by volume 0.788 N + 0.197 O + 0.001 CO2 + 0.014 H2O
----------------------------------------------------
by weight 0.771 N + 0.218 O + 0.009 CO2 + 0.017 H2O
This law is, however, subject to some apparent exceptions. Carbon
burned in protoxide of nitrogen, or laughing gas, N_{2}O, produces
about 38 per cent. more heat than the same substance burned in pure
oxygen, notwithstanding that the work of decomposing the protoxide of
nitrogen has to be performed. In marsh gas, or methane, CH_{4}, again,
the energy of combustion is considerably less than that due to the
burning of its carbon and hydrogen separately. These exceptions
probably arise from the circumstance that the energy of chemical
action is absorbed to a greater or less degree in effecting molecular
changes, as, for example, the combustion of 1 pound of nitrogen to
form protoxide of nitrogen results in the absorption of 1,157 units of
heat. Berthelot states, as one of the fundamental principles of
thermochemistry, "that the quantity of heat evolved is the measure of
the sum of the chemical and physical work accomplished in the
reaction"; and such a law will no doubt account for the phenomena
above noted. The equivalent heat of combustion of the compounds we
have practically to deal with has been experimentally determined, and
therefore constitutes a secure basis on which to establish
calculations of the caloric value of fuel; and in doing so, with
respect to substances composed of carbon, hydrogen, and oxygen, it is
convenient to reduce the hydrogen to its heat-producing equivalent of
carbon. The heat of combustion of hydrogen being 62,032 units, that of
carbon 14,544 units, it follows that 4.265 times the weight of
hydrogen will represent an equivalent amount of carbon. With respect
to the oxygen, it is found that it exists in combination with the
hydrogen in the form of water, and, being combined already, abstracts
its combining equivalent of hydrogen from the efficient ingredients of
the fuel; and hence hydrogen, to the extent of 1/8 of the weight of
the oxygen, must be deducted. The general formula then becomes:
Heat of combustion = 14,544 {C + 4.265 (H-(O/8))},
and water evaporated from and at 212°, taking 966 units as the heat
necessary to evaporate 1 pound of water,
lb. evaporated = 15.06 {C + 4.265 (H-(O/8))},
carbon, hydrogen, and oxygen being taken at their weight per cent. in
the fuel. Strictly speaking, marsh gas should be separately
determined. It often happens that available energy is not in a form in
which it can be applied directly to our needs. The water flowing down
from the mountains in the neighborhood of the Alpine tunnels was
competent to provide the power necessary for boring through them, but
it was not in a form in which it could be directly applied. The
kinetic energy of the water had first to be changed into the potential
energy of air under pressure, then, in that form, by suitable
mechanism, it was used with signal success to disintegrate and
excavate the hard rock of the tunnels. The energy resulting from
combustion is also incapable of being directly transformed into useful
motive power; it must first be converted into potential force of steam
or air at high temperature and pressure, and then applied by means of
suitable heat engines to produce the motions we require. It is
probably to this circumstance that we must attribute the slowness of
the human race to take advantage of the energy of combustion. The
history of the steam engine hardly dates back 200 years, a very small
fraction of the centuries during which man has existed, even since
historic times.
The apparatus by means of which the potential energy of fuel with
respect to oxygen is converted into the potential energy of steam, we
call a steam boiler; and although it has neither cylinder nor piston,
crank nor fly wheel, I claim for it that it is a veritable heat
engine, because it transmits the undulations and vibrations caused by
the energy of chemical combination in the fuel to the water in the
boiler; these motions expend themselves in overcoming the liquid
cohesion of the water and imparting to its molecules that vigor of
motion which converts them into the molecules of a gas which,
impinging on the surfaces which confine it and form the steam space,
declare their presence and energy in the shape of pressure and
temperature. A steam pumping engine, which furnishes water under high
pressure to raise loads by means of hydraulic cranes, is not more
truly a heat engine than a simple boiler, for the latter converts the
latent energy of fuel into the latent energy of steam, just as the
pumping engine converts the latent energy of steam into the latent
energy of the pumped-up accumulator or the hoisted weight.
If I am justified in taking this view, then I am justified in applying
to my heat engine the general principles laid down in 1824 by Sadi
Carnot, namely, that the proportion of work which can be obtained out
of any substance working between two temperatures depends entirely and
solely upon the difference between the temperatures at the beginning
and end of the operation; that is to say, if T be the higher
temperature at the beginning, and _t_ the lower temperature at the end
of the action, then the maximum possible work to be got out of the
substance will be a function of (T-_t_). The greatest range of
temperature possible or conceivable is from the absolute temperature
of the substance at the commencement of the operation down to absolute
zero of temperature, and the fraction of this which can be utilized is
the ratio which the range of temperature through which the substance
is working bears to the absolute temperature at the commencement of
the action. If W = the greatest amount of effect to be expected, T and
_t_ the absolute temperatures, and H the total quantity of heat
(expressed in foot pounds or in water evaporated, as the case may be)
potential in the substance at the higher temperature, T, at the
beginning of the operation, then Carnot's law is expressed by the
equation:
/ T - t \
W = H( ------- )
\ T /
I will illustrate this important doctrine in the manner which Carnot
himself suggested.
[Illustration: THE GENERATION OF STEAM. Fig 2.]
