that heat when applied to a bar of metal produces two distinct and separate effects; one shown in the rise of temperature, and the other in the increase of volume. We may reasonably suppose that if the solid body were heated under such conditions as to preclude its expansion, the same quantity of heat would produce a much greater thermometric effect than in the former case. A similar remark applies to liquids and gases, and can be easily verified by experiment in the case of these latter. Here, then, is the first instance of a physical phenomenon of very frequent occurrence, namely, the conversion of heat into work, or reciprocally, of work into heat. Whenever a quantity of heat appears to be lost, the reason is that a corresponding amount of work is produced. If, on the other hand, work is done in compressing a body, so as to reduce it to the volume which it would occupy at a lower temperature, a rise of temperature is necessarily produced.

CHAPTER XXII.

EXPANSION OF LIQUIDS.

206. Relation between Real and Apparent Expansion.-If a vessel containing a liquid be heated, the level of the liquid rises, in consequence of the excess of the expansion of the liquid over that of the vessel. The observed increase of volume, not corrected for the expansion of the vessel, is called the apparent expansion. It is evidently less than the real expansion, for if the volume of the vessel had remained the same, the level would have risen higher.

The coefficients of real and apparent expansion are connected with the coefficient of expansion of the vessel by a very simple relation. Let us take the case of a liquid contained in a vessel similar to a thermometer in shape, that is, suppose the tube to be divided into parts of equal capacity, and that we know by previous gauging how many divisions are equivalent to the volume of the reservoir.

Let no denote the number of divisions occupied by the liquid at zero, and n, the number of divisions occupied at temperature ťo.

nt

no

Then is the factor of apparent expansion, and 2-1 is the apparent expansion.

no

Let us, for simplicity, take for our unit of volume the volume of a division at zero. Then if K be the expansion of the glass, the volume of a division at t° will be 1+K.

The volume of the liquid at t° is n of these divisions, and is therefore nt (1+K).

But if m be the real expansion of the liquid, the volume at t° is (1+m) n, since n is the volume at zero.

That is, the factor of apparent expansion is equal to the factor of real expansion of the liquid divided by that of the vessel. Denote the factor of apparent expansion by 1+ a.

or since AK is much smaller than either A or K, and may in general be neglected,

m=A+K.

That is, the real expansion of the liquid is equal to the apparent expansion plus the expansion of the vessel; and consequently, the coefficient of real expansion is equal to the coefficient of apparent expansion plus the coefficient of expansion of the vessel.

207. Expansion of Glass.-By means of this relation we can find the coefficient of expansion of any kind of glass; we have only to measure the coefficient of apparent expansion of the mercury in a thermometer made of this glass, and to subtract it from the coefficient of absolute expansion of the metal, which, as we shall see afterwards, is equal to 550 The coefficient of apparent expansion varies a little according to the quality of the glass employed; if we take it as which is Dulong and Petit's determination of its mean value, we shall have for the coefficient of expansion of glass

1

1

6480

208. Expansion of any Liquid.-The coefficient of expansion of the glass of which a thermometer is composed being known, we may use the instrument to measure the expansion of any liquid. For this purpose, the liquid whose coefficient of expansion is to be determined is introduced into the thermometer, and the number of divisions n and n, occupied by the liquid at the temperatures 0° and ť° respectively, are observed. Then, if D, A, K, be the coefficients of real expansion, of apparent expansion, and of expansion of the glass, each reckoned per degree Centigrade, we have

1+D=(1+A) (1+K), or D=A+ K nearly, whence D is known. M. Pierre has performed an extensive series of experiments by this method upon a great number of

liquids.

The apparatus employed by him is shown in Fig. 209. The thermometer containing the given liquid is fixed beside a mercurial thermometer, which marks the temperature. The reservoir and a small part of the tube are im mersed in the bath contained in the cylinder below. The upper parts of the stems are inclosed in a second and smaller cylinder, the water in which is maintained at a sensibly constant temperature indicated by a very delicate thermometer.

From these experiments it appears that the expansions of liquids are in general much greater than those of solids. Further, expansion does not proceed uni

formly, as compared with the indications of a mercurial ther

Fig. 209.-Pierre's Apparatus.

mometer, but increases very perceptibly as the temperature rises. This is shown by the following table:

209. Maximum Density of Water. By applying the experimental method just described to the case of water, we may easily observe the volume occupied by the same weight of this liquid at different temperatures, and it has thus been found that this volume is least at 4° Centigrade. At this temperature, accordingly, the density of water is a maximum, so that if a quantity of water at this temperature be

either heated or cooled it undergoes an increase of volume. This is a curious and unique exception to the general law of expansion by heat

This anomaly may be exhibited by means of the apparatus represented in Fig. 210, which consists of two thermometers, one of alcohol, and the other of water. The reservoir of this latter, on account of the smaller expansive power of the liquid, is a long spiral,

enveloping that of the alcohol thermometer. Both the reservoirs are contained in a metal box, which is at first filled with melting ice. The two instruments are so placed, that at zero the extremities of the two liquid columns are on the same horizontal line. This being the case, if the ice be now removed, and the apparatus left to itself, or if the process be accelerated by placing a spirit-lamp below the box, the alcohol will immediately be seen. to rise, while the water will descend; and the two liquids will thus continue to move in opposite directions until a temperature of about 4° is attained. From this moment the water ceases to descend, and begins to move in the same direction as the alcohol. This experiment, although very well adapted for exhibiting the phenomenon, does not enable us to measure exactly the temperature of maximum density, since it is the apparent, and not the real, expansion of water which is thus observed. The following experiment, which is due to Hope, is more rigorous.

A glass jar is employed, having two lateral openings, one near the top and the other near the bottom, which admit two thermometers placed horizontally. The tube is filled with water, and its middle is surrounded with a frigorific mixture. The following phenomena will then be observed.

The lower thermometer descends steadily to 4°., and there remains stationary. The upper thermometer at first undergoes very little change, but when the lower one has reached the fixed temperature, the upper one begins to fall, reaches the temperature of zero, and, finally, the water at the surface freezes, if the action of the frigorific