Thermometry and Thermal Expansion

The temperature of a body may be defined as its thermal condition, considered with reference to its power of communicating heat to or receiving heat from other bodies. This definition gives no direction as to how the temperature of a body is to be measured numerically. We may amplify it by saying that if, when a body A is placed in contact with another body B, heat passes from A to B, the body A is at a higher temperature than B; but this extension only indicates the order in which a scale of temperatures should be arranged.

In order to measure temperature we may select one of the effects produced by an accession of heat in a particular instrument, and estimate the range of temperature through which that instrument is raised or lowered when placed in contact with the body whose temperature is to be measured by measuring the amount of the effect produced. This is the method practically adopted. The instrument which is so used is called a thermometer, and the branch of the science of heat which treats of the application of such instruments is called thermometry.

A continuous accession of heat produces continuous alteration in many of the physical properties of bodies, and any one of them might have been selected as the basis of a system of thermometry. Attempts, which have met with more or less success, have been made to utilise several of these continuous alterations for the purpose. The change of volume of various liquids enclosed in glass vessels; the change in pressure of a gas when the volume is kept constant, or the change in volume when the pressure is kept constant; the change in the electrical resistance of a wire; the change in the electromotive force in a thermo-electric circuit; the change in length of a metallic bar; the change in the pressure of the vapour of a liquid; change of shape of a spiral composed of strips of different metals, as in Bréguet's thermometer, have all been thus employed.

Of all these methods of forming a system of thermometry, the one first mentioned is by far the most frequently employed. It owes its general acceptance to the fact that the change of volume of a liquid in a glass vessel is very easily measured with great accuracy. Moreover, if it were not for certain slow-working changes of very small magnitude in the volume of the glass envelope, of which we shall speak later, the indication of such an instrument would practically depend upon the temperature and upon nothing else. The liquids which have been employed are mercury, alcohol, and ether. Mercury can easily be obtained pure, and remains a liquid, with a vapour-pressure less than the ordinary atmospheric pressure for a wide range of temperatures, including those most frequently occurring in practice. Ether has a larger coefficient of expansion, but can only be used for a small range of low temperatures. The thermometers most generally in use are accordingly filled with mercury, and the expansion of mercury in a glass vessel has thus been adopted as the effect of heat to be employed as the basis of the numerical measurement of temperature.

A mercury thermometer consists of a stem, a glass tube of very fine and uniform bore, having a cylindrical or spherical bulb blown at the end. The bulb and part of the tube are filled with mercury, and the top of the stem is hermetically sealed, when the bulb is so heated that the whole instrument is filled with the liquid. When the mercury cools and contracts the space above it is left empty. The numerical measurement is introduced by marking upon the stem the points reached by the mercury when the thermometer is maintained successively at each of two temperatures which can be shown to be constant, and dividing the length of the stem between the two marks into a certain number of equal parts. These two fixed temperatures are usually the temperature of melting ice, and the temperature of steam which issues from water boiling under a standard pressure of 760 mm. They have been experimentally shown to be constant, and can always be obtained by simple apparatus (see §33).

The two marks referred to are called the freezing and the boiling point respectively, and the distance between them on the stem is divided into 100 parts for the centigrade thermometer, and 180 for the Fahrenheit, each part being called a degree.

On the former the freezing point is marked 0°, and on the latter 32°. The remarks which follow, when inapplicable to both kinds, may be held to refer to the centigrade thermometer.

It should first be noticed that this system, which supplies the definition of the numerical measure of temperature, is completely arbitrary. A number of degrees of temperature corresponds to a certain percentage of the total expansion of mercury in a glass vessel between 0° and 100°. Two quantities of mercury will doubtless expand by the same fraction of their volume for any given range of temperature, and thus two mercury thermometers, similarly graduated, may be expected to give identical indications at the same temperature, provided each tube is of uniform bore, and the expansion of the glass, as referred to the corresponding expansion of the mercury, is uniform for each instrument. This is in general sufficiently nearly the case for two thermometers which have been very recently graduated. But a thermometer filled with any other liquid, and agreeing with a mercury thermometer at two points, cannot be expected to, and does not in fact, agree with it for temperatures other than those denoted by the two points. If it did it would show that the rate of expansion of its liquid in glass was uniform for successive intervals of temperature, as defined by the mercury thermometer, and this is generally not the case.

