56. The steam-engine being universally employed at present as the means
for deriving motive power from heat, it is extremely interesting to
examine, according to Carnot’s theory, the economy actually attained in
its use. In the first place we remark, that out of the entire “fall”
from the temperature of the coals to that of the atmosphere it is only
part—that from the temperature of the boiler to the temperature of the
condenser—that is made available; while the very great fall from the
temperature of the burning coals to that of the boiler, and the
comparatively small fall from the temperature of the condenser to that
of the atmosphere, are entirely lost as far as regards the mechanical
effect which it is desired to obtain. We infer from this, that the
temperature of the boiler ought to be kept as high as, according to the
strength, is consistent with safety, while that of the condenser ought
to be kept as nearly down at the atmospheric temperature as possible. To
take the entire benefit of the actual fall, Carnot showed that the
“principle of expansion” must be pushed to the utmost.[66]
57. To obtain some notion of the economy which has actually been
obtained, we may take the alleged performances of the best Cornish
engines, and some other interesting practical cases, as examples.[67]
(1) The engine of _the Fowey Consols mine_ was reported, in 1845, to
have given 125,089,000 foot-pounds of effect, for the consumption of one
bushel or 94 lbs. of coals. Now the average amount evaporated from
Cornish boilers, by one pound of coal, is 8½ lbs. of steam; and hence
for each pound of steam evaporated 156,556 foot-pounds of work are
produced.
The pressure of the saturated steam in the boiler may be taken as 3½
atmospheres;[68] and, consequently, the temperature of the water will be
140°. Now (Regnault, end of Mémoire X.) the latent heat of a pound of
saturated steam at 140° is 508, and since, to compensate for each pound
of steam removed from the boiler in the working of the engine, a pound
of water, at the temperature of the condenser, which may be estimated at
30°, is introduced from the hot-well; it follows that 618 units of heat
are introduced to the boiler for each pound of water evaporated. But the
work produced, for each pound of water evaporated, was found above to be
156,556 foot-pounds. Hence ¹⁵⁶⁵⁵⁶⁄₆₁₈, or 253 foot-pounds, is the amount
of work produced for each unit of heat transmitted through the Fowey
Consols engine. Now in Table II. we find 583.0 as the theoretical effect
due to a unit descending from 140° to 0°, and 143 as the effect due to a
unit descending from 30° to 0°. The difference of these numbers, or
440,[69] is the number of foot-pounds of work that a _perfect_ engine
with its boiler at 140° and its condenser at 30° would produce for each
unit of heat transmitted. Hence the Fowey Consols engine, during the
experiments reported on, performed ²⁵³⁄₄₄₀ of its theoretical duty, or
57½ per cent.
(2) The best duty on record, as performed by an engine at work (not for
merely experimental purposes), is that of Taylor’s engine, at the United
Mines, which in 1840 worked regularly for several months at the rate of
98,000,000 foot-pounds for each bushel of coals burned. This is ⁹⁸⁄₁₂₅,
or .784 of the experimental duty reported in the case of the Fowey
Consols engine. Hence the best useful work on record is at the rate of
198.3 foot-pounds for each unit of heat transmitted, and is
(198.3)/(440) or 45 per cent of the theoretical duty, on the supposition
that the boiler is at 140° and the condenser at 30°.
(3) French engineers contract (in Lille, in 1847, for example) to make
engines for mill-power which will produce 30,000 metre-pounds or 98,427
foot-pounds of work for each pound of steam used. If we divide this by
618, we find 159 foot-pounds for the work produced by each unit of heat.
This is 36.1 per cent of 440, the theoretical duty.[70]
(4) English engineers have contracted to make engines and boilers which
will require only 3⅓ lbs. of the best coal per horse-power per hour.
Hence in such engines each pound of coal ought to produce 565,700
foot-pounds of work, and if 7 lbs. of water be evaporated by each pound
of coal, there would result 83,814 foot-pounds of work for each pound of
water evaporated. If the pressure in the boiler be 3½ atmospheres
(temperature 140°) the amount of work for each unit of heat will be
found, by dividing this by 618, to be 130.7 foot-pounds, which is
(130.7)/(440) or 29.7 per cent of the theoretical duty.[71]
(5) The actual average of work performed by good Cornish engines and
boilers is 55,000,000 foot-pounds for each bushel of coal, or less than
half the experimental performance of the Fowey Consols engine, more than
half the actual duty performed by the United Mines engine in 1840; in
fact, about 25 per cent of the theoretical duty.
