---------------------+----------+------------+---------------------+
| | | |
| | | Products of |
| | Oxygen | Combustion at 32° F.|
| Analyses | required +--------+------------+
| of 1 lb. | for | | |
| of Coal. | Combustion.| Cubic | Volume |
| | Pounds. | feet. | per cent. |
---------------------+----------+------------+--------+------------+
Carbon........... | 0.8497 | 2.266 | 25.3 | 11.1 |
Hydrogen......... | 0.0426 | 0.309 | 7.6 | 3.4 |
Oxygen........... | 0.0350 | --- | --- | --- |
Sulphur.......... | 0.0042 | --- | --- | _ --- |
Nitrogen......... | 0.1045 | --- | 0.18 | | |
Ash.............. | 0.0540 | --- | --- | | |
+----------+------------+ | | 85.5 |
| | | | | |
Total........... | 1.0000 | 2.572 | --- | | |
9-1/3.lb nitrogen | --- | --- | 118.9 | | |
6 lb. excess of air. | --- | --- | 71.4 | _| |
+----------+------------+--------+------------+
Total cubic feet of | | | | |
products per 1 lb. | | | | |
of coal........... | -- | -- | 226.4 | 100.0 |
---------------------+----------+------------+--------+------------+
The temperature of the furnace not having been determined, we must
calculate it on the supposition, which will be justified later on,
that 50 per cent more air was admitted than was theoretically
necessary to supply the oxygen required for perfect combustion. This
would make 18 lb. of air per 1 lb. of coal; consequently 19 lb. of
gases would be heated by 14,727 units of heat. Hence:
14,727 u.
T = ---------------- = 3,257°
19 lb. × 0.238
above the temperatures of the air, or 3,777° absolute. The temperature
of the smoke, _t_, was 849° absolute; hence the maximum duty would be
3,777° - 849°
--------------- = 0.7752.
3,777°
The specific heat of coal is very nearly that of gases at constant
pressure, and may, without sensible error, be taken as such. The
potential energy of 1 lb. of coal, therefore, with reference to the
oxygen with which it will combine, and calculated from absolute zero,
is:
Units.
19 lb. of coal and air at the temperature
of the air contained 19 lb. × 520° × 0.238 2,350
Heat of combustion 14,727
-------
17,078
Deduct heat expended in displacing atmosphere 151 cubic feet - 422
------
Total potential energy 16,656
Hence work to be expected from the boiler:
/ 3,777° - 849° \
= 17,078 units X ( --------------- ) - 422 units
\ 3,777° /
---------------------------------------------- = 13.27 lb.
966 units
of water evaporated from and at 212°, corresponding to 12,819 units.
The actual result obtained was 11.83 lb.; hence the efficiency of this
boiler was
11.83
------- = 0.892.
13.27
I have already claimed for a boiler that it is a veritable heat
engine, and I have ventured to construct an indicator diagram to
illustrate its working. The rate of transfer of heat from the furnace
to the water in the boiler, at any given point, is some way
proportional to the difference of temperature, and the quantity of
heat in the gases is proportional to their temperatures. Draw a base
line representing -460° Fahr., the absolute zero of temperature. At
one end erect an ordinate, upon which set off T = 3,777°, the
temperature of the furnace. At 849° = _t_, on the scale of
temperature, draw a line parallel to the base, and mark on it a length
proportional to the heating surface of the boiler; join T by a
diagonal with the extremity of this line, and drop a perpendicular on
to the zero line. The temperature of the water in the boiler being
uniform, the ordinates bounded by the sloping line, and by the line,
_t_, will at any point be approximately proportional to the rate of
transmission of heat, and the shaded area above _t_ will be
proportional to the quantity of heat imparted to the water. Join T by
another diagonal with extremity of the heating surface on the zero
line, then the larger triangle, standing on the zero line, will
represent the whole of the heat of combustion, and the ratio of the
two triangles will be as the lengths of their respective bases, that
is, as (T - _t_) / T, which is the expression we have already used. The
heating surface was 220 square feet, and it was competent to transmit
the energy developed by 41 lb. of coal consumed per hour = 12,819 u. ×
41 u. = 525,572 units, equal to an average of 2,389 units per square
foot per hour; this value will correspond to the mean pressure in an
ordinary diagram, for it is a measure of the energy with which
