Inventing Temperature
Page 34
Air-thermometer temperatureb
20
20+0.0298
40
40+0.0403
60
60+0.0366
80
80+0.0223
100
100
120
120−0.0284
140
140−0.0615
160
160−0.0983
180
180−0.1382
200
200−0.1796
220
220−0.2232
240
240−0.2663
260
260−0.3141
280
280−0.3610
300
300−0.4085
Source: Joule and Thomson [1854] 1882, 395-396.
a Joule and Thomson designed the size of one absolute degree to be the same as one centigrade degree as much as possible, by making the two scales agree exactly at the freezing and the boiling (steam) points by definition. But this new absolute temperature had a zero point, which Joule and Thomson estimated at −273.7°C. Hence the absolute temperature of the freezing point is 273.7° (we would now say 273.7 Kelvin), though it is displayed here as 0 (and all other absolute temperature values shifted by 273.7) in order to facilitate the comparison with ordinary air-thermometer temperatures.
b Given by a constant-volume air thermometer filled with a body of air at atmospheric pressure at the freezing point of water.
Source: Adapted from the second series of data given in Regnault 1847, 188.
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The clearest problem is that they used the uncorrected mercury thermometer in the Joule-Thomson experiment, so that it is far from clear that the corrections of the air thermometer on the basis of their data can be trusted. In the analysis I will enter into detailed philosophical and historical discussions of that matter.
Analysis: Operationalization—Making Contact between Thinking and Doing
We have no right to measure these [Joule-Thomson] heating and cooling effects on any scale of temperature, as we have not yet formed a thermometric scale. William Thomson, "Heat," 1880
In the narrative part of this chapter, I traced the long and tortuous process by which temperature became established as a concept that is both theoretically cogent and empirically measurable. Now I will attempt to reach a more precise understanding of the nature of that achievement. To simplify our progress so far, the stories in the first three chapters of this book were about how to construct a coherent quantitative concept based on concrete physical operations. But such operational concept building is not sufficient in a genuinely theoretical science. For many important reasons scientists have desired abstract theoretical structures that are not purely and directly constructed from observable processes. However, if we also want to maintain our commitment to having an empirical science by giving empirical significance and testability to our abstract theories, we must face up to the challenge of operationalization: to link abstract theoretical structures to concrete physical operations. To put it in the terminology developed in "Beyond Bridgman" in chapter 3, operationalization is the act of creating operational meaning where there was none before.
Operationalizing an abstract theory involves operationalizing certain individual concepts occurring in it, so that they can serve as clear and convenient bridges between the abstract and the concrete. And one sure way of operationalizing a concept is to make it physically measurable, although the category of the operational includes much more than what can be considered measurements in the narrow sense of the term. Therefore measurement is the most obvious place where the challenges of operationalization can manifest themselves, though it is not the only place. In the following sections I will revisit the history of the attempts to measure Thomson's absolute temperature, in relation to the two main tasks involved in operationalization: to do it and to know whether it has been done well.
The Hidden Difficulties of Reduction
Most authors who have given accounts of the physics and the history of absolute temperature measurement seem to take comfort in the fact that absolute temperature
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Figure 4.10. Herbert Feigl's (1970, 6) representation of the connection of abstract theoretical concepts to empirical observations. Reprinted by permission of the University of Minnesota Press.
can be expressed as a function of other quantities, which are measurable. Thomas Preston (1860-1900), the Irish physicist who discovered the anomalous Zeeman effect, expressed the situation perspicaciously in his textbook on heat: If we possess any thermodynamic relation, or any equation involving τ [absolute temperature] and other quantities which can be expressed in terms of p [pressure] and v [volume], then each such relation furnishes a means of estimating τ when the other quantities are known. (Preston 1904, 797)
In other words, absolute temperature can be measured through reduction to pressure and volume, which are presumably easily measurable. The structure of that reductive scheme is in fact quite similar to what one had in Irvinism: Irvinist absolute temperature could be expressed in terms of heat capacity and latent heat, both of which were regarded as straightforwardly measurable. Both Preston's and Irvine's views both fit nicely into a rather traditional philosophical idea, that the operationalization of a theoretical concept can be achieved by a chain of relations that ultimately link it to directly observable properties. Figure 4.10 gives a graphic representation of that reductive conception, taken from Herbert Feigl; figure 4.11 is a similar picture, due to Henry Margenau. In figure 4.12 I have made a graphic representation of Preston's idea about absolute temperature, which fits perfectly with the other pictures.
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Figure 4.11. Henry Margenau's (1963, 2) representation of the connection of abstract theoretical concepts to empirical observations. Reprinted by permission of the University of Chicago Press.
