—It was shown in the preceding paragraph that in the combustion of carbon, one atom of oxygen may unite with one atom of carbon to form carbonic oxide, or two atoms of oxygen may unite with one atom of carbon to form carbonic acid. When the combination takes place according to the former proportions, the reaction is described as “imperfect combustion,” because the carbon is not fully oxidized; but when the combination is effected in the latter proportions, the combustion is said to be “perfect,” because no more oxygen can be taken up. The products of combustion are in both cases gaseous. Carbonic oxide, the product of imperfect combustion, is an extremely poisonous gas; it is this gas which is so noisome in close headings, and in all ill-ventilated places, after a blast has been fired. A cubic foot of carbonic oxide, the specific gravity of which is 0·975, weighs, at the mean atmospheric pressure, 0·075 lb., so that 1 lb. will occupy a space of 13·5 cubic feet. Thus 1 lb. of carbon imperfectly oxidized will give 21⁄3 lb. of carbonic oxide, which, at the mean atmospheric pressure of 30 inches and the mean temperature of 62° Fahr., will occupy a space of 13·5 × 21⁄3 = 31·5 cubic feet. The product of perfect combustion, carbonic acid, is a far less noxious gas than the oxide, and it is much more easily expelled from confined places, because water possesses the property of absorbing large quantities of it. In an ill-ventilated but wet heading, the gas from a blast is soon taken up. Carbonic acid is a comparatively heavy gas, its specific gravity relatively to that of common air being 1·524. Hence a cubic foot at the ordinary pressure and temperature will weigh 0·116 lb., and 1 lb. of the gas under the same conditions will occupy a space of 8·6 cubic feet. Thus if 1 lb. of carbon be completely oxidized, there will result 32⁄3 lb. of carbonic acid, which will fill a space of 8·6 × 32⁄3 = 31·5 cubic feet. It will be observed that, though an additional pound of oxygen has been taken up during this reaction, the product occupies the same volume as the oxide. In complete combustion, therefore, a contraction takes place.
In the oxidation of hydrogen, as already pointed out, one atom of oxygen combines with two atoms of the former substance to form water. In this case, the product is liquid. But the heat generated by the combustion converts the water into steam, so that we have to deal with this product also in the gaseous state, in all considerations relating to the effects of an explosion. A cubic foot of steam, at atmospheric pressure and a temperature of 212° Fahr., weighs 0·047 lb.; 1 lb. of steam under these conditions will, therefore, occupy a space of 21·14 cubic feet. Thus the combustion of 1 lb. of hydrogen will produce 9 lb. of steam, which, under the conditions mentioned, will fill a space of 21·14 × 9 = 190·26 cubic feet.
Usually in an explosion a large quantity of nitrogen gas is liberated. This gas, which is not in itself noxious, has a specific gravity of 0·971, so that practically a cubic foot will weigh 0·075 lb., and 1 lb. will occupy a space of 13·5 cubic feet, which are the weight and the volume of carbonic oxide. Other gases are often formed as products of combustion; but the foregoing are the chief, viewed as the results of an explosion, since upon these the force developed almost wholly depends.
Force developed by an Explosion.
—A consideration of the facts enunciated in the foregoing paragraphs will show to what the tremendous energy developed by an explosion is due. It was pointed out that the combustion of 1 lb. of carbon gives rise to 31·5 cubic feet of gas. If this volume of gas be compressed within the space of 1 cubic foot it will obviously have a tension of 31·5 atmospheres; that is, it will exert upon the walls of the containing vessel a pressure of 472 lb. to the square inch. If the same volume be compressed into a space one-eighth of a cubic foot in extent, say a vessel of cubical form and 6 inches side, the tension will be 31·5 × 8 = 252 atmospheres, and the pressure 472 × 8 = 3776 lb. to the square inch. Assuming now the oxygen to exist in the solid state, and the two bodies carbon and oxygen to occupy together a space of one-eighth of a cubic foot, the combustion of the carbon will develop upon the walls of an unyielding containing vessel of that capacity a pressure of 252 atmospheres. Also the combustion of 1 lb. of hydrogen gives rise, as already remarked, to 190·26 cubic feet of steam; and if combustion take place under similar conditions with respect to space, the pressure exerted upon the containing vessel will be 22,830 lb., or nearly 10·5 tons, to the square inch, the tension being 190·26 × 8 = 1522 atmospheres.
