Taking a as .0036625 (the mean value for hydrogen between o° and

I

100), the absolute zero will be -.0036625' or -273.0 C. Although it is impossible actually to cool a body down to the absolute zero, it is interesting to note that temperatures as low as −250° C. have been obtained by allowing liquid hydrogen to boil at reduced pressure. The true value of such low temperatures is, however, difficult to estimate, since it is hardly safe to say that any property of matter which we may use to measure temperature will, at such low temperatures, change with temperature according to the same law as is found to hold at temperatures near o° and 100° C. In order to convert temperatures referred to o° C. to the corresponding temperatures referred to the absolute zero, we have to add 273. Thus if T and represent the temperature reckoned from the absolute zero and the temperature of melting ice respectively,

Hence, substituting for a its value 1'273, and reckoning the temperature from the absolute zero, the above equations become

At any other temperature 7, if the pressure when the volume is conand the volume when the pressure is constant is v', we have

stant is

or the pressure of a gas at constant volume varies directly as the absolute temperature, and the volume, at constant pressure, also varies directly as the absolute temperature.

Suppose that the conditions of a certain mass of gas, as far as pressure, volume, and temperature are concerned, are indicated by the symbols p, v, t respectively, while when the temperature of the same mass of gas is reduced to o°, the pressure being po, the volume is . Then if the temperature is maintained constant we have, by Boyle's law, pov=pv, v' = pv po

or

Now, keeping the pressure po constant, let the temperature of the gas

be reduced to o°, and let v, be the volume under these conditions. By Charles's law we have

v=vo(I+at),

where a is the coefficient of expansion of the gas. Hence, equating the two values of v', we get

pv=pov。(1+at).

I

Taking the value of a as .003663, or and writing T for the tempera

273'

ture measured from the absolute zero, i.e. - 273° C., we get

For a given mass of gas the quantity pov, is a constant, hence we may write the above equation—

pv=RT,

where R is a constant, depending only on the nature and quantity of the gas.

198. The Gas Thermometer.-Since the standard thermometric substance employed for all accurate measurements of temperature is either hydrogen or nitrogen, the problem of comparing the readings of the ordinary liquid-in-glass thermometers, such as are actually used to note the temperature, with the gas thermometer, and hence deducing the corrections to be applied to the readings to reduce them to the gas scale, is of very considerable importance. There are several forms of so-called

air thermometers, which are all more or less modifications of the instruments used by Regnault, and we shall content ourselves with describing the form employed at the Bureau International des Poids et Mesures at Paris.

The instrument consists of two distinct parts, the bulb, containing the gas (hydrogen), and the manometer, used to measure the pressure to

bulb A, which is made of platinum iridium, and has a capacity of about a litre, is connected with the manometer (shown in Fig. 158) by a fine metal tube B, about a metre long, and having a bore of 0.07 cm. For the comparisons at comparatively low temperatures the bulb A and the thermometers T, which are to be compared with the gas thermometer, are placed side by side in a long water-bath, which is kept well stirred. For the higher temperatures the arrangement shown in Fig. 157 is employed. Steam, or the vapour of some other liquid, enters the apparatus by the tube E, passes up alongside the bulb A and the bulbs of the thermometers T, and then at the end passes to the outside of the metal screen DD and back along the outside, finally escaping by the tube F. The arrangement resembles that used for determining the upper fixed point of an ordinary mercurial thermometer (see Fig. 144).

