Inventing Temperature Page 12
Such impulsive and intuitive advocacy, from any side, failed to convince. In the days before the caloric theory there was only one tradition of cogent reasoning and experimentation with a potential to settle the argument. This was the method of mixtures. Mix equal amounts of freezing water (at 0° centigrade, by definition) and boiling water (at 100°, again by definition) in an insulated vessel; if a thermometer inserted in that mixture reads 50°, it indicates the real temperature. Such mixtures could be made in various proportions (1 part boiling water and 9 parts freezing water should give 10° centigrade, and so on), in order to test thermometers for correctness everywhere on the scale between the two fixed points. Given this technique, it was no longer necessary to get into the circular business of judging one type of thermometer against another.
The earliest employment of the method of mixtures intended for the testing of thermometers was probably by Brook Taylor (1685-1731), English mathematician of the Taylor series fame, and secretary of the Royal Society from 1714 to 1718. Taylor (1723) published a brief account reporting that the linseed oil thermometer performed satisfactorily when tested by the method of mixtures. His test was not a very precise one, and he did not even give any numbers in his one-page report. It was also not a test designed to compare the performances of different fluids (which is understandable considering that this was before Boerhaave and Réaumur
7. Du Crest (1741, 9-10) believed that the temperature of the bulk of the Earth (as indicated by the supposedly constant temperature of deep cellars and mines) was fundamentally fixed, and therefore the most extreme temperatures observed on the surface of the earth (in Senegal and Kamchaka, respectively) should be equally far from that median temperature. His spirit thermometers gave readings more in accord with that hypothesis than did his mercury thermometers. See also Middleton 1966, 90-91.
8. See Lambert 1779, 78, and Amontons 1702. See also Middleton 1966, 108 on Lambert, and 63 on Amontons.
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reported the discrepancy between spirit and quicksilver thermometers). A few decades later, in 1760, the method of mixtures was revived by Joseph Black, who carried out similar experiments on the mercury thermometer and obtained a satisfactory verdict regarding its accuracy.9
The person who brought the tradition of mixtures to its culmination was Jean-André De Luc (1727-1817), Genevan meteorologist, geologist, and physicist; I have discussed some aspects of his life and work in detail in chapter 1 (see especially "The Vexatious Variations of the Boiling Point" and "Superheating and the Mirage of True Ebullition"). When we left him there, he had just spent four weeks shaking air out of a flask full of water to investigate the boiling behavior of pure water. De Luc had examined almost every conceivable aspect of thermometry in his 1772 treatise, and the choice of fluids was one of his chief concerns. He observed that the choice of thermometric fluids was just that—a matter of choice. However, De Luc insisted that there should be some principle guiding the choice. The "fundamental principle" for him was that the fluid "must measure equal variations of heat by equal variations of its volume" (De Luc 1772, 1:222-223, §§410b-411a). But which fluid, if any, actually satisfied this requirement had not been established.
De Luc's investigations resulted in the conclusion that mercury was the most satisfactory thermometric liquid.10 What he regarded as the "direct proof" of mercury's superiority and "first reason" for using it in thermometers was the result of the mixing experiments (1:285-314, §422). He attributed the method of mixtures primarily to his mentor and friend George-Louis Le Sage the Younger (1724-1803), a hardly published but highly influential figure in Geneva at this time. Generally speaking, De Luc mixed two samples of water at previously known temperatures and compared the reading given by a thermometer with the calculated temperature. To imagine the simplest case again: equal amounts of water at freezing (0°C) and boiling (100°C) should make a mixture of 50°C; the correct thermometer should read 50°C when inserted into that mixture.11
9. See Black 1770, 8-12, and Black 1803, 1:56-59.
10. As for non-liquid thermometric substances, De Luc dismissed solids relatively quickly and gave many detailed reasons against air, with particular reference to Amontons's air thermometer. See De Luc 1772, 1:275-283, §§420-421.
11. It should be noted that De Luc did not use water exactly at the boiling and freezing points, so his reasoning was slightly more complicated than Taylor's. This seems to be a fact often ignored by his commentators, friend and foe, but De Luc himself stated well-considered reasons for his practice. Regarding water at the boiling point, he said: "[B]oiling water can be neither measured (in volume) nor weighed [accurately]"; see De Luc 1772, 1:292, §422. One might try to weigh the water before bringing it to boil, but then there would be a significant loss by evaporation once it starts to boil. There was no such problem with the freezing point, but he noted that it was difficult to prepare a large enough volume of liquid water exactly at the freezing point (pp. 298-299). So he was forced to use water that was only nearly boiling and nearly freezing. At first glance it would seem that this saddled De Luc with a vicious circularity, since he first had to use a thermometer to measure the temperatures of his hot and cold waters. He did have a process of correction with which he was satisfied (pp. 299-306), but in any case the basic procedure is not problematic if it is viewed as a test of consistency. If the mercury thermometer is correct, and we mix equal amounts of water at temperatures a° and b° as measured by it, then the mercury thermometer should give (a + b)/2° for the temperature of the mixture.
