Gas Thermometry

It is possible to avoid this difficulty, and to make the dead space very small, by employing oil or sulphuric acid or other non volatile liquid to confine the gas in place of mercury (Phil. Trans., A. 1887, p. I71). The employment of a liquid which wets the tube makes it possible to use a much smaller bore, and also greatly facilitates the reading of small changes of pressure. At the same time the instrument may be arranged so that the dead space cor rection is automatically eliminated with much greater accuracy than it can be calculated. This is effected as shown diagram matically in fig. 4, by placing side by side with the tube AB, con necting the bulb B to the manometer A, an exact duplicate CD, closed at the end D, and containing liquid in the limb C, which is of the same size as the branch A of the manometer and in di rect communication with it. The tube CD, which is called the compensating tube, contains a constant mass of gas under ex actly similar conditions of volume and temperature to the tube AB. If therefore the level of the liquid is always adjusted to be the same in both tubes AB and CD, the mass of gas contained in the dead space AB will also be constant, and is au tomatically eliminated from the equations, as they contain differences only.

Gravimetric Method.

In the writ er's opinion, the gravimetric or overflow method, although it has seldom been adopted, and is not generally regarded as the most accurate, is much to be preferred to the manometric method, especially for work at high temperatures. It is free from the uncertain corrections above enumer ated as being peculiar to the manometric method. The apparatus is much simpler to manipulate and less costly to construct. If the pressure is kept constant and equal to the external atmospheric pressure, there is no strain of the bulb, which is particu larly important at high temperatures. There is no dead space correction so long as the temperature of the dead space is kept constant. The troublesome operation of reading and adjusting the mercury col umns of the manometer is replaced by the simpler and more accurate operation of weighing the mercury displaced, which can be performed at leisure. The uncertain cor rection for the temperature of the mercury in the manometer is entirely avoided.

The reasons which led Regnault to prefer the constant-volume thermometer are frequently quoted, and are generally accepted as entirely conclusive, but it is very easy to construct the con stant-pressure or gravimetric instrument in such a manner as to escape the objections which he urges against it.

Compensated Differential Gas Thermometer.—The chief advantage of the gravimetric method, which Regnault and others appear to have missed, is that it is possible to make the meas urements altogether independent of the atmospheric pressure and of the observation of mercury columns. This is accomplished by using, as a standard of constant pressure, a bulb S, fig. 5, contain ing a constant mass of gas in melting ice, side by side with the bulb M, in which the volume of the overflow is measured. The pressure in the thermometric bulb T is adjusted to equality with the standard by means of a delicate oil-gauge G of small bore, in which the difference of pressure is observed by means of a cathetometer microscope.

This kind of gauge permits the rapid observation of small changes of pressure, and is far more accurate and delicate than the mercury manometer. The fundamental measurement of the volume of the overflow in terms of the weight of mercury displaced at o° C involves a single weighing made at leisure, and requires no temperature correction. The accuracy obtainable at ordinary temperatures in this measurement is about ten times as great as that attainable under the best conditions with the mercury manometer. At higher temperatures the rela tive accuracy diminishes in proportion to the absolute tempera ture, or the error dt increases according to the formula where w is the weight of the overflow and dw the error. This diminution of the sensitiveness of the method at high tempera tures is commonly urged as a serious objection to the method, but the objection is really without weight in practice, as the pos sible accuracy of measurement is limited by other conditions. So far as the weighing alone is concerned, the method is sensitive to one-hundredth of a degree at r,000° C, which is far beyond the order of accuracy attainable in the application of the other cor rections.

Method of Using the Instrument.—A form of gas thermome ter constructed on the principles above laid down, with the addi tion of a duplicate set of connecting tubes C for the elimination of the stem-exposure correction by the method of automatic corn pensation already explained, is shown in fig. 5.

In setting up the instrument, after cleaning, and drying and calibrating the bulbs and connecting tubes, the masses of gas on the two sides are adjusted as nearly as possible to equality, in order that any changes of temperature in the two sets of connect ing tubes may compensate each other. This is effected with all the bulbs in melting ice, by adjusting the quantities of mercury in the bulbs M and S and equalizing the pressures. The bulb T is then heated in steam to determine the fundamental interval. A weight of mercury is removed from the overflow bulb M in order to equalize the pressures again. If W is the weight of the mercury at o° C which would be required to fill the bulb T at o° C, and if is the weight of mercury at o° which would be required to fill a volume equal to that of the bulb in steam at we have the following equation for determining the coefficient of expansion a, or the fundamental zero T., ati=ti/T0=(wi-FdWi)/(W (9) Similarly if w is the overflow when the bulb is at any other tem perature t, and the expansion of the bulb is dW, we have a pre cisely similar equation for determining t in terms of but with t and w and dW substituted for t, and and In practice, if the pressures are not adjusted to exact equality, or if the volumes of the connecting tubes do not exactly compensate, it is only neces sary to include in w a small correction dw, equivalent to the ob served difference, which need never exceed one part in ten thousand.