Part 12

According to the experiments of MM. Delaroche and Bérard on the specific heat of gases, that of air is, for equal weights, 0.267 that of water. If, then, we take for the unit of heat the quantity necessary to raise 1 kilogram of water 1 degree, that which will be required to raise 1 kilogram of air 1 degree would have for its value 0.267. Thus the quantity of heat furnished by the body A is

0.267 units.

This is the heat capable of producing 0.000000372 units of motive power by its fall from 0°.001 to zero.

For a fall a thousand times greater, for a fall of one degree, the motive power will be very nearly a thousand times the former, or

0.000372.

If, now, instead of 0.267 units of heat we employ 1000 units, the motive power produced will be expressed by the proportion

(0.267)/(0.000372) = (1000)/(x), whence x = (372)/(267) = 1.395.

Thus 1000 units of heat passing from a body maintained at the temperature of 1 degree to another body maintained at zero would produce, in acting upon the air,

1.395 units of motive power.

We will now compare this result with that furnished by the action of heat on the vapor of water.

FIG. 4. ]

Let us suppose one kilogram of liquid water enclosed in the cylindrical vessel abcd (Fig. 4), between the bottom ab and the piston cd. Let us suppose, also, the two bodies A, B maintained each at a constant temperature, that of A being a very little above that of B. Let us imagine now the following operations:

(1) Contact of the water with the body A, movement of the piston from the position cd to the position ef, formation of steam at the temperature of the body A to fill the vacuum produced by the extension of volume. We will suppose the space abef large enough to contain all the water in a state of vapor.

(2) Removal of the body A, contact of the vapor with the body B, precipitation of a part of this vapor, diminution of its elastic force, return of the piston from ef to ab, liquefaction of the rest of the vapor through the effect of the pressure combined with the contact of the body B.

(3) Removal of the body B, fresh contact of the water with the body A, return of the water to the temperature of this body, renewal of the former period, and so on.

The quantity of motive power developed in a complete cycle of operations is measured by the product of the volume of the vapor multiplied by the difference between the tensions that it possesses at the temperature of the body A and at that of the body B. As to the heat employed, that is to say, transported from the body A to the body B, it is evidently that which was necessary to turn the water into vapor, disregarding always the small quantity required to restore the temperature of the liquid water from that of B to that of A.

Suppose the temperature of the body A 100 degrees, and that of the body B 99 degrees: the difference of the tensions will be, according to the table of M. Dalton, 26 millimetres of mercury or 0^m.36 head of water.

The volume of the vapor is 1700 times that of the water. If we operate on one kilogram, that will be 1700 litres, or 1^{mc}.700.

Thus the value of the motive power developed is the product

1.700 × 0.36 = 0.611 units,

of the kind of which we have previously made use.

The quantity of heat employed is the quantity required to turn into vapor water already heated to 100°. This quantity is found by experiment. We have found it equal to 550°, or, to speak more exactly, to 550 of our units of heat.

Thus 0.611 units of motive power result from the employment of 550 units of heat. The quantity of motive power resulting from 1000 units of heat will be given by the proportion

⁵⁵⁰⁄₀.611 = 1000/x, whence x = ⁶¹¹⁄₅₅₀ = 1.112.

Thus 1000 units of heat transported from one body kept at 100 degrees to another kept at 99 degrees will produce, acting upon vapor of water, 1.112 units of motive power.

The number 1.112 differs by about ¼ from the number 1.395 previously found for the value of the motive power developed by 1000 units of heat acting upon the air; but it should be observed that in this case the temperatures of the bodies A and B were 1 degree and zero, while here they are 100 degrees and 99 degrees. The difference is much the same; but it is not found at the same height in the thermometric scale. To make an exact comparison, it would have been necessary to estimate the motive power developed by the steam formed at 1 degree and condensed at zero. It would also have been necessary to know the quantity of heat contained in the steam formed at one degree.

The law of MM. Clement and Desormes referred to on page 92 gives us this datum. The constituent heat of vapor of water being always the same at any temperature at which vaporization takes place, if 550 degrees of heat are required to vaporize water already brought up to 100 degrees, 550 + 100 or 650 will be required to vaporize the same weight of water taken at zero.

Making use of this datum and reasoning exactly as we did for water at 100 degrees, we find, as is easily seen,