Gas Thermometry

The value of the fundamental coefficient f can be determined with much greater accuracy than the coefficient over any other range of temperature. The most satisfactory method is to use the bulb itself as a mercury weight thermometer, and deduce the cubical expansion of the glass from the absolute expansion of mercury as determined by Regnault. Unfortunately the reductions of Regnault's observations by different calculators differ consid erably even for the fundamental interval. The values of the fundamental coefficient range from .00018153 Regnault, and .00018210 Moss, to .00018257 Chappuis. The extreme difference represents an uncertainty of about 4 per cent. (I in 25) in the expansion of the glass. This uncertainty is about 'co times as great as the probable error of the weight thermometer observa tions. But the expansion is even less certain beyond the limits of the fundamental interval. Another method of determining the expansion of the bulb is to observe the linear expansion of a tube or rod of the same material, and deduce the cubical expansion on the assumption that the expansion is isotropic. It is probable that the uncertainty involved in this assumption is greater in the case of glass or porcelain bulbs, on account of the difficulty of perfect annealing, than in the case of metallic bulbs.

Except for small ranges of temperature, the assumption of a constant coefficient of expansion is not sufficiently exact. It is therefore usual to assume that the coefficient is a linear function of the temperature, so that the whole expansion from o° C may be expressed in the form dV= t(a+bt)V., in which case the fun damental coefficient f =a+ roob. Making this substitution in the formula already given, we obtain the whole correction dt=(f-EbT)t(t—loo). (i4) It will be observed that the term involving b becomes of consid erable importance at high temperatures. Unfortunately, it cannot be determined with the same accuracy as f, because the conditions of observation at the fixed points are much more perfect than at other temperatures. Provided that the range of the observations for the determination of the expansion is co-extensive with the range of the temperature measurements for which the correction is required, the uncertainty of the correction will not greatly exceed that of the expansion observed at any point of the range. It is not unusual, however, to deduce the values of b and f from ob servations confined to the range o° to oo° C, in which case an error of 1 per cent., in the observed expansion at 5o° C, would mean an error of 6o per cent. at or of 36o per cent. at ' 5,000° C. (Callendar, Phil. Mag. December 1899.) Moreover, it

by no means follows that the average value of b between o° and Too° C should be the same as at higher or lower temperatures. Tne method of extrapolation would therefore probably lead to erroneous results in many cases, even if the value could be deter mined with absolute precision over the fundamental interval. It is probable that this expansion correction, which cannot be re duced or eliminated like many of the other corrections which have been mentioned, is the chief source of uncertainty in the realiza tion of the absolute scale of temperature at the present time. The uncertainty is of the order of one part in five or ten thousand on the fundamental interval, but may reach 0.5° at 5oo° C, and 2° or 3° at 1,000° C.

Thermodynamical Correction.

Of greater theoretical in terest, but of less practical importance on account of its small ness, is the reduction of the scale of the gas thermometer to the thermodynamical scale. The deviations of a gas from the ideal equation pv =R0 may be tested by a variety of different meth ods, which should be employed in combination to determine the form of the characteristic equation. The principal methods by which the problem has been attacked are the following :— ( I) By the comparison of gas thermometers filled with different gases or with the same gas at different pressures (employing both gravimetric and manometric methods) the differences in their indications are observed through as wide a range of temperature as possible. Regnault, employing this method, found that the differences in the scales of the permanent gases were so small as to be beyond the limits of accuracy of his observations. Applying greater refinements of measurement, Chappuis and others have succeeded in measuring small differences, which have an important bearing on the type of the characteristic equation. They show, for instance, that the equation of van der Waals, according to which all manometric gas thermometers should agree exactly in their indications, requires modification to enable it to represent the behaviour of gases even at moderate pressures.

(2) By measuring the pressure and expansion coefficients of different gases between o° and oo° C the values of the funda mental zero (the reciprocal of the coefficient of expansion or pres sure) for each gas under different conditions may be observed and compared. The evidence goes to show that the values of the fundamental zero for all gases tend to the same limit, namely, the absolute zero, when the pressures are indefinitely reduced. The type of characteristic equation adopted must be capable of representing the variations of these coefficients.