AVAILABILITY OF HEAT OF COMBUSTION 24. Taking the value of 1•13 kilogrammet:es per kilo-calorie for 1 ° C fall of temperature at 100° C, Carnot attempted to estimate the possible performance of a steam-engine receiving heat at 160° C and rejecting it at 4o° C. Assuming the performance to be simply proportional to the temperature fall, the work done for Ito° fall would be 134 kilogrammetres per kilo-calorie. To make an accurate calculation required a knowledge of the variation of the function F't with temperature. Taking the accurate formula of § 22, the work obtainable is 118 kilogrammetres per kilo-calorie, which is 28% of 426, the mechanical equivalent of the kilo-calorie in kilogrammetres. Carnot pointed out that the fall of Ito° C utilized in the steam-engine was only a small fraction of the whole temperature fall obtainable by combustion, and made an estimate of the total power available if the whole fall could be utilized, allowing for the probable diminution of the function F't with rise of temperature. His estimate was 3.9 million kilogrammetres per kilogramme of coal. This was certainly an over-estimate, but was surprisingly close, considering the scanty data at his disposal.
In reality the fraction of the heat of combustion available, even in an ideal engine and apart from practical limitations, is much less than might be inferred from the efficiency formula of the Carnot cycle, by taking the temperature obtainable by the combustion of the fuel as the upper limit of temperature in the formula. For carbon burnt in air at constant pressure without any loss of heat, the products of combustion might be raised 2,300° C in temperature, assuming that the specific heats of the products were constant and that there was no dissociation. If all the heat could be supplied to the working fluid at this temperature. that of the condenser being 4o° C, the possible efficiency by the formula of § 22 would be 89%. But it is obvious that this could not be done even under the most ideal conditions. The heat given up by the products of combustion in cooling to atmospheric tern perature could not be received by the boiler at 2,300° but at intermediate temperatures from 2,300°, to 4o°, which would re duce the mean effective temperature of heat reception from 2,300° to 1,64o°, and the ideal efficiency from 89 to 62%. This, how ever, assumes a perfect regenerative boiler in which the working fluid leaves the boiler at a temperature of 2,300°, although the mean temperature of heat reception cannot exceed 1,640°. Carnot foresaw that there would be further limitations in the case of the steam-engine owing to the properties of the working fluid.
The greater part of the heat required for generating steam in a boiler is the latent heat of vaporization, which is necessarily re ceived by the steam at the saturation temperature corresponding to the pressure at which the boiler is designed to work. Thus at a pressure of 68olb. per sq.in., which is about the highest at present utilized on a large scale, the latent heat of vaporization, amounting to about 40o calories, would be received at a tem perature of only 26o° C (5oo° F) permitting an ideal efficiency of 41% for the conversion of this part of the heat. But if the feed-water from the condenser at 4o° is pumped directly into the boiler, to heat it to 26o°, the heat required, amounting to about 230 cals., would be received by the feed-water at intermediate tem peratures, and could not be so efficiently utilized. Rankine (Phil. Trans. 1854) was the first to show how the work obtainable from this part of the heat could be calculated. His formula gives an ideal efficiency of conversion of 25% for heat supplied in equal instal ments between 4o° and 26o°. This would reduce the efficiency of an engine using the Rankine cycle with saturated steam at 68o1b. pressure to 35% as compared with 41% for the Carnot cycle, in terms of the heat actually received by the steam. If the temperature of the boiler were further raised to 36o° C, corre sponding to a pressure of 2,7oolb. (nearly four times as great as at 260°), the ideal efficiency of the Carnot cycle would be just over 5o%, or half the latent heat could be utilized by a perfect engine. But the latent heat at 36o° is only 177 calories, and is less than half the heat required for feed-heating, which amounts to 40o calories, so that the corresponding efficiency of the Rankine cycle is only 38%, which is very near the limit theoretically at tainable in this cycle with saturated steam.
25. Advantages of Internal Combustion.—As Carnot pointed out, the chief advantage of using atmospheric air as a working fluid in a heat-engine lies in the possibility of imparting heat to it directly by internal combustion. Even with internal com bustion, however, the full range of temperature is not available, because the heat cannot in practice be communicated to the working fluid at constant temperature, owing to the large range of expansion at constant temperature required for the absorption of a sufficient quantity of heat. Air-engines of this type, such as Stirling's or Ericsson's, taking in heat at constant temperature, though theoretically the most perfect, are bulky and mechanically inefficient.