The force thus developed is due wholly to the volume of the gas generated, and by no means represents the total amount developed by the explosion. The volume of the gases evolved by an explosion is estimated for a temperature of 62°; but it was shown in a former paragraph that the temperature of the products of combustion at the moment of their generation is far above this. Now it is a well-known law of thermo-dynamics that, the volume remaining the same, the pressure of a gas will vary directly as the temperature; that is, when the temperature is doubled, the pressure is also doubled. By temperature is understood the number of degrees measured by Fahrenheit’s scale on a perfect gas thermometer, from a zero 461°·2 below the zero of Fahrenheit’s scale, that is, 493°·2 below the freezing point of water. Thus the temperature of 62° for which the volume has been estimated is equal to 461·2 + 62 = 523°·2 absolute.
It was shown that the temperature of the product of combustion when carbon is burned to carbonic oxide is 9718° Fahr., which is equivalent to 10179°·2 absolute. Hence it will be observed that the temperature has been increased 10179°·2 523°·2 = 19·45 times. According to the law above enunciated, therefore, the pressure will be increased in a like ratio, that is, it will be, for the volume and the space already given, 3776 × 19·45 = 73,443 lb. = 32·8 tons to the square inch.
When carbon is burned to carbonic acid, the temperature of the product was shown to be 23,516° Fahr., which is equivalent to 23977·2 absolute. In this case, it will be observed that the temperature has been increased 23977·2 523·2 = 45·83 times. Hence the resulting pressure will be 3776 × 45·83 = 173,154 lb. = 77·3 tons to the square inch. It will be seen from these pressures that when combustion is complete, the force developed is 2·36 greater than when combustion is incomplete; and also that the increase of force is due to the larger quantity of heat liberated, since the volume of the gases is the same in both cases. If we suppose the carbon burned to carbonic oxide in the presence of a sufficient quantity of oxygen to make carbonic acid, we shall have 31·5 cubic feet of the oxide + 15·7 cubic feet of free oxygen, or a total volume of 42·7 cubic feet of gases. If this volume be compressed within the space of one-eighth of a cubic foot, it will have a tension of 42·7 × 8 = 341·6 atmospheres, and will exert upon the walls of the containing vessel a pressure of 5124 lb. to the square inch. The temperature of the gases will be 32 + 4400 0·190 × 3·667 = 6347° Fahr. = 6808°·2 absolute, the mean specific heat of the gases being 0·190; whence it will be seen that the temperature has been increased 6808°·2 523·2 = 13·01 times. According to the law of thermo-dynamics, therefore, the pressure under the foregoing conditions will be 5124 × 13·01 = 66,663 lb. = 29·8 tons to square inch. So that, under the conditions assumed in this case, the pressures developed by incomplete and by complete combustion are as 29·8 to 77·3, or as 1 to 2·59.
Similarly, when hydrogen is burned to water, the temperature of the product will be, as shown in a former paragraph, 16,049 Fahr. = 16510·2 absolute; and the pressure will be 22,830 × 16510·2 523·2 = 720,286 lb. = 321·1 tons to the square inch.
It will be observed, from a consideration of the foregoing facts, that a very large proportion of the force developed by an explosion is due to the heat liberated by the chemical reactions which take place. And hence it will plainly appear that, in the practical application of explosive agents to rock blasting, care should be taken to avoid a loss of the heat upon which the effects of the explosion manifestly so largely depend.