The laws of thermo-dynamics teach, as has been stated, that the proportion of the heat-energy contained in the steam or other working fluid which may be transformed into mechanical energy is a fraction (H1 - H2)∕H1, of the total, in which H1 and H2 are the quantities of heat contained in the steam at the beginning and at the end of its operation, measuring from the absolute zero of heat-motion. In perfect gases,
| H1 - H2 | = | τ1 - τ2 | = | T1 - T2 | ; |
| H1 | τ1 | T1 + 461.2° Fahr. |
but in imperfect gases, and especially in vapors which, like steam, condense, or otherwise change their physical state, this equality may still exist, (H1 - H2)∕H1 = (τ1 - τ2)∕τ1; and the fluid is equally efficient with the perfect gas as a working substance in a heat-engine. In any case it is seen that the efficiency is greatest when the whole of the heat is received at the maximum and rejected at the minimum attainable temperatures.
Assuming this expression strictly accurate, a hot-air engine working from 413.6° Fahr, or 874.8° absolute temperature, down to 122° Fahr, or 583.2° absolute, should have an efficiency of 0.263, transforming that proportion of available heat into mechanical work. The engines of the steamer Ericsson closely approached this figure, and gave a horse-power for each 1.87 pound of coal burned per hour.
Steam expands in the steam-cylinder quite differently under different circumstances. If no heat is either communicated to it or abstracted from it, however, it expands in an hyperbolic curve, losing its tension much more rapidly than when expanded without doing work, in consequence both of its change of volume and its condensation. The algebraic expression for this method of expansion is, according to Rankine, PV1.111 = C, a constant, or, according to other authorities, from PV1.135 = C to PV1.140 = C. The greater the value of the exponent of V, the greater the efficiency of the fluid between any two temperatures. The maximum value has been found to be given where the steam is saturated, but perfectly dry, at the commencement of its expansion. The loss due to condensation on the cooled interior surface of the cylinder at the commencement of the stroke and the subsequent reëvaporation as expansion progresses is least when the cylinder is kept hot by its steam-jacket and when least time is given during the stroke for this transfer of heat between the metal and the vapor.
It may be said that, all things considered, therefore, losses of heat in the steam-cylinder are least when the steam enters dry, or moderately superheated, where the interior surfaces are kept hottest by the steam-jacket or by the hot-air jacket sometimes used, and where piston-speed and velocity of rotation are highest.[115] The best of compound engines, using steam of seventy-five pounds pressure and condensing, usually require about two pounds of coal per hour—20,000,000 foot-pounds of energy at the furnace—to develop a horse-power, i. e., about ten times the heat-equivalent of the mechanical work which they accomplish. Were the steam to expand like the permanent gases, they would have a theoretical efficiency of about one-quarter; actually, the efficiency is only one-tenth. The steam-engine, therefore, utilizes about two-fifths the heat-energy theoretically available with the best type of engine in general use. By far the greater part, nearly all, in fact, of the nine-tenths wasted is rejected in the exhaust steam, and can only be saved by some such method as is hereafter to be suggested of retaining that heat and returning it to the boiler.
The mechanical power which has now been communicated to the mechanism of the engine by the transfer of the kinetic energy of the hot steam to the piston is finally usefully applied to whatever “mechanism of transmission” forms the connection with the machinery driven by the engine. In this transfer, there is some loss in the engine itself, by friction. This is an extremely variable amount, and it can be made very small by skillful design and good workmanship and management. It may be taken at one-half pound per square inch of piston for good engines of 100 horse-power and upward, but is often several pounds in very small engines. It is least when the rubbing surfaces are of different materials, but both of smooth, hard, close-grained metal, well lubricated, and where advantage is taken of any arrangement of parts which permits the equilibration of pressure, as on the shaft-bearings of double and triple engines. The friction of a steam-engine of large size and good design is usually between five and seven per cent. of its total power. It increases rapidly as the size of engine decreases.
Having now traced somewhat minutely the growth of the steam-engine from the beginning of the Christian era to the present time, having rapidly outlined the equally gradual, though intermittent, growth of its philosophy, and having shown how the principles of science find application in the operation of this wonderful machine, we are now prepared to study the conditions which control the intelligent designer, and to endeavor to learn what are the lessons taught us by science and by experience in regard to the essential requisites of efficient working of steam and economy in the consumption of fuel. We may even venture to point out definitely the direction in which improvement is now progressing as indicated by a study of these requisites, and may be able to perceive the natural limits to such progress, and possibly to conjecture what must be the character of that change of type which only can take the engineer beyond the limit set to his advance so long as he is confined to the construction of the present type of engine.
First, we must consider the question: What is the problem, stated precisely and in its most general form, that engineers have been here attempting to solve?
After stating the problem, we will examine the record with a view to determine what direction the path of improvement has taken hitherto, to learn what are the conditions of efficiency which should govern the construction of the modern steam-engine, and, so far as we may judge the future by the past, by inference, to ascertain what appears to be the proper course for the present and for the immediate future. Still further, we will inquire, what are the conditions, physical and intellectual, which best aid our progress in perfecting the steam-engine.