that the air within is hardly able to keep up with it and therefore unable to do much work, and then let the temperature be brought to its former value.

The work done on the piston by the contents of the cylinder being clearly different in the two cases, we are led to the same conclusions with respect to dW and dQ as before.

33. If a body be subjected to a uniform normal pressure p, the work done on it during a small increase of volume dv is pdv. The equation dU=dW+dQ then becomes dQdU+ pdv. Hence if either p or v be constant, the heat absorbed by the body in any change of state will depend only on the initial and final states. We are accordingly led to the following definitions, in which the state of the body is supposed to depend only on the temperature when either p or v is given a supposition which requires that there should be neither electric actions nor mechanical motions:

(1) At any temperature, the 'thermal capacity of a body at constant pressure' is the heat required to raise its temperature one degree C. while the pressure remains constant.

The pressure which most frequently occurs is that of the air, which, at any instant, may be supposed to remain constant for a short time.

(2) At any temperature, the 'thermal capacity of a body at constant volume' is the heat required to raise its temperature one degree C. while the volume remains constant.

If the body is homogeneous, the thermal capacity of a mass of one gramme is called its 'specific heat.'

The specific heat of water at 0°C. under a constant pressure of one atmo is called a Calorie, and is used as an arbitrary unit of heat.

34. In Joule's experiments on the agitation of water, the apparatus cannot be arranged so that the water rises in temperature exactly from 0° C. to 1° C. In order to find the mechanical value of a calorie, we must therefore determine the specific heats of water at different temperatures. This may be done by a method known as the method of mixtures.' Thus let a quantity of water at 0° C. be added to an equal quantity at some other temperature, say 100° C., and let the mixture be protected from all external influences except the pressure of the air, which may be taken to be an atmo. Then if the uniform temperature which the water finally assumes be C., and if no appreciable amount of work has been done either by gravity or in mixing them together, it follows that, since the work done by the pressure of the air is negligible, the heat required to raise the temperature of any mass of water from 0° C. to C., under a constant pressure of one atmo, is equal to that required to raise the temperature of an equal mass of water from C. to 100° C. under the same pressure. In this way, the specific heats of water under a constant pressure of one atmo have been determined in calories at different temperatures, thus:

at 0° C.,......1.000

10° C.,......10005 ... 20° C.,......1.0012

... 30° C.,......10020.

By means of these results, it is found from Joule's

experiments that a calorie is equivalent to 42350 grammecentimetres, or 41,539,759.8 ergs, or about 3 foot-pounds. In English measure, the heat required to raise the temperature of 1 lb. of water from 0° C. to 1° C. under a pressure of one atmo is equivalent to about 1390 footpounds.

Now if a mass of one gramme be moving without rotation or vibration at a speed of v centimetres per second, its mechanical kinetic energy will be v2 ergs. If this be equivalent to a calorie, we shall have

Thus the velocity must be 91.148 metres, or 299 feet, per second, that is, 5-469 kilometres, or 3-4 miles, per minute. Hence if two equal masses of water at 0° C. be moving with this velocity and impinge on one another in such a way that they are both brought to rest; then if no steam be formed, the impact will be sufficient to raise the temperature by 1° C. For a rise from 0° C. to 100° C., a velocity of about 55 kilometres, or 34 miles, per minute is required. In the case of iron, the specific heat is only of a calorie, and therefore the velocities are only as large as for water.

about about

Again, let x be the latent heat of liquefaction of ice, in calories, under a pressure of one atmo, that is, the number of calories required to convert one gramme of ice at 0° C. into water at the same temperature. Also suppose that i grammes of ice at 0° C. are mixed with w grammes of water at C., and that, in consequence, the whole of the ice is melted under a constant pressure of one atmo. Then if no heat be allowed to escape, and if

'C. be the final temperature, the heat gained by the water from the ice will be, very approximately, w (0′ – 0) calories, and the heat gained by the ice from the water, i (x+0') calories. Hence, very approximately,

It is thus found that the latent heat of ice under a pressure of one atmo is 79-25 calories, or 3,292,025,964 ergs.

Bunsen's calorimeter is a small instrument by which the heat coming from a small solid body under the constant pressure of the air is easily and accurately determined by the melting of ice. It consists of the three parts, a, b, c,

2

made of glass, and sealed together with the blow-pipe. The part b contains distilled water freed from air by boiling, and the bottom of b and the tube c are filled with boiled mercury, the upper part of the tube being bent horizontally, calibrated, and graduated. In preparing the calorimeter for use, a coating of ice is formed round the test tube a by passing a stream of alcohol, previously

cooled below 0° C. in a freezing mixture, down to the bottom of a and back again. The calorimeter is then placed in a vessel filled with clean snow, a substance which soon acquires and long maintains a temperature 0° C., unless the temperature of the room is below 0° C. Lastly, the test tube a is partially filled with water or some other fluid which does not dissolve the body to be experimented on, and as soon as the whole is at the temperature 0° C., the calorimeter is ready for use.

In making an experiment, the body which is to give off the heat is dropped into the test tube a. This will cause the water in a to become warmer, and then, by the conduction of heat through its sides, some of the ice which surrounds it will be melted. This will go on till the temperature of the whole is again reduced to 0° C. If n grammes of ice be melted in the process, the heat given off by the body will be 79-25 calories. The value of n is determined by the movement of the mercury in the graduated tube, depending on the fact that at a pressure of one atmo and at 0° C., one gramme of ice occupies 1087 cubic centimetres and one gramme of water, only 100011. It should be observed that if any air be allowed to remain in the water in b, it will be expelled in the form of a small bubble during the process of freezing the water around the test tube a, and partially re-dissolved when the ice is melted. A small error will thus be introduced into the indications of the calorimeter.