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Table 2.2. Results of De Luc's test of the mercury thermometer by the method of mixtures
Degree of real heat (calculated)a
Reading of the mercury thermometer
Condensation of mercury between last two points
Boiling water
z+80
80.0
−
z+75
74.7
5.3
z+70
69.4
5.3
z+65
64.2
5.2
z+60
59.0
5.2
z+55
53.8
5.2
z+50
48.7
5.1
z+45
43.6
5.1
z+40
38.6
5.0
z+35
33.6
5.0
z+30
28.7
4.9
z+25
23.8
4.9
z+20
18.9
4.9
z+15
14.1
4.8
z+10
9.3
4.8
z+5
4.6
4.7
Melting ice
z
0.0
4.6
Source: The data are taken from De Luc 1772, 1:301, §422.
a All temperatures in this table are on the Réaumur scale. The "z" in the degrees of real heat signifies that the "absolute zero" point of temperature (indicating a complete absence of heat) is not known.
The verdict from De Luc's experiments was unequivocal. The deviation of the mercury thermometer from degrees of real heat was pleasingly small, as shown in table 2.2 (note that De Luc was using the "Réaumur" temperature scale, in which the temperature of boiling water was set at 80° rather than 100°). Even more decisive than this consideration of mercury alone was the comparative view. From De Luc's results juxtaposing the performance of eight different liquids, shown in table 2.3, there was no question that mercury gave the best available approximation to the "real" degrees of heat.
These results were in accord with theoretical considerations as well. De Luc reasoned that the condensation of liquids proceeded uniformly according to temperature until contraction so crowded the molecules that they resisted further condensation.12 So he infer
red that a significant "slowing down" of condensation was a sign that the liquid has entered the crowded phase in which its volume ceases to reflect the true variation in the quantity of heat. Therefore, as temperature goes down "the liquid whose rate of condensation increases in comparison to that of all other liquids is very probably the one in which differences of volume are closest to
12. Here he was certainly not adopting the assumption that particles of matter have inherent mutual attraction only to be counterbalanced by the repulsive action of heat, which would later become a centerpiece of the caloric theory, in the years around 1800.
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Table 2.3. De Luc's comparison of the readings of various thermometers with the "real" degree of heat Real degree of heat (calculated)a
40.0
Mercury thermometer
38.6
Olive oil thermometer
37.8
Camomile oil thermometer
37.2
Thyme oil thermometer
37.0
Saturated salt water thermometer
34.9
Spirit thermometer
33.7
Water thermometer
19.2
Source: Adapted from De Luc 1772, 1:311, §422.
a All temperatures in this table are on the Réaumur scale.
being proportional to differences of heat." On this criterion, too, mercury was shown to be the best choice.13 De Luc was so confident of his results that he declared that mercury deserved "an exclusive preference" in the construction of the thermometer. Borrowing the words of an acquaintance impressed by his demonstration, he expressed his elation: "[C]ertainly nature gave us this mineral for making thermometers!" (De Luc 1772, 1:330, §426) Unlike his work on the boiling point discussed in chapter 1, De Luc's experiments and arguments in favor of mercury gained wide acceptance, with endorsements from various leading authorities in physics and chemistry throughout Europe. By around 1800 De Luc had created an impressive degree of consensus on this issue, cutting through significant disciplinary, national, and linguistic boundaries.14
Caloric Theories against the Method of Mixtures
This consensus on mercury, however, began to crumble just as it was being secured. Trouble developed around De Luc's crucial assumption that the amount of heat needed in heating a given amount of water was simply proportional to the amount of change in its temperature. For instance, in presenting the results listed in table 2.2, De Luc was assuming that it would take the same amount of heat to raise the temperature of a given amount of water by each 5° increment. When applied generally, this amounted to the assumption that the specific heat of water was constant and did not depend on temperature. This was a convenient assumption, and there were no particular reasons for De Luc to doubt it at the time.15 However,
13. De Luc 1772, 1:284-285, §421. See also his table comparing the "marche" of seven different liquids on p. 271, §418.
14. For further details of the impressive degree of support De Luc gained, see Chang 2001b, 256-259.
15. In that sense the status of this assumption was the same as that of the other major assumption in De Luc's experiments (and in all related calorimetric measurements), which was that heat was a conserved quantity.