The reductive view of operationalization is comforting, but we must not be lulled into epistemological sleep so easily. Seemingly operational concepts that allegedly serve as the reductive base of operationalization are often unoperationalized themselves, and in fact very difficult to operationalize. In Preston's case, the apparent comfort in his statement is provided by an ambiguity in the meaning of the terms "pressure" and "volume." The p and v that occur in thermodynamic theory are abstract concepts; they do not automatically become operationalized simply because we designate them by the same words "pressure" and "volume" as we use in everyday circumstances, in which those concepts are indeed full of operational meaning. In other words, figure 4.12 is an embodiment of an unwarranted equivocation. A more accurate picture is given in figure 4.13, where the thermodynamic relations linking p, v, and τ are placed squarely in the realm of the abstract, and the
end p.199
Figure 4.12. A diagram representing Thomas Preston's idea regarding the operationalization of absolute temperature.
necessity to operationalize p and v becomes apparent. Preston's equivocation is just the kind of thing that we have learned to be wary of in "Travel Advisory from Percy Bridgman" in chapter 3. There Bridgman warned that "our verbal machinery has no built-in cutoff": it is easy to be misled by the use of the same word or mathematical symbol in various situations into thinking that it means the same thing in all of those situations. (Bridgman focused most strongly on the unwarranted jump from one domain of phenomena to another, but his warning applies with equal force to the jump between the abstract and the concrete.)
If pressure and volume in thermodynamics were themselves very easy to operationalize, my disagreement with Preston would be a mere quibble, and the redrawing of the picture as given in figure 4.13 would be the end of the matter. But the discussions of temperature in earlier chapters of this book should be a sufficient reminder that concepts that seem easy to operationalize may actually be very difficult to operationalize. Consider pressure. Even if we take a primitive and macroscopic theoretical notion of pressure
, there is no reason to assume that the mercury manometer was any more straightforward to establish than the mercury thermometer.45 When we get into thermodynamic theory, the pressure concept is meant to apply universally, even in situations to which no actual manometer can be applied; among those situations would be microscopic processes and perfectly
45. See the extensive history of the barometer in Middleton 1964b.
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Figure 4.13. A revised version of Preston's picture of the operationalization of absolute temperature.
reversible processes. And as soon as we engage in thermodynamic theorizing of any power, we are dealing with differential equations involving pressure as a continuous variable, well defined down to infinitesimal precision. If we take one step further and also pick up the kinetic theory of gases, then pressure is theoretically defined in terms of the aggregate impact of countless molecules bouncing off a barrier. By that point there is simply no hope that the operationalization of the pressure concept will be trivial in general; most likely, it will be of the same order of difficulty as the operationalization of temperature.
A slightly different kind of problem emerges if we look back at Thomson's own definitions of absolute temperature. In Thomson's second definition, absolute temperature was expressed in terms of heat, not pressure and volume. With the first definition, Thomson's attempt at operationalization had led to its expression in terms of pressure, density, air-thermometer temperature, and latent heat (see equation (11) in "Semi-Concrete Models of the Carnot Cycle"). Even Preston gives an operationalization that involves latent heat in addition to volume and pressure, right after the statement quoted above. Generally speaking, any definition of temperature referring to the efficiency of the Carnot cycle (via Carnot's function μ) will have to involve the measure of heat in some way. But defining temperature in terms of quantities of heat raises an intriguing problem of circularity, since the quantitative concept of heat is usually operationalized by reduction to temperature. Consider Thomson's own experimental practice, in which the unit of heat was: "the quantity necessary to elevate the temperature of a kilogram of water from 0° to 1° of the air-thermometer" (Thomson [1848] 1882, 105). In the Joule-Thomson
end p.201
experiment, heat measurement was made by means of Joule's mercury thermometer. One way to avoid this circularity would be to measure heat in some other way. But as I have noted already, at least in the period covered in this chapter there were no viable calorimetric methods that did not rely on thermometers. Given that state of calorimetry, any attempts to operationalize temperature by reducing it to heat would not have got very far.
All in all, no simple reductive scheme has been adequate for the operationalization of absolute temperature. More generally speaking, if operationalization by reduction seems to work, that is only because the necessary work has already been done elsewhere. Reduction only expresses the concept to be operationalized in terms of other concepts, so it achieves nothing unless those other concepts have been operationalized. Operationalization has to come before reduction. Somewhere, somehow, some abstract concepts have to become operationalized without reference to other concepts that are already operationalized; after that, those operationalized concepts can serve as reductive bases of reduction for other concepts. But how can that initial operationalization be done?