In Regnault's form of the constantvolume air thermometer, the manometer employed only measures the excess or defect of the pressure to which the gas is exposed over the ordinary atmospheric pressure, so that to obtain the actual pressure the barometric height has also to be determined. In the Bureau instrument the manometer and barometer are combined in a single instrument, so that the height of a single column of mercury only has to be measured, and thus the chances of error are reduced. The tube B, coming from the bulb, is attached to a steel block A (Fig. 158), which is clamped air-tight on the end of a glass tube c. The lower end of this glass tube is cemented into a steel block D, to which is also cemented a second glass

FIG. 158.

tube E. These two glass tubes communicate with each other through a channel in the steel block, as well as with a tap and flexible steel tube K. The block D is attached to an upright metal pillar P, which also carries a movable cradle Q, the position of which can be adjusted by the screw S. The cradle Q carries the upper end of a barometer tube HG, the lower end of which dips in the mercury contained in the tube E. The lower surface of the steel plug a is made plain, except for a fine metal point, shown on a larger scale at N, which serves as a fixed mark to which the surface of the mercury in the tube C is always brought back. The height of the reservoir L is altered, roughly by sliding the cradle R up and down by hand, and finally by means of the screw M, till this adjustment is complete at each temperature.

When the surface of the mercury at J is exactly in contact with the steel point, the excess of the pressure within the bulb above the atmospheric pressure is equal to the weight of a column of mercury of height OJ. The atmospheric pressure is equal to the weight of a column of mercury, of height 10. Hence the pressure acting on the gas in the bulb is equal to the weight of a column of mercury of height 10+0J or IJ, and the measurement of the vertical distance between the two mercury surfaces I and J suffices to give the pressure. The measurement of this height is effected by means of a cathetometer, which is carried on a pillar fixed alongside the instrument, the measurement being facilitated by the fact that the two surfaces I and J are placed vertically one over the other. The temperature of the mercury column is measured by a series of thermometers attached to the upright P.

The readings obtained have to be corrected to allow for the expansion of the bulb on account of (1) rise of temperature and (2) the increase of the pressure of the gas inside. Allowance has also to be made for the decrease in volume, as the pressure is increased, of the air contained in the tube BB and the space between the mercury meniscus J and the lower surface of the steel block A. The coefficient of cubical expansion of the platinum-iridium bulb was determined by measuring, directly on the comparator, its coefficient of linear expansion.

CHAPTER II

CALORIMETRY

199. Quantity of Heat.-In order to measure the quantity of heat which a body loses or gains when its temperature changes, or when its physical state changes, we generally use as the unit that quantity of heat which, acting on a given mass of some chosen substance, alters its temperature by some fixed amount. The substance employed almost exclusively for this purpose is water. Thus the unit of heat might be defined as the heat necessary to raise the temperature of one gram of water through one degree Centigrade. This definition, however, will only be complete if a gram of water requires the same quantity of heat to raise its temperature one degree, whatever the temperature at which we start; that is, if it required the same quantity of heat to raise a gram of water from o° to 1°, as from 15° to 16°, or from 90° to 91°. Since it has been found that the quantity of heat required at different temperatures is different, it is necessary to specify between what two temperatures the water has to be taken, and there are a number of thermal units in use differing from one another in the temperature at which the water is taken. The chief of these are as follows:

(1) The heat required to raise 1 grm. of water from o° C. to 1° C. (2) The heat required to raise 1 grm. of water from 3°.5 C. to 4°.5 C. (3) The heat required to raise I grm. of water from 14°.5 C. to 15°.5 C. Each of the above units has, at some time or other, been called a calorie, and so in accurate work it is necessary to say at what temperature the calorie is taken.

A unit of heat largely used in England in engineering is the heat required to raise 1 lb. of water through 1° F. As this unit is only used for comparatively rough measurements, the question as to the temperature at which the water is taken does not come in.

For theoretical purposes (and practical also, now that electrical measurements play such an important part in engineering), it is convenient to measure heat in terms of the units of work or energy, since, as will be seen later (§ 250), heat and energy are convertible, and it has been proposed to adopt as the practical unit of heat 4.2 × 107 ergs—the reason for the adoption of this number will be seen later (§ 251)—and to call this unit a joule.

200. Specific Heat.-If 100 grams of water at 100° is mixed with 100 grams of water at o°, the temperature of the mixture is found to be