In practical engines the heat is generated by the combustion of an explosive mixture at constant volume or at constant pres sure. The heat is not all communicated at the highest tempera ture, but over a range of temperature from that of the mixture at the beginning of combustion to the maximum temperature. The earliest instance of this type of engine is the lycopodium engine of M. M. Niepce, discussed by Carnot, in which a com bustible mixture of air and lycopodium powder at atmospheric pressure was ignited in a cylinder, and did work on a piston. The early gas-engines of E. Lenoir (186o) and N. Otto and E. Langen (1866), operated in a similar manner with illuminating gas in place of lycopodium. Combustion in this case is effected practi cally at constant volume, and the maximum efficiency theoretically obtainable is I I), where r is the ratio of the maximum temperature T to the initial temperature In order to obtain this efficiency it would be necessary to follow Carnot's rule, and expand the gas after ignition without loss or gain. of heat from T down to and then to compress it at to its initial volume. If the rise of temperature in combustion were 2,300°C, and the initial temperature were o° C or 273°A, the theoretical efficiency would be 73.3%, which is much greater than that obtainable with a boiler. But in order to reach this value, it would be to expand the mixture to about 270 times its initial volume, which is obviously impracticable. Owing to incomplete expansion and rapid cooling of the heated gases by the large surface exposed, the actual efficiency of the Lenoir engine was less than 5%, and of the Otto and Langen, with more rapid expansion, about i o%. Carnot foresaw that in order to render an engine of this type practically efficient, it would be necessary to compress the mix ture before ignition. Compression is beneficial in three ways: (1) it permits a greater range of expansion after ignition; (2) it raises the mean effective pressure, and thus improves the me chanical efficiency and the power in proportion to size and weight ; (3) it reduces the loss of heat during ignition by reducing the surface exposed to the hot gases. In the modern gas or petrol motor, compression is employed as in Carnot's cycle, but the efficiency attainable is limited not so much by considerations of temperature as by limitations of volume. It is impracticable before combustion at constant volume to compress a rich mix ture to much less than one-fifth of its initial volume, and, for mechanical simplicity, the range of expansion is made equal to that of compression. The cycle employed was patented in 1862 by Beau de Rochas, but was first successfully carried out by Otto (1876). It differs from the Carnot cycle in employing reception and rejection of heat at constant volume instead of at constant temperature. This cycle is not so efficient as the Carnot cycle for given limits of temperature, but, for the given limits of vol ume imposed, it gives a much higher efficiency than the Carnot cycle. The efficiency depends only on the range of temperature in expansion and compression, and is given by the formula where T, is the maximum temperature, and the temperature at the end of expansion. The formula is the same as that for the Carnot cycle with the same range of temperature in expansion. The ratio is where r is the given ratio of ex pansion or compression, and y is the ratio of the specific heats of the working fluid. Assuming the working fluid to be a perfect gas with the same properties as air, we should have 7=1.41. Taking r=5, the formula gives 48% for the maximum possible efficiency. The actual products of combustion vary with the nature of the fuel employed, and have different properties from air, but the efficiency is found to vary with compression in the same manner as for air. For this reason a committee of the Institution of Civil Engineers in 1905 recommended the adoption of the air-standard for estimating the effects of varying the compression ratio, and defined the relative efficiency of an internal combustion engine as the ratio of its observed efficiency to that of a perfect air-en gine with the same compression.
26. Effect of Dissociation, and Increase of Specific Heat. —One of the most important effects of heat is the decomposition or dissociation of compound molecules. Just as the molecules of a vapour combine with evolution of heat to form the more complicated molecules of the liquid, and as the liquid molecules require the addition of heat to effect their separation into mole cules of vapour; so in the case of molecules of different kinds which combine with evolution of heat, the reversal of the process can be effected either by the agency of heat, or indirectly by supplying the requisite amount of energy by electrical or other methods. Just as the latent heat of vaporization diminishes with rise of temperature, and the pressure of the dissociated vapour molecules increases, so in the case of compound molecules in general the heat of combination diminishes with rise of tempera ture, and the pressure of the products of dissociation increases. There is evidence that the compound carbon dioxide, is partly dissociated into carbon monoxide and oxygen at high tem peratures, and that the proportion dissociated increases with rise of temperature. There is a very close analogy between these phenomena and the vaporization of a liquid. The laws which govern dissociation are the same fundamental laws of thermo dynamics, but the relations involved are necessarily more complex on account of the presence of different kinds of molecules, and present special difficulties for accurate investigation in the case where dissociation does not begin to be appreciable a high temperature is reached.
