First, with respect to the furnace. The object is to combine the carbon and the hydrogen of the coal with a sufficient quantity of the oxygen of the air to effect complete combustion into carbonic acid and water. In order to do this, we have to use a quantity of air much larger than is theoretically necessary, and also to heat an amount of inert nitrogen five times greater than the necessary oxygen; and we are therefore obliged to create a draught which carries away to the chimney a considerable portion of the heat developed. The combustion, moreover, is never perfect; and some heat is lost by conduction and radiation. The principal loss is by hot gases escaping from the flues to the chimney. Even with well-set boilers, the temperature in the chimney varies from 400° to 600° Fahr. Taking the mean of 500°, this would represent a large proportion of the total heat, even if the combustion were perfect; for, as a general rule, the supply of air to a furnace is double that which is theoretically necessary. For our present purpose, it will be sufficient to see how much the whole loss is, without dividing it under the several heads of "imperfect combustion," "radiation," and "convection," by the heated gases passing to the chimney.
With a very good boiler and furnace each pound of coal evaporates 10 pounds of water from 62° Fahr., changing it into steam of 65 lb. pressure at a temperature of 312°, or 250° above that of the water from which it is generated. Besides these 250°, each pound of steam contains 894 units of latent heat, or 1,144 units in all. A very good condensing engine will work with 2.2 lb. of coal and 22 lb. of steam per horse power per hour. Now. 1 lb. of good coal will, by its combustion, produce 14,000 heat-units; and the 2.2 lb. of coal multiplied by 14,000 represent 30,800 θ. Of these we find in the boiler 22 × 1,144, or 25,168 units, or about 81½ per cent., of the whole heat of combustion; so that the difference (5,632 units, or 18½ per cent.) has been lost by imperfect combustion, radiation, or convection. The water required for condensing this quantity of steam is 550 lb.; and, taking the temperature in the hot well as 102°, 550 lb. have been raised 40° from 62°. Thus we account for 550 × 40 = 22,000, or (say) 71½ per cent. still remaining as heat. If we add this 71½ per cent. to 18½ per cent. we have 90 per cent., and there remain only 10 per cent. of the heat that can possibly have been converted into power. But some of this has been lost by radiation from steam-pipes, cylinder, etc. Allowing but 1 per cent. for this, we have only 9 per cent. as the efficiency of a really good condensing engine. This estimate agrees very closely with the actual result; for the 2.2 lb. of coal would develop 30,800 θ; and this, multiplied by Joule's equivalent, amounts to nearly 24 millions of foot-pounds. As 1 horse power is a little less than 2 million foot-pounds per hour, only one-twelfth, or a little more than 8 per cent. of the total heat is converted; so that whether we look at the total quantity of heat which we show unconverted, or the total heat converted, we find that each supplements and corroborates the other. If we take the efficiency of the engine alone, without considering the loss caused by the boiler, we find that the 25,168 θ which entered the boiler should have given 19,429,696 foot-pounds; so that the 2 millions given by the engine represent about 10 per cent. of the heat which has left the boiler. The foregoing figures refer to large stationary or marine engines, with first-rate boilers. When, however, we come to high-pressure engines of the best type, the consumption of coal is twice as much; and for those of any ordinary type it is usual to calculate 1 cubic foot, or 62½ lb., of water evaporated per horse power. This would reduce the efficiency to about 6 per cent. for the best, and 3 per cent. for the ordinary non-condensing engines; and if to this we add the inefficiency of some boilers, it is certain that many small engines do not convert into power more than 2 per cent. of the potential energy contained in the coal.
At one time the steam-engine was threatened with serious rivalry by the hot-air engine. About the year 1816 the Rev. Mr. Stirling, a Scotch clergyman, invented one which a member of this Institute (Mr. George Anderson) remembers to have seen still at work at Dundee. The principle of it was that a quantity of air under pressure was moved by a mass, called a "displacer," from the cold to the hot end of a large vessel which was heated by a fire beneath and cooled by a current of water above. The same air was alternately heated and cooled, expanded and contracted; and by the difference of pressure moved the piston in a working cylinder. In this arrangement the furnace was inefficient. As only a small portion of heat reached the compressed air, the loss by radiation was very great, and the wear and tear exceedingly heavy. This system, with some modifications, was revived by Rankine, Ericsson, Laubereau, Ryder, Buckett, and Bailey. Siemens employed a similar system, only substituting steam for air. Another system, originally proposed by Sir George Cayley, consisted in compressing by a pump cold air which was subsequently passed partly through a furnace, and, expanding, moved a larger piston at the same pressure; and the difference of the areas of the pistons multiplied by the pressure common to both represented the indicated power. This principle was subsequently developed by a very able mechanic, Mr. Wenham; but his engine never came much into favor. The only hot-air engines at present in use are Ryder's, Buckett's, and Bailey's, employed to a limited extent for small powers. I have not said anything of the thermal principles involved in the construction of these engines, as they are precisely the same as those affecting the subject of the present paper.
