—It is known that if a certain quantity of heat will raise the temperature of a body one degree, twice that quantity will raise its temperature two degrees, three times the quantity, three degrees, and so on. Thus we may obtain a measure of heat by which to determine, either the temperature to which a given quantity of heat is capable of raising a given body, or the quantity of heat which is contained in a given body at a given temperature. The quantity of heat requisite to produce a change of one degree in temperature is different for different bodies, but is practically constant for the same body, and this quantity is called the “specific heat” of the body. The standard which has been adopted whereby to measure the specific heat of bodies is that of water, the unit being the quantity of heat required to raise the temperature of 1 lb. of water through 1° Fahr., say from 32° to 33°. The quantity of heat required to produce this change of temperature in 1 lb. of water is called the “unit of heat,” or the “thermal unit.” Having determined the specific heat of water, that of air may in like manner be ascertained, and expressed in terms of the former. It has been proved by experiments that if air be heated at constant pressure through 1° Fahr., the quantity of heat absorbed is 0·2375 thermal units, whatever the pressure or the temperature of the air may be. Similarly it has been shown that the specific heat of air at constant volume is, in thermal units, 0·1687; that is, if the air be confined so that no expansion can take place, 0·1687 of a thermal unit will be required to increase its temperature one degree.
Heat liberated by an Explosion.
—In the oxidation of carbon, one atom of oxygen may enter into combination with one atom of that substance; the resulting body is a gas known as “carbonic oxide.” As the weight of carbon is to that of oxygen as 12 is to 16, 1 lb. of the former substance will require for its oxidation 11⁄3 lb. of the latter; and since the two enter into combination, the product, carbonic oxide, will weigh 1 + 11⁄3 = 21⁄3 lb. The combining of one atom of oxygen with one of carbon throughout this quantity, that is, 11⁄3 lb. of oxygen, with 1 lb. of carbon, generates 10,100 units of heat. Of this quantity, 5700 units are absorbed in changing the carbon from the solid into the gaseous state, and 4400 are set free. The quantity of heat liberated, namely, the 4400 units, will be expended in raising the temperature of the gas from 32° Fahr., which we will assume to be that of the carbon and the oxygen previous to combustion, to a much higher degree, the value of which may be easily determined. The 4400 units would raise 1 lb. of water from 32° to 32 + 4400 = 4432°; and as the specific heat of carbonic oxide is 0·17 when there is no increase of volume, the same quantity of heat will raise 1 lb. of that gas from 32° to 32 + 4400 0·17 = 25,914°. But in the case under consideration, we have 21⁄3 lb. of the gas, the resulting temperature of which will be 25,91421⁄3 = 9718°.
In the oxidation of carbonic oxide, one atom of oxygen combines with one atom of the gaseous carbon; the resulting body is a gas known as “carbonic acid.” Since 21⁄3 lb. of carbonic oxide contains 1 lb. of carbon, that quantity of the oxide will require 11⁄3 lb. of oxygen to convert it into the acid, that is, to completely oxidize the original pound of solid carbon. By this combination, 10,100 units of heat are generated, as already stated, and since the carbon is now in the gaseous state, the whole of that quantity will be set free. Hence the temperature of the resulting 32⁄3 lb. of carbonic acid will be
32 + 4400 + 10,100 0·17 × 3·667 = 23,516°.
It will be seen from the foregoing considerations that if 1 lb. of pure carbon be burned in 22⁄3 lb. of pure oxygen, 32⁄3 lb. of carbonic acid is produced, and 14,500 units of heat are liberated; and further, that if the gas be confined within the space occupied by the carbon and the oxygen previously to their combination, the temperature of the product may reach 23,516° Fahr.
In the oxidation of hydrogen, one atom of oxygen combines with two atoms of the former substance; the resulting body is water. As the weight of hydrogen is to that of oxygen as 1 is to 16, 1 lb. of the former gas will require for its oxidation 8 lb. of the latter; and since the two substances enter into combination, the product, water, will weigh 1 + 8 = 9 lb. By this union, 62,032 units of heat are generated. Of this quantity, 8694 are absorbed in converting the water into steam, and 53,338 are set free. The specific heat of steam at constant volume being 0·37, the temperature of the product of combustion, estimated as before, will be
32 + 53,338 0·37 × 9 = 16,049°.
Hence it will be observed that if 1 lb. of hydrogen be burned in 8 lb. of oxygen, 9 lb. of steam will be produced, and 53,338 units of heat will be liberated; and further, that the temperature of the product may reach 16,049°.