Dealing with Abstractions
In order to reach a deeper understanding of the process of operationalization, we need to be clearer about the distinction between the abstract and the concrete. At this point it will be useful to be more explicit about what I mean by "abstraction."46 I conceive abstraction as the act of removing certain properties from the description of an entity; the result is a conception that can correspond to actual entities but cannot be a full description of them. To take a standard example, the geometrical triangle is an abstract representation of actual triangular objects, deprived of all qualities except for their form. (A triangle is also an idealization by virtue of having perfectly straight lines, lines with no width, etc., but that is a different matter.) In principle the deletion of any property would constitute an abstraction, but most pertinent for our purposes is the abstraction that takes away the properties that individuate each entity physically, such as spatio-temporal location, and particular sensory qualities.
Thomson should be given credit for highlighting the issue of abstraction, by insisting that the theoretical concept of temperature should make no reference to the properties of any particular substances. Thus, he pointed to the gap between the concreteness of an operational concept and the abstractness that many scientists considered proper for a theoretical concept. It is instructive to make a comparison with earlier heat theorists discussed in "Theoretical Temperature before Thermodynamics." The Irvinists made an unreflective identification between the abstract concept of heat capacity and the operational concept of specific heat; some of them may even have failed to see the distinction very clearly. The chemical calorists, on the other hand, did not do very much to operationalize their concept of combined
46. For a more nuanced view on the nature of abstraction in scientific theories, see Cartwright 1999, 39-41 and passim.
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caloric. What truly set Thomson apart was his dual insistence: that theoretical concepts should be defined abstractly, and that they should be operationalized.
In one of his less phenomenalistic moments, Regnault stated the desired relationship between a concept and its measurement operation: "In the establishment of the fundamental data of physics … it is necessary that the adopted procedure should be, so to speak, the material realization of the definition of the element that is being sought."47 (Whether or not Regnault himself really ever put this maxim into practice, it is a very suggestive idea.) In order to follow that idea straightforwardly in the case of Thomson's absolute temperature, we would need to build a physical Carnot engine. But, as discussed in "Semi-Concrete Models of the Carnot Cycle," it is impossible to make an actual heat engine that qualifies as a Carnot cycle. One might imagine that this impossibility is only a practical problem; the Carnot cycle is an idealized system, but surely we could try to approximate it, and see how close our approximation is?48 That line of thinking misses the most essential feature of the situation: the Carnot cycle of post-Thomson thermodynamics is abstract, and real heat engines are concrete. It is possible that Carnot himself conceived his cycle simply as an idealized version of actual heat engines, but in later thermodynamics the Carnot cycle is an abstraction.
At the heart of the abstract character of the Carnot cycle is the fact that the concept of temperature that occurs in its description is not temperature measured by a concrete thermometer, but Thomson's absolute temperature. Therefore no such thing as an "actual Carnot cycle" (or even approximations to it) can exist at all, unless and until the absolute temperature concept has been operationalized. But the operationalization of absolute temperature requires that we either create an actual Carnot cycle or at least have the ability to judge how much actual systems deviate from it. So we end up with a nasty circularity: the operationalization of absolute temperature is impossible unless the Carnot cycle has sufficient operational meaning, and the Carnot cycle cannot have sufficient operational meaning unless absolute temperature is operationalized.
A similar problem plagues the use of the Joule-Thomson effect for the operationalization of absolute temperature. The Joule-Thomson experiment was intended to give us a comparison between actual gases and ideal gases, but such a comparison is not so straightforward as it may sound. That is because the concept of the "ideal gas" is an abstract one. It would be a mistake to think that the ideal gas of modern physics is one that obeys the ideal gas law, PV = nRT, where T
47. Regnault, quoted in Langevin 1911, 49. This statement suggests that Regnault, despite his hostility to theories, still recognized very clearly the fact that measurement must answer to a pre-existing concept. In other words, perhaps in contrast to Bridgman's variet
y of empiricism, Regnault's empiricism only sought to eliminate the use of hypotheses in measurements, not to deny non-operational components to a concept's meaning.
48. Shouldn't it be easy enough to tell how much the efficiency of an actual heat engine departs from that of the ideal Carnot engine? Carnot himself did make such estimates, and Thomson carried on with the same kind of calculation; see, for example, Thomson [1849] 1882, sec. 5 of the appendix (pp. 150-155). But it is an epistemic illusion that a direct comparison can be made between the Carnot cycle and a physical heat engine, for reasons that will become clearer in the next section.
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is temperature measured by an ordinary thermometer. No, T in that equation is Thomson's absolute temperature (or some other abstract theoretical temperature concept). If we ever found a gas in which the product of pressure and volume actually were proportional to temperature as measured by an ordinary thermometer (in degrees Kelvin), it would certainly not be an ideal gas, unless our ordinary thermometer actually indicated absolute temperature, which is highly unlikely. Not only is it highly unlikely but it is impossible for us to know whether it is the case or not, without having done the Joule-Thomson experiment and interpreted it correctly.