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A Proposal to Redefine the Thermodynamic Temperature Scale: with a Parable of Measures to Improve Weights

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A Proposal to Redefine the Thermodynamic Temperature Scale: with a Parable of Measures to Improve Weights Xo. 3624, APRIL 15, 1939 NATURE 623 A Proposal to Redefine the Thermodynamic Temperature Scale: with a Parable of Measures to Improve Weights By Prof. W. F. Giauque, University of California N several papers published between 1848 and The only basic temperature scale defined with I 1854, Lord Kelvin1 proposed the establish­ sufficient completeness to enable the determination ment of an absolute scale of temperature, based of any temperature is the thermodynamic scale. on Carnot's principle and "quite independent of For example, the centigrade scale gives the freezing the physical properties of any specific substance" . point and the boiling point of water by definition On such a scale "the absolute values of two tem­ and nothing more. If it were necessary, for peratures are to one another in the proportion of example, to interpolate and extrapolate linearly, the heat taken in to the heat rejected in a perfect by means of such devices as those based on the thermodynamic engine working with a source and expansion of liquids and gases, various thermo­ a refrigerator at the higher and lower of the couples, resistance thermometers, etc., there would temperatures respectively". be little or no agreement as to the value of a The size of the degree used in connexion with given temperature. As a matter of fact, there is Kelvin's thermodynamic scale is arbitrary. The agreement only because the thermodynamic natural way to define the size of the degree is criterion of Kelvin is used in conjunction with the also the easiest way and the one which best enables one hundred degree centigrade interval. Inter­ the widest attainment of accuracy, namely, to polation or extrapolation by means of the ideal select one easily obtained and accurately re­ gas law happens to be a convenient special case producible fixed point, for example, a melting of the thermodynamic method. point, and assign to it a number such that degrees The basic equations of gas thermometry may of the desired size are obtained. Unfortunately, be written as : this has not been done. In practice, two fixed points are selected. The T 100 (I) temperature interval between the freezing point O'C. = [(PVhoo'C. / (PV)o,c.J -1' and the boiling point of water is assigned some and definite number of degrees, for example, 100 on the centigrade and 180 on the Fahrenheit scales (2) of temperature. The above two points define the size of the degree and thus the number of degrees where, in each case, PV is the product of gas between the ice point and the absolute zero. As a pressure and volume corrected for gas imperfection. consequence of this procedure, the values of the The T's refer to the absolute temperatures. ice point and the boiling point of water on the In Equation 1 the per cent error in T O'C. is absolute scale are frequently changed, depending 3 ·73 times that in the experimental ratio on the experimental observations accepted as being (PVhoo'c./(PV) O'C.• and this error is super­ the more reliable. imposed on the experimental inaccuracy involved When an experiment is performed to measure in the determination of the ratio (PV)T/(PV)o'c. a temperature by means of the fundamental of Equation 2. Moreover, observations at the criterion which Kelvin has pointed out, the final boiling point of water offer greater difficulties than result contains not only the experimental error of do those at the melting point of ice, and thus con­ the measurement itself, but also any error which tribute more to the inaccuracy of measurement exists in the particular value of the ice point which of the ratio (PVhoo'c.f(PV)o'c.· may have been adopted as the 'best value'. The The errors in temperatures on the thermo­ value of the ice point on the absolute scale has dynamic scale which have their origin in Equa­ been the subject of many investigations which tion l may be eliminated by using the natural certainly must be classed among the more accurate method mentioned above, namely, by defining of scientific measurements. Nevertheless, even T 0,0 . as equal to a suitable number. It appears now the values of the several investigators vary unlikely that a reference point more useful and bythelargerpart of the range 273 ·10° to 273·20° K., satisfactory than the ice point can be found. although an intermediate value may be selected A proposal of this kind should be advanced only which is almost certainly correct within two or after a careful examination of its consequences. three hundredths of a degree. In this connexion, we ask the simple yet significant © 1939 Nature Publishing Group 624 NATURE APRIL 15, 1939, VoL. 143 question : Why is it important to know tempera­ a path rather than to continue avoiding it by tures accurately in terms of any particular scale ? what often amounts to the expenditure of con­ For many purposes it would obviously be sufficient siderable time. This type of confusion caused by to refer temperatures to any arbitrarily adopted emphasis given to the centigrade temperature scale ; for example, this would suffice to permit scale approaches its limit when one laboratory the reproduction of a desired set of conditions. may report an observation at - 273·18° C., It would also permit the accurate use of all energy whereas another laboratory says there are only considerations based on the first law of thermo­ 273 ·13 degrees below 0° C. dynamics. However, even if one did not care to It is not our purpose here to discuss the various inquire further into the basic laws of Nature, there observed values of To·c .• but as mentioned above is no escape from their consequences, and it would it appears probable that a value can be selected be found difficult and inconvenient to represent which will not differ from the true value by more certain important properties by simple equations ; than two or three hundredths of a degree. Thus a for example, the gas law would appear complex T 0 can be selected which will not disagree with if data were obtained in terms of a linear inter­ the centigrade scale by more than one hundredth polation on a thermometer based on the expansion of one per cent. We 1mow of no thermodynamic of a liquid. observations which are accurate enough to require The insurmountable objection to an entirely a correction if a 'best value' of To·c should be arbitrary scale became evident when Clausius and selected to define permanently the absolute scale Kelvin discovered the wide implications of the of temperature. Thus no corrections to any existing second law of thermodynamics, which requires the literature would be necessitated merely because a use of a temperature based on Cam0t's principle. best value of T o•c. is adopted permanently. The use of this temperature leads to the simplest It is not suggested that the centigrade scale be possible representations of all natural phenomena. discarded, although, since its main advantages In fact, all other temperature scales are forced to would appear to be only traditional and to permit be as consistent as possible with the thermo­ the use of one less digit in representing ordinary dynamic scale or they would long since have fallen temperatures, it might be desirable to substitute into disuse. a scale with degrees defined as above but with the In addition to the unnecessary inclusion of the ice point taken as zero. At most, the difference experimental error in Equation 1 in the funda­ between the boiling point and the freezing point mental thermodynamic scale, there is a very on the two scales would not be found to differ common type of mistake that would be per­ by more than one hundredth of a degree, and until manently eliminated by defining the value of at least one experimenter succeeds in making To•c.· This may be illustrated by an example. thermodynamic measurements with an accuracy Let us say that Laboratory A uses a value of exceeding 0 ·01 per cent the difference may be To•c. = 273·19° K., whereas Laboratories Band C ignored. If it should become necessary to make have decided that To•c. = 273 ·13° K. Each of corrections for a few measurements of extra­ these laboratories makes a determination of the ordinary accuracy, it would be a comparatively boiling point of oxygen. Their results for the simple matter to do so. actual observed quantity, (PV)pj(PV)o•c. are in It should also be made clear that while the exact agreement. A finds T = 90 ·16° K. but thermodynamic criterion is regarded as basic, reports it as - 183 ·03° C. whereas B and C find there is no suggestion of discarding such valuable T = 90·14° K. and each reports - 182·99° C. A secondary reference standards as resistance thermo­ calculation is carried out in a fourth laboratory meters. It is obviously impractical to measure that favours To•c. = 273·19 but the calculator small temperature differences as accurately by accepts the value - 182 ·99° C. because two direct observation with a gas thermometer as observers have given it. As is practically always with a resistance thermometer. For example, a the case, the absolute temperature is required. difference of 0 ·01 o C. is near the limit of error with The calculator obtains it incorrectly by adding a gas thermometer, but it can be determined with 273 ·19 and - 182 ·99, which gives 90 ·20° K. in considerable precision by many other thermo­ place of the correct 90·16° K. metric devices.
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