It is easy, however, to see that the general effect of dissocia tion must be to diminish the available temperature of combus tion, and all experiments go to show that in ordinary combustible mixtures the rise of temperature actually attained is much less than that calculated as in § 24, on the assumption that the whole heat of combustion is developed and communicated to products of constant specific heat. The defect of temperature observed can be represented by supposing that the specific heat of the products of combustion increases with rise of temperature. This is the case for even at ordinary temperatures, according to Reg nault, and probably also for air and steam at higher temperatures. Increase of specific heat is a necessary accompaniment of disso ciation, and from some points of view may be regarded as merely another way of stating the facts. It is the most convenient method to adopt in the case of products of combustion consisting of a mixture of and steam with a large excess of inert gases, be cause the relations of equilibrium of dissociated molecules of so many different kinds would be too complex to permit of any other method of expression.
It appears from the researches of Dugald Clerk, H. le Chateller and others that the apparent specific heat of the products of combustion in a gas-engine may be taken as approximately •34 to •33 in place of .24 at working temperatures between 1,000°C and 1,7oo° C, and that the ratio of the specific heats is about 1.29 in place of 1.41. This limits the availability of the heat of com bustion by reducing the rise of temperature actually obtainable in combustion at constant volume by 30 or 40%, and also by re ducing the range of temperature for a given ratio of expan sion r from to The formula given in § 23 is no longer quite exact, because the ratio of the specific heats of the mixture during compression is not the same as that of the products of combustion during expansion. But since the work done depends principally on the expansion curve, the ratio of the range of temperature in expansion to the maximum temperature T, will still give a very good approximation to the possible effi ciency. Taking r=5, as before, for the compression ratio, the possible efficiency is reduced from 48% to 38%, if 7=1.29 in stead of 1.41. A large gas-engine of the present time with r=5 may actually realize as much as 34% indicated efficiency, which is 90% of the maximum possible, showing how perfectly all avoidable heat losses have been minimized.
It is often urged that the gas-engine is relatively less efficient than the steam-engine, because, although it has a much higher absolute efficiency, it does not utilize so large a fraction of its temperature range, reckoning that of the steam-engine from the temperature of the boiler to that of the condenser, and that of the gas-engine from the maximum temperature of combustion to that of the air. This is not quite fair, and has given rise to the mistaken notion that "there is an immense margin for im provement in the gas-engine," which is not the case if the prac tical limitations of volume are rightly considered. If expansion could be carried out in accordance with Carnot's principle of maximum efficiency, down to the lower limit of temperature with rejection of heat at during compression to the original volume it would no doubt be possible to obtain an ideal effi ciency of nearly 8o%. But this would be quite impracticable, as it would require expansion to about 1 oo times or 500 times the compression volume. Some advantage no doubt might be ob tained by carrying the expansion beyond the original volume. This has been done, but is not found to be worth the extra com plication. A more practical method, which has been applied by Diesel for liquid fuel, is to introduce the fuel at the end of com pression, and adjust the supply in such a manner as to give com bustion at nearly constant pressure. This makes it possible to employ higher compression, with a corresponding increase in the ratio of expansion and the theoretical efficiency. With a com pression ratio of 14, an indicated efficiency of 4o% has been obtained in this way, but owing to additional complications the brake efficiency was only 31%, which is hardly any improvement on the brake efficiency of 3o% obtained with the ordinary type of gas-engine.
Although Carnot's principle makes it possible to calculate in every case what the limiting possible efficiency would be for any kind of cycle if all heat losses were abolished, it is very necessary, in applying the principle to practical cases, to take account of the possibility of avoiding the heat losses which are supposed to be absent, and of other practical limitations in the working of the actual engine. An immense amount of time and ingenuity has been wasted in striving to realize impossible margins of ideal efficiency, which a close study of the practical conditions would have shown to be illusory. As Carnot remarks at the conclusion of his essay : "Economy of fuel is only one of the conditions a heat-engine must satisfy; in many cases it is only secondary, and must often give way to considerations of safety, strength and wearing qualities of the machine, of smallness of space occupied, or of expense in erecting. To know how to appreciate justly in each case the considerations of convenience and economy, to be able to distinguish the essential from the accessory, to balance all fairly, and finally to arrive at the best result by the simplest means, such must be the principal talent of the man called on to direct and co-ordinate the work of his fellows for the attainment of a useful object of any kind."