Even the conditions necessary for two mercury thermometers to give identical indications at the same temperature are not, as a rule, satisfied. In the first place, the bore of a thermometer is not generally uniform. The variation may, indeed, be allowed for by calibration (see §8), so that we may correct the indications for want of uniformity of bore; the determination of the corrections in this way is a somewhat tedious operation. Moreover, the volume of the glass envelope undergoes a slow secular change. A thermometer bulb, when blown and allowed to cool, goes on contracting long after the glass has attained its normal temperature, the contraction not being quite complete even after the lapse of years. If the bulb be again heated, the same phenomenon of slow contraction is repeated, so that, after a thermometer is filled, the bulb gradually shrinks, forcing the mercury higher up the tube. If the thermometer has been already graduated, the effect of this slow contraction will appear as a gradual rise of the freezing point.

In some thermometers the error in the freezing point due to this cause amounts to more than half a degree, and the error will affect the readings of all temperatures between 0° and 100° by nearly the same amount. The instrument should, therefore, not be graduated until some considerable time after being filled; but even when this precaution is taken the change in the zero point is not completely eliminated, but only considerably diminished. A corresponding small change of the zero point is set up whenever the thermometer is raised to the boiling point.

The reading of a mercury thermometer does not, therefore, give an indication of temperature which will be clearly understood by persons who do not measure temperatures by that particular thermometer. To ensure the reading being comparable with those of other instruments, the tube must have been calibrated, and the fixed points quite recently re-determined, and the readings thus corrected; or, adopting another and more usual method, the individual thermometer in question may be compared experimentally with some instrument generally accepted as a standard. A set of such are kept at the Kew Observatory; they have been very carefully made and calibrated, and their fixed points are repeatedly determined, and a standard scale is thus established. With one or more of these standards any thermometer can be compared by immersing them in water which is kept well stirred, and taking simultaneous readings of the two at successive intervals of temperature. In this way a table of corrections is formed for the thermometer which is tested, and its indications can be referred to the Kew standard by means of the table. However, the secular contraction of the bulb may still be going on; but to allow for any contraction subsequent to the Kew comparison, it is sufficient to ascertain if there has been any change in the freezing point, and in that case consider that an equal change has taken place for every temperature, and that, therefore, each correction on the table is changed by that amount.

A specimen table of Kew corrections is appended as an example of the way in which this method of referring thermometers to a common standard is worked.

This gives some idea of the principles of the method of measuring temperatures within the range included between the freezing and boiling points of water. In order to extend the measurement beyond these limits various plans have been adopted The mercury thermometer is sometimes used, its stem beyond the limits being divided into degrees equal in length to those within the limits. A thermometer divided in this way can be used for temperatures down to -40°, and up to 350°C.; but, unfortunately, the difference in the expansion of different specimens of glass is such that at the higher temperatures two thermometers, similarly graduated, may differ by as much as ten degrees, and hence the mercury thermometer thus used does not give a satisfactory standard. Two air thermometers, on the other hand, when properly corrected for the expansion of the glass, always give the same readings, and thus the air thermometer has come to be recognised as the temperature standard for high and low temperatures. It is referred to the mercury standard for the freezing and boiling points and intermediate temperatures; thus the higher temperatures are expressed in centigrade degrees by a species of extrapolation, using the formula for the expansion of a permanent gas as determined by observations within the limits of the mercury thermometric standard.

Other methods of extrapolation from a formula verified by comparison, either with the mercury or air thermometer, have sometimes been employed with more or less success, in order to determine temperatures so high that the air thermometer is unsuitable, such as, for instance, the temperature of a furnace. In the case of Siemens' resistance pyrometer, a formula is obtained by experiments at low temperatures, expressing the relation between the resistance of a platinum wire and its temperature; the temperature of the furnace is then deduced from an observation of the resistance of the platinum on the supposition that the formula holds, although the temperature is a long way outside the limits of verification. The temperature obtained in some manner, generally analogous to this, is often expressed as so many degrees centigrade or Fahrenheit. It is evident that numbers obtained by different methods may be widely different, as all are arbitrary. At present it is a matter of congratulation if two different instruments on the same principle give comparable results; and, until some more scientific, or rather, less arbitrary, method of measuring temperatures is introduced, the precise numbers quoted for such temperatures as those of melting silver or platinum must remain understood only with reference to the particular system of extrapolation adopted to extend the range of numbers from those properly included in the range of the mercury thermometer, namely, those between the freezing and boiling points of water.