pressure to w2- w at t°. If, then, a be the coefficient of expansion at constant pressure, and Vo the volume of the same mass of air at o° C., we have

The calculation is a good deal simplified if tą is zero, for then w2w, is the volume of air at o° C., which expands, on being heated to 1,°, to w-w. Thus w2-w=(W2-W1) (1+at1).

This may be attained by using water cooled down to zero as the liquid in which the bulb is immersed, and this course has the additional advantage that the correction for vapour pressure is thereby greatly reduced, the vapour pressure of water at o° being 46 cm. of mercury, or about 64 cm. of water, and the error committed by entirely neglecting the correction will be only about 0.

Experiment.-Determine coefficient of expansion of air at

CHAPTER X.

CALORIMETRY.

By Calorimetry we mean the measurement of quantities of heat. There are three different units of heat which are employed to express the results: (1) the amount of heat required to raise the temperature of unit mass of water from o°C. to 1oC.; (2) the amount of heat required to melt unit mass of ice; (3) the amount of heat required to convert unit mass of water at 100° into steam at the same temperature. Experiments will be detailed below ($ 39) by which the last two units may be expressed in terms of the first, which is generally regarded as the normal standard. Calorimetric measurements are deduced generally from one of the following observations: (1) the range of temperature through which a known quantity of water is raised, (2) the quantity of ice melted, (3) the quantity of water evaporated or condensed; or from combinations of these. The results

obtained from the first observation are usually expressed in terms of the normal unit on the assumption that the quantity of heat required to raise a quantity of water through one degree is the same, whatever be the position of the degree in the thermometric scale. This assumption is very nearly justified by experiment. As a matter of fact, the quantity of heat required to raise unit mass of water from 99° C. to 100° C. is said to be 1016 nornal units.

The results of the second and third observations mentioned above give the quantities of heat directly in terms of the second and third units respectively, and may therefore be expressed in terms of normal units when the relations. between the various units have once been established.

39. The Method of Mixture.

Specific Heat.

In this method a known mass of the material of which the specific heat is required is heated to a known temperature, and then immersed in a known mass of water also at a known temperature. A delicate thermometer is immersed in the water, and the rise of temperature produced by the hot body is thereby noted. The quantity of heat required to produce a rise of temperature of 1° in the calorimeter itself, with the stirrer and thermometer, is ascertained by a preliminary experiment. We can now find an expression for the quantity of heat which has been given up by the hot body, and this expression will involve the specific heat of the body. This heat has raised the temperature of a known mass of water, together with the calorimeter, stirrer, and thermometer, through a known number of degrees, and another expression for its value can therefore be found, which will involve only known quantities. Equating these two expressions for the same quantity of heat, we can determine the specific heat of the material. Let м be the mass of the hot body, T its temperature, and c its specific heat; let m be the mass of the water, t its temperature initially, and be the common temperature of the water and body after the latter has been immersed and the temperature become steady; let m1 be the quantity of heat required to raise the temperature of the calorimeter, stirrer, and thermometer 1°. This is numerically the same as the 'water equivalent' of the calorimeter. We shall explain shortly how to determine it experimentally.

The specific heat of a substance is the ratio of the quantity of heat required to raise the temperature of a given mass of the substance 1° to the quantity of heat required to raise the temperature of an equal mass of water 1°. If we adopt as the unit of heat the quantity of heat required to raise the temperature of 1 gramme of water 1°, then it

follows that the specific heat of a substance is numerically equal to the number of units of heat required to raise the temperature of 1 gramme of that substance through 1o.

The mass M is cooled from T° to 6°. The quantity of heat evolved by this is therefore

MC (T-0),

assuming that the specific heat is the same throughout the range. The water in the calorimeter, the calorimeter itself, the stirrer, and the thermometer are raised from t° to 0°; the heat necessary for this is

m (0-1)+m, (0-1),

for m, is the heat required to raise the calorimeter, stirrer, and thermometer 1°, and the unit of heat raises 1 gramme of water 1°.

But since all the heat which leaves the hot body passes into the water, calorimeter, &c., these two quantities of heat are equal.

The reason for the name 'water equivalent' is now apparent, for the value found for m, has to be added to the mass of water in the calorimeter. We may work the problem as if no heat were absorbed by the calorimeter if we suppose the quantity of water in it to be increased by m, grammes. The quantity m, is really the 'capacity for heat' of the calorimeter, stirrer, and thermometer.

We proceed to describe the apparatus, and give the practical details of the experiments.

The body to be experimented on should have considerable surface for its mass; thus, a piece of wire, or of thin sheet, rolled into a lump is a convenient form. Weigh it,

1

and suspend it by means of a fine thread in the heater. This consists of a cylinder, A (fig. 20), of sheet copper,

FIG. 20.

closed at both

ends, but with

B

an open tube, B, running down through the mid

dle. Two small tubes pass through the outer casing of the cylinder; one is connected with the boiler, and through this steam can be sent; the other communicates with a condenser to remove the waste steam.

The cylinder

can turn round a vertical axis, D,

which is secured to a horizontal board, and the board closes the bottom end of the central tube. A circular hole is cut in the board, and by turning the cylinder round the axis the end of the tube can be brought over this hole. The upper end of the tube is closed with a cork, which is pierced. with two holes; through the one a thermometer, P, is fixed. and through the other passes the string which holds the mass M. The thermometer bulb should be placed as close as possible to M.

The steam from the boiler is now allowed to flow through the outer casing, raising the temperature of the mass м; the cylinder is placed in such a position that the