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this assumption was challenged with increasing readiness and confidence as a consequence of the growing sophistication of the caloric theory, which is the main feature in the development of the chemistry and physics of heat in the decades around 1800. For readers unfamiliar with the history of the caloric theory, a few words of background explanation are necessary.16
The core of the caloric theory was the postulation of caloric, a material substance that was regarded as the cause of heat or even as heat itself. Most commonly caloric was seen as a subtle fluid (all-penetrating and weightless or nearly so) that was attracted to ordinary matter but self-repulsive (therefore elastic). The self-repulsion of caloric was a crucial quality, since it explained a whole host of effects of heat, ranging from the melting of solids to the increased pressure of gases. There were different versions of the caloric theory developing in competition with each other. I follow Robert Fox (1971) in dividing the caloric theorists (or "calorists") into two broad categories, depending on their views on the meaning of specific and latent heat. I will call these groups "Irvinist" (following Fox) and "chemical."
The Irvinists followed the doctrine of William Irvine (1743-1787), a pupil and collaborator of Black's in Glasgow, who postulated that the amount of caloric contained in a body was the product of its capacity for caloric (heat capacity) and its "absolute temperature" (which would be zero degrees at the point of a total absence of heat). If a body preserved its heat content but its heat capacity was increased for some reason, its temperature would go down; this was explained by an analogy to a bucket that suddenly widens, lowering the level of liquid contained in it. Irvine conceptualized latent heat as the heat required just to keep the temperature at the same level in such a case. (I will discuss Irvinist heat theory further in "Theoretical Temperature before Thermodynamics" in chapter 4.)
In contrast, in the chemical view of caloric, latent heat was seen as a different state of heat, postulated to lack the power of affecting the thermometer. Black had viewed the melting of ice as the combination of ice and caloric to produce liquid water. Though Black himself chose to remain ultimately agnostic about the metaphysical nature of heat,17 his view on latent heat was taken up and generalized by some chemists into the notion of caloric as a substance that could enter into chemical combinations with ordinary matter. Antoine-Laurent Lavoisier (1743-1794) developed a similar view through the 1770s and went so far as to include caloric (and also light) in the table of chemical elements in his authoritative textbook of the new chemistry, Elements of Chemistry (1789).18 On this chemical view of heat, the latent caloric that entered into combination with particles of matter was the cause of increased fluidity as solids melted into liquids and liquids evaporated into gases; this latent caloric would become sensible again in condensation or congelation.
16. The best source on the history of the caloric theory is still Fox 1971. For a brief yet informative account, see Lilley 1948.
17. For Black's view on the metaphysical nature of heat, see Black 1803, 1:30-35.
18. For the development of Lavoisier's view on heat, see Guerlac 1976. His "table of simple substances" can be found in Lavoisier [1789] 1965, 175.
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The absorption and emission of heat in ordinary chemical reactions were also explained in the same manner. The notion of the chemical combination of caloric with matter was even incorporated into the terminology of "combined" vs. "free" caloric, which was used alongside the more phenomenological terminology of "latent" and "sensible" caloric (Lavoisier [1789] 1965, 19).
To return to the method of mixtures now: among the Irvinists, the most prominent critic of De Luc was the English Quaker physicist-chemist John Dalton (1766-1844). Dalton's attack was published in his New System of Chemical Philosophy, the first part of which (1808) was mostly about heat, although it is now more famous for the statement of his chemical atomic theory. Dalton (1808, 11) confessed that he had been "overawed by the authority of Crawford" initially to trust the mercury thermometer, only to be dissuaded by further considerations. (Here Dalton was referring to the Irish physician Adair Crawford [1748-1795], an Irvinist who had strongly advocated De Luc's method of mixtures in his well-known treatise on animal heat, first published in 1779.) Referring to De Luc's work specifically, Dalton laid the constancy of specific heat open to doubt and declared: "Till this point is settled, it is of little use to mix water of 32° and 212° [in Fahrenheit's scale], with a view to obtain the true mean temperature" (1808, 49-50). According to Dalton, there was an easy argument against the validity of the method of mixtures. The mixing of hot and cold water was observed to result in a slight decrease in overall volume. In Dalton's version of the caloric theory a decrease in volume literally mea
nt less space for caloric to fit in, therefore a decrease in heat capacity. That meant, by basic Irvinist reasoning, that temperature would go up. So Dalton (1808, 3-9) thought that mixtures generally had higher temperatures than those given by De Luc's simple calculations.19 Although Dalton may not have had any significant following in thermometry, his argument against De Luc would not have been easy to ignore, since it was just the same argument as involved in Dalton's more influential work (1802a) on the explanation of adiabatic heating and cooling by the mechanical compression and decompression of gases.
De Luc's method of mixtures was even more readily questioned by those calorists who inclined toward the chemical view of caloric. Since combined or latent caloric was conceived as the kind of caloric that did not register in thermometers, judging the correctness of thermometers seemed to require knowing the relation between the whole amount of caloric in a body and the amount that was free. That, in turn, required knowing when and how caloric would get bound and unbound to matter, but the exact causes of the transition of caloric between its combined and free states remained under serious dispute. This threw the question of specific heat wide open: specific heat was the amount of total heat input used in raising the temperature of a body by a unit amount, and that would have to include any