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of melting ice to that of steam under a pressure of 76 cm. A thermometer in which the scale is divided in this way is called a centigrade thermometer.

Thermometers graduated on the centigrade scale are used almost exclusively in scientific work, and also for ordinary purposes in most countries which have adopted the metric system. This scale was first devised in 1742 by Celsius, of Upsala, Sweden. For this reason it is sometimes called the Celsius instead of the centigrade scale.

According to the kinetic theory an increase in temperature in a liquid, as in a gas, means an increase in the mean kinetic energy of the molecules; and, conversely, a decrease in temperature means a decrease in this average kinetic energy. 156. Fahrenheit thermometers. The common household thermometer in England and the United States differs from the centigrade only in the manner of its graduation. In its construction the temperature of melting ice is marked 32° instead of 0°, and that of boiling water 212° instead of 100°. The intervening stem is then divided into 180 parts. The zero of this scale is the temperature obtained by mixing equal weights of sal ammoniac (ammonium chloride) and snow. In 1714, when Fahrenheit devised this scale, he chose this zero because he thought it represented the lowest possible temperature that could be obtained in the laboratory.













157. Comparison of centigrade and Fahrenheit thermometers. From the methods of graduation of the Fahrenheit and centigrade thermometers it will be seen that 100° on the centigrade scale denotes the same difference ature as 180° on the Fahrenheit scale (Fig. 146).













FIG. 146. The centigrade and Fahrenheit scales

of temperHence five

centigrade degrees are equal to nine Fahrenheit degrees. In Fig. 147, Crepresents the number of degrees in the centigrade reading, while F represents the number in the Fahrenheit reading. Since five centigrade degrees cover the same space on the stem as nine of the smaller Fahrenheit degrees, it is evident that

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By this expression of the relation of the two scales it is very easy to reduce the readings of one thermometer to the scale of the other.


For example, to find what Fahrenheit reading corresponds to 20° C. we have


==› F= 68°.



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FIG. 147. Comparison of centigrade and Fahrenheit scales

158. The range of the mercury thermometer. Since mercury freezes at 39° C., temperatures lower than this are very often measured by means of alcohol thermometers, for the freezing point of alcohol is - 130° C. Similarly, since the boiling point of mercury is about 360° C., mercury thermometers cannot be used for measuring very high temperatures. For both very high and very low temperatures in fact, for all temperatures — a gas thermometer is the standard instrument.

159. The standard hydrogen thermometer. The modern gas thermometer (Fig. 148) is, however, widely different from that devised by Galileo (Fig. 143). It is not usually the increase in the volume of a gas kept under constant pressure which is taken as the measure of temperature change, but rather the increase in pressure which the molecules of a confined gas exert against the walls of a vessel whose volume is kept constant. The essential features of the method of calibration and use

of the standard hydrogen thermometer at the International Bureau of Weights and Measures at Paris are as follows:

The bulb B (Fig. 148) is first filled with hydrogen and the space above the mercury in the tube a made as nearly a perfect vacuum as possible. B is then surrounded with melting ice (as in Fig. 144) and the tube a raised or lowered until the mercury in the arm b stands exactly opposite the fixed mark c on the tube. Now, since the space above D is a vacuum, the pressure exerted by the hydrogen in B against the mercury surface at c just supports the mercury column ED. The point D is marked on a strip of metal behind the tube a. The bulb B is then placed in a steam bath like that shown in Fig. 145. The increased pressure of the gas in B at once begins to force the mercury down at c and up at D. But by raising the arm a the mercury in b is forced back again to c, the increased pressure of the gas on the surface of the mercury at c being balanced by the increased height of the mercury column supported, which is now EF instead of ED. When the gas in B is thoroughly heated to the temperature of the steam, the arm a is very carefully adjusted so that the mercury in b stands very exactly at c, its original level. A second mark is then placed on the metal strip exactly opposite the new level of the mercury, that is, at F. Then D is marked 0° C., and F is marked 100° C. The vertical distance between these marks is divided into 100 exactly equal parts. Divisions of exactly the same length are carried above the 100° mark and below the 0° mark. One degree of change in temperature is then defined as any change in temperature which will cause the pressure of the gas in B to change by the amount represented by the distance between any two of these divisions. This distance is found to be of the height ED.

100°C P373°A


-E 0°A or 273°C


FIG. 148. The standard gas thermometer

In other words, one degree of change in temperature on the centigrade scale is such a temperature change as will cause the

pressure exerted by a confined volume of hydrogen to change by 273 of its pressure at the temperature of melting ice (0° C.).



160. Absolute temperature. Since, then, cooling the hydrogen through 1o C., as defined above, reduces the pressure 213 of its value at 0° C., it is clear that cooling it 273° below 0° C. would reduce its pressure to zero. But from the standpoint of the kinetic theory this would be the temperature at which all motions of the hydrogen molecules would cease. This temperature is called the absolute zero, and the temperature measured from this zero is called absolute temperature. Thus, if A is used to denote the absolute scale, we have 0° C. = 273° A., 100° C. = 373° A., 15° C. = 288° A., etc. It is customary to indicate temperatures on the centigrade scale by t, and on the absolute scale by T. We have, then,



161. Comparison of gas and mercury thermometers. Since an international committee has chosen the hydrogen thermometer described in § 159 as the standard of temperature measurement, it is important to know whether mercury thermometers, graduated in the manner described in § 155, agree with gas thermometers at temperatures other than 0° and 100° (where, of course, they must agree, since these temperatures are in each case the starting points of the graduation). A careful comparison has shown that although they do not agree exactly, yet fortunately the disagreements at ordinary temperatures are small, not amounting to more than 20 anywhere between 0° and 100°. At 300° C., however, the difference amounts to about 4°. (Mercury thermometers are actually used for measuring temperatures above the boiling point of mercury, 360°C. They are then filled with nitrogen, the pressure of which prevents boiling.)

Hence for all ordinary purposes mercury thermometers are sufficiently accurate, and no special standardization of them is necessary. But in all scientific work, if mercury thermometers are used at all, they must first be compared with a gas thermometer and a table of corrections obtained. The errors of an alcohol thermometer are considerably larger than those of a mercury thermometer.

162. Low temperatures. The absolute zero of temperature can, of course, never be attained, but in recent years rapid



One of the best known and most prolific of nineteenth-century physicists; born in Belfast, Ireland; professor of physics in Glasgow University, Scotland, for more than fifty years; especially renowned for his investigations in heat and electricity; originator of the absolute thermodynamic scale of temperature; formulator of the second law of thermodynamics; inventor of the electrometer, the mirror galvanometer, and many other important electrical devices

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