very high temperatures with an ice calorimeter, and the same temperatures were also measured by a Wedgwood pyrometer. If one adopted Wedgwood's own conversion of Wedgwood degrees into Fahrenheit degrees (the second column in

  43. Lodwig and Smeaton also note that Wedgwood's criticism was quite influential at least in England and discuss various other criticisms leveled against the Laplace-Lavoisier calorimeter.

  44. See Guyton 1811b, 104-105, and the data in table 7. As far as I can ascertain, Clément and Desormes's pyrometric work was not published anywhere else; the reference that Guyton gives in his article seems misplaced. The biographical information is cited from Jacques Payen's entry on Clément in the Dictionary of Scientific Biography, 3:315-317.

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  the table), the resulting temperatures were about 10,000 to 20,000 higher than the numbers given by ice calorimetry. Even using Guyton's revised conversion gave numbers that were thousands of degrees higher than those obtained by ice calorimetry.

  Clément and Desormes's ice-calorimetry results were scant and lacked independent confirmation. But the real problem lay in the theoretical principles, as mentioned briefly earlier. We have already seen the same kind of problem in De Luc's method of mixtures for testing thermometers (see "Caloric Theories against the Method of Mixtures" in chapter 2), which is a calorimetric technique (though it is more akin to water calorimetry, to be discussed shortly). Ice calorimetry measures the amount of heat lost by the hot object in coming down to the temperature of melting ice, not the temperature initially possessed by the hot object. Ice calorimetry at that time relied on the assumption that the specific heat of the hot object was constant throughout the temperature range. That assumption was clearly open to doubt, but it was difficult to improve on it because of the circularity that should be familiar by now to the readers of this book: the only direct solution was to make accurate measurements of specific heats as a function of temperature, and that in turn required an accurate method of temperature measurement, which is precisely what was missing in the pyrometric range. In a work that I will be discussing later, Dulong and Petit (1816, 241-242) regarded the "extreme difficulty" of determining the specific heat of bodies with precision, especially at high temperatures, as one of the greatest obstacles to the solution of the thermometry problem.

  Water Calorimetry

  How about the other major calorimetric method, using the temperature changes in water? Water calorimetry had fewer problems than ice calorimetry in practice, but it was open to the same problem of principle, namely not knowing the specific heat of the object that is being cooled down. In fact the theoretical problem was worse in this case, since there was also a worry about whether the specific heat of water itself varied with temperature. The history of water calorimetry was long, but it seems that Clément and Desormes were the first people to employ the method in the pyrometric range. As shown in table 3.2, they only obtained three data points by this method. The melting point of copper by this method was in good agreement with Guyton's result by platinum pyrometry and also in rough agreement with the two later results from Daniell by the same method. The number for the melting point of soft iron was drastically lower than the value obtained by the Wedgwood method, and in quite good agreement with the result by ice calorimetry. The estimate of "red heat" was nearly 200 degrees higher than Wedgwood's, and over 700 degrees higher than Guyton's, and not much of anything could be concluded from that disagreement.

  Time of Cooling

  Another method of avoiding the taking of data in the pyrometric range was to estimate the temperature of a hot object from the amount of time taken for it to cool

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  down to a well-determined lower temperature. As I mentioned earlier, this method had been used by Newton for temperatures above the melting point of lead. Dulong and Petit revived the method and employed it with more care and precision than Newton, but the fundamental problem remained: verifying the law of cooling would have required an independent measure of temperature. For Dulong and Petit, that independent measure of temperature was the air thermometer, which made sense for them, since they regarded the air thermometer as the true standard of temperature, as discussed in "Regnault and Post-Laplacian Empiricism" in chapter 2.

  Air Pyrometry

  The thermometer in general theoretical favor by the beginning of the nineteenth century was the air thermometer, so it might have made sense to compare the readings of the various pyrometers with the readings of the air thermometer as far as possible. However, as discussed at length in chapter 2, no conclusive argument for the superiority of the air thermometer to the mercury thermometer was available until Regnault's work in the 1840s. And Regnault never claimed that his work showed that air expanded linearly with temperature. Moreover, Regnault's painstaking work establishing the comparability of air thermometers was only carried out in relatively low temperatures, up to about 340°C (644°F). In short, there was no definite assurance that comparison with the air thermometer was an absolutely reliable test for the accuracy of pyrometers. Even so, the air thermometer certainly provided one of the most plausible methods of measuring high temperatures.

  In practical terms, if one was going to rely on the expansion of anything in the pyrometric range, air was an obvious candidate as there were no conceivable worries at that time about any changes of state (though lat
er the dissociation of air molecules at very high temperatures would become an issue). But that was illusory comfort: an air thermometer was good only as long as the container for the air remained robust. Besides, air thermometers were usually large and very unwieldy, especially for high temperatures. Clément and Desormes took the air-in-glass thermometer to its material limits, using it to measure the melting point of zinc, which they reported as 932°F (Guyton 1811b, table 7). Dulong and Petit's work with the air thermometer was more detailed and precise, but did nothing to extend its range; in fact, in order to ensure higher precision they restricted the range in which they experimented, going nowhere beyond 300°C (572°F). Even Regnault only managed to use air thermometers credibly up to temperatures around 400°C (around 750°F).

  The obvious solution was to extend the range of the air thermometer by making the reservoir with materials that were more robust in high temperatures.45 The first

  45. As an alternative (or additional) solution, Pouillet had the idea that the range of the air thermometer might be extended in the high-temperature domain by the employment of the constant-pressure method, which had the advantage of putting less strain on the reservoirs. Regnault agreed with this idea (1847, 260-261, 263), but he criticized Pouillet's particular setup for having decreasing sensitivity as temperature increased (170), and also expressed worries about the uncertainty arising from the lack of knowledge in the law of expansion of the reservoir material (264-267).

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