Before explaining the principle upon which the gas-engine and every other hot-air engine depends, I shall remind you of a few data with which most of you are already familiar. The volume of every gas increases with the temperature; and this increase was the basis of the air thermometer—the first ever used. It is to be regretted that it was not the foundation of all others; for it is based on a physical principle universally applicable. Although the volume increases with the temperature, it does not increase in proportion to the degrees of any ordinary scale, but much more slowly. Now, if to each of the terms of an arithmetical series we add the same number, the new series so formed increases or decreases more slowly than the original; and it was discovered that, by adding 461 to the degrees of Fahrenheit's scale, the new scale so formed represented exactly the increment of volume caused by increase of temperature. This scale, proposed by Sir W. Thomson in 1848, is called the "scale of absolute temperature." Its zero, called the "absolute zero," is 461° below the zero of Fahrenheit, or 493° below the freezing point of water; and the degree of heat measured by it is termed the "absolute temperature." It is often convenient to refer to 39° Fahr. (which happens to be the point at which water attains its maximum density), as this is the same as 500° absolute; for, counting from this datum level, a volume of air expands exactly 1 per cent. for 5°, and would be doubled at 1,000° absolute, or 539° Fahr.
Whenever any body is compressed, its specific heat is diminished; and the surplus portion is, as it were, pushed out of the body—appearing as sensible heat. And whenever any body is expanded, its specific heat is increased; and the additional quantity of heat requisite is, as it were, sucked in from surrounding bodies—so producing cold. This action may be compared to that of a wet sponge from which, when compressed, a portion of the water is forced out, and when the sponge is allowed to expand, the water is drawn back. This effect is manifested by the increase of temperature in air-compressing machines, and the cold produced by allowing or forcing air to expand in air-cooling machines. At 39° Fahr., 1 lb. of air measures 12½ cubic feet. Let us suppose that 1 lb. of air at 39° Fahr. = 500° absolute, is contained in a non-conducting cylinder of 1 foot area and 12½ feet deep under a counterpoised piston. The pressure of the atmosphere on the piston = 144 square inches × 14.7 lb., or 2,116 lb. If the air be now heated up to 539° Fahr. = 1,000° absolute, and at the same time the piston is not allowed to move, the pressure is doubled; and when the piston is released, it would rise 12½ feet, provided that the temperature remained constant, and the indicator would describe a hyperbolic curve (called an "isothermal") because the temperature would have remained equal throughout. But, in fact, the temperature is lowered, because expansion has taken place, and the indicator curve which would then be described is called an "adiabatic curve," which is more inclined to the horizontal line when the volumes are represented by horizontal and the pressures by vertical co-ordinates. In this case it is supposed that there is no conduction or transmission (diabasis) of heat through the sides of the containing vessel. If, however, an additional quantity of heat be communicated to the air, so as to maintain the temperature at 1,000° absolute, the piston will rise until it is 12½ feet above its original position, and the indicator will describe an isothermal curve. Now mark the difference. When the piston was fixed, only a heating effect resulted; but when the piston moved up 12½ feet, not only a heating but a mechanical, in fact, a thermodynamic, effect was produced, for the weight of the atmosphere (2,116 lb.) was lifted 12½ feet = 26,450 foot-pounds.
The specific heat of air at constant pressure has been proved by the experiments of Regnault to be 0.2378, or something less than one-fourth of that of water—a result arrived at by Rankine from totally different data. In the case we have taken, there have been expended 500 × 0.2378, or (say) 118.9 θ to produce 26,450 f.p. Each unit has therefore produced 26,450 / 118.9 = 222.5 f.p., instead of 772 f.p., which would have been rendered if every unit had been converted into power. We therefore conclude that 222.5 / 772 = 29 per cent. of the total heat has been converted. The residue, or 71 per cent., remains unchanged as heat, and may be partly saved by a regenerator, or applied to other purposes for which a moderate heat is required.
The quantity of heat necessary to raise the heat of air at a constant volume is only 71 per cent. of that required to raise to the same temperature the same weight of air under constant pressure. This is exactly the result which Laplace arrived at from observations on the velocity of sound, and may be stated thus—
| Specific heat. | Foot- pounds. | Per cent. | |
| Kp= 1 lb. of air at constant pressure | 0.2378 × 772 = | 183.5 = | 100 |
| Kv= 1 lb. of air at constant volume | 0.1688 × 772 = | 130.3 = | 71 |
| Difference, being heat converted into power | 0.0690 × 772 = | 53.2 = | 29 |
Or, in a hot-air engine without regeneration, the maximum effect of 1 lb. of air heated 1° Fahr. would be 53.2 f.p. The quantity of heat Ky necessary to heat air under constant volume is to Kv, or that necessary to heat it under constant pressure, as 71:100, or as 1:1.408, or very nearly as 1:√2—a result which was arrived at by Masson from theoretical considerations. The 71 per cent. escaping as heat may be utilized in place of other fuel; and with the first hot-air engine I ever saw, it was employed for drying blocks of wood. In the same way, the unconverted heat of the exhaust steam from a high-pressure engine, or the heated gases and water passing away from a gas-engine, may be employed.