molecular motion is transferred from the heated gases to the
boiler-plate, and so to the water. The mean rate of transmission,
multiplied by the area of heating surface, gives the area of the
shaded portion of the figure, which is the total work which should
have been done, that is to say, the work of evaporating 544 lb. of
water per hour. The actual work done, however, was only 485 lb. To
give the speculations we have indulged in a practical turn, it will be
necessary to examine in detail the terms of Carnot's formula. Carnot
labored under great disadvantages. He adhered to the emission theory
of heat; he was unacquainted with its dynamic equivalent; he did not
know the reason of the difference between the specific heat of air at
constant pressure and at constant volume, the idea of an absolute zero
of temperature had not been broached; but the genius of the man, while
it made him lament the want of knowledge which he felt must be
attainable, also enabled him to penetrate the gloom by which he was
surrounded, and enunciate propositions respecting the theory of heat
engines, which the knowledge we now possess enables us to admit as
true. His propositions are:
1. The motive power of heat is independent of the agents employed to
develop it, and its quantity is determined solely by the temperature
of the bodies between which the final transfer of caloric takes place.
2. The temperature of the agent must in the first instance be raised
to the highest degree possible in order to obtain a great fall of
caloric, and as a consequence a large production of motive power.
3. For the same reason the cooling of the agent must be carried to as
low a degree as possible.
4. Matters must be so arranged that the passage of the elastic agent
from the higher to the lower temperature must be due to an increase of
volume, that is to say, the cooling of the agent must be caused by its
rarefaction.
This last proposition indicates the defective information which Carnot
possessed. He knew that expansion of the elastic agent was accompanied
by a fall of temperature, but he did not know that that fall was due
to the conversion of heat into work. We should state this clause more
correctly by saying that "the cooling of the agent must be caused by
the external work it performs." In accordance with these propositions,
it is immaterial what the heated gases or vapors in the furnace of a
boiler may be, provided that they cool by doing external work and, in
passing over the boiler surfaces, impart their heat energy to the
water. The temperature of the furnace, it follows, must be kept as
high as possible. The process of combustion is usually complex. First,
in the case of coal, close to the fire-bars complete combustion of the
red hot carbon takes place, and the heat so developed distills the
volatile hydrocarbons and moisture in the upper layers of the fuel.
The inflammable gases ignite on or near the surface of the fuel, if
there be a sufficient supply of air, and burn with a bright flame for
a considerable distance around the boiler. If the layer of fuel be
thin, the carbonic acid formed in the first instance passes through
the fuel and mixes with the other gases. If, however, the layer of
fuel be thick, and the supply of air through the bars insufficient,
the carbonic acid is decomposed by the red hot coke, and twice the
volume of carbonic oxide is produced, and this, making its way through
the fuel, burns with a pale blue flame on the surface, the result, as
far as evolution of heat is concerned, being the same as if the
intermediate decomposition of carbonic acid had not taken place. This
property of coal has been taken advantage of by the late Sir W.
Siemens in his gas producer, where the supply of air is purposely
limited, in order that neither the hydrocarbons separated by
distillation, nor the carbonic oxide formed in the thick layer of
fuel, may be consumed in the producer, but remain in the form of crude
gas, to be utilized in his regenerative furnaces.
[Illustration: THE GENERATION OF STEAM. Fig 3.]
[Illustration: THE GENERATION OF STEAM. Fig 4.]
[Illustration: THE GENERATION OF STEAM. Fig 5.]
[Illustration: THE GENERATION OF STEAM. Fig 6.]
[Illustration: THE GENERATION OF STEAM. Fig 7.]
_(To be continued.)_
* * * * *
[Continued from SUPPLEMENT No. 437, page 6970.]