Fig. 2 represents a hillside rising from the sea. Some distance up
there is a lake, L, fed by streams coming down from a still higher
level. Lower down on the slope is a millpond, P, the tail race from
which falls into the sea. At the millpond is established a factory,
the turbine driving which is supplied with water by a pipe descending
from the lake, L. Datum is the mean sea level; the level of the lake
is T, and of the millpond _t_. Q is the weight of water falling
through the turbine per minute. The mean sea level is the lowest level
to which the water can possibly fall; hence its greatest potential
energy, that of its position in the lake, = QT = H. The water is
working between the absolute levels, T and _t_; hence, according to
Carnot, the maximum effect, W, to be expected is--
/ T - t \
W = H( ------- )
\ T /
/ T - t \
but H = QT [therefore] W = Q T( ------- )
\ T /
W = Q (T - t),
that is to say, the greatest amount of work which can be expected is
found by multiplying the weight of water into the clear fall, which
is, of course, self-evident.
Now, how can the quantity of work to be got out of a given weight of
water be increased without in any way improving the efficiency of the
turbine? In two ways:
1. By collecting the water higher up the mountain, and by that means
increasing T.
2. By placing the turbine lower down, nearer the sea, and by that
means reducing _t_.
Now, the sea level corresponds to the absolute zero of temperature,
and the heights T and _t_ to the maximum and minimum temperatures
between which the substance is working; therefore similarly, the way
to increase the efficiency of a heat engine, such as a boiler, is to
raise the temperature of the furnace to the utmost, and reduce the
heat of the smoke to the lowest possible point. It should be noted, in
addition, that it is immaterial what liquid there may be in the lake;
whether water, oil, mercury, or what not, the law will equally apply,
and so in a heat engine, the nature of the working substance, provided
that it does not change its physical state during a cycle, does not
affect the question of efficiency with which the heat being expended
is so utilized. To make this matter clearer, and give it a practical
bearing, I will give the symbols a numerical value, and for this
purpose I will, for the sake of simplicity, suppose that the fuel used
is pure carbon, such as coke or charcoal, the heat of combustion of
which is 14,544 units, that the specific heat of air, and of the
products of combustion at constant pressure, is 0.238, that only
sufficient air is passed through the fire to supply the quantity of
oxygen theoretically required for the combustion of the carbon, and
that the temperature of the air is at 60° Fahrenheit = 520° absolute.
The symbol T represents the absolute temperature of the furnace, a
value which is easily calculated in the following manner: 1 lb. of
carbon requires 2-2/3 lb. of oxygen to convert it into carbonic acid,
and this quantity is furnished by 12.2 lb. of air, the result being
13.2 lb. of gases, heated by 14,544 units of heat due to the energy of
combustion; therefore:
14,544 units
T = 520° + ------------------ = 5,150° absolute.
13.2 lb. X 0.238
The lower temperature, _t_, we may take as that of the feed water, say
at 100° or 560° absolute, for by means of artificial draught and
sufficiently extending the heating surface, the temperature of the
smoke may be reduced to very nearly that of the feed water. Under such
circumstances the proportion of heat which can be realized is
5,150° - 560°
= --------------- = 0.891;
5,150°
that is to say, under the extremely favorable if not impracticable
conditions assumed, there must be a loss of 11 per cent. Next, to give
a numerical value to the potential energy, H, to be derived from a
pound of carbon, calculating from absolute zero, the specific heat of
carbon being 0.25, and absolute temperature of air 520°:
Units.
1 lb. of carbon X 0.25 X 520 = 130
12.2 of air X 0.238 X 520 = 1,485
Heat of combustion = 14,544
------
16,159
Deduct heat equivalent to work of \
displacing atmosphere by products of }
combustion raised from 60° to 100°, } 32
or from 149.8 cubic feet to 161.3 }
cubic feet, /
------
Total units of heat available 16,127
Equal to 16.69 lb. of water evaporated from and at 212°. Hence the
greatest possible evaporation from and at 212° from a lb. of carbon--
16,159 u. X 0.891 - 32 u.
W = --------------------------- = 14.87 lb.
966 u.
I will now take a definite case, and compare the potential energy of a
certain kind of fuel with the results actually obtained. For this
purpose the boiler of the eight-horse portable engine, which gained
the first prize at the Cardiff show of the Royal Agricultural Society
in 1872, will serve very well, because the trials, all the details of
which are set forth very fully in vol. ix. of the _Journal_ of the
Society, were carried out with great care and skill by Sir Frederick
Bramwell and the late Mr. Menelaus; indeed, the only fact left
undetermined was the temperature of the furnace, an omission due to
the want of a trustworthy pyrometer, a want which has not been
satisfied to this day.[2]
[Footnote 2: In the fifty-second volume of the _Proceedings_
(1887-78), page 154, will be found a remarkable experiment on the
evaporative power of a vertical boiler with internal circulating
pipes. The experiment was conducted by Sir Frederick Bramwell and
Dr. Russell, and is remarkable in this respect, that the quantity
of air admitted to the fuel, the loss by convection and
radiation, and the composition of the smoke were determined. The
facts observed were as follows:
Steam pressure 53 lb................................... = 300.6° F.
lb.
Fuel--Water in coke and wood........................... 26.08
Ash.............................................. 10.53
Hydrogen, oxygen, nitrogen, and sulphur.......... 7.18
------
Total non-combustible..................... 43.79
Carbon, being useful combustible................. 194.46
------
Total fuel................................ 238.25
Air per pound of carbon................................ 17-1/8 lb.
Time of experiment..................................... 4 h. 12 min.
Water evaporated from 60° into steam at 53 lb. pressure 1,620 lb.
Heat lost by radiation and convection.................. 70,430 units.
Mean temperature of chimney............................ 700° F.
" " " air................................ 70° F.
No combustible gas was found in the chimney.