(6) The average performances of a number of Lancashire engines and
boilers have been recently found to be such as to require 12 lbs. of
Lancashire coal per horse-power per hour (i.e., for performing 60 ×
33,000 foot-pounds), and of a number of Glasgow engines such as to
require 15 lbs. (of a somewhat inferior coal) for the same effect. There
are, however, more than twenty large engines in Glasgow at present[72]
which work with a consumption of only 6½ lbs. of dross, equivalent to 5
lbs. of the best Scotch or 4 lbs. of the best Welsh coal, per
horse-power per hour. The economy may be estimated from these data, as
in the other cases, on the assumption which, with reference to these, is
the most probable we can make, that the evaporation produced by a pound
of best coal is 7 lbs. of steam.
58. The following tables afford a synoptic view of the performances and
theoretical duties in the various cases discussed above.
In Table A the numbers in the second column are found by dividing the
numbers in the first by 8½ in cases (1), (2), and (5), and by 7 in cases
(4), (6), and (7), the estimated numbers of pounds of steam actually
produced in the different boilers by the burning of 1 lb. of coal.
The numbers in the third column are found from those in the second, by
dividing by 618 in Table A, and 614 in Table B, which are respectively
the quantities of heat required to convert a pound of water taken from
the hot-well at 30°, into saturated steam, in the boiler, at 140° or at
121°.
With reference to the cases (3), (4), (6), (7), the hypothesis of Table
B is probably in general nearer the truth than that of Table A. In (4),
(6), and (7), especially upon hypothesis B, there is much uncertainty as
to the amount of evaporation that will be actually produced by 1 lb. of
fuel. The assumption on which the numbers in the second column in Table
B are calculated, is, that each pound of coal will send the same number
of units of heat into the boiler, whether hypothesis A or hypothesis B
be followed. Hence, except in the case of the French contract, in which
the _evaporation_, not the fuel, is specified, the numbers in the third
column are the same as those in the third column of Table A.
TABLE A.
VARIOUS ENGINES IN WHICH THE TEMPERATURE OF THE BOILER IS 140° C. AND
THAT OF THE CONDENSER 30° C.
_Theoretical Duty for each Unit of Heat transmitted, 440[73]
foot-pounds._
─────────────────┬─────────────┬──────────────┬─────────────┬──────────
CASES. │Work produced│Work produced │Work produced│Percentage
│for each lb. │ for each lb. │for each unit│ of
│ of coal │ of water │ of heat │theoretical
│ consumed. │ evaporated. │transmitted. │ duty.
─────────────────┼─────────────┼──────────────┼─────────────┼──────────
│ Ft.-lbs. │ Ft.-lbs. │ Ft.-lbs. │
(1) Fowey Consols│ │ │ │
experiment,│ 1,330,734│ 156,556│ 253│ 57.5
reported in│ │ │ │
1845 │ │ │ │
(2) Taylor’s │ │ │ │
engine at │ │ │ │
the United │ 1,042,553│ 122,653│ 198.4│ 45.1
Mines, │ │ │ │
working in │ │ │ │
1840 │ │ │ │
(3) French │ │ │ │
engines, │ │ 98,427│ 159│ 36.1
according │ │ │ │
to contract│ │ │ │
(4) English │ │ │ │
engines, │ 565,700│ 80,814│ 130.8│ 29.7
according │ │ │ │
to contract│ │ │ │
(5) Average │ │ │ │
actual │ │ │ │
performance│ 585,106│ 68,836│ 111.3│ 25.3
of Cornish │ │ │ │
engines │ │ │ │
(6) Common │ │ │ │
engines, │ │ │ │
consuming │ │ │ │
12 lbs. of │ 165,000│ 23,571│ 38.1│ 8.6
best coal │ │ │ │
per │ │ │ │
horse-power│ │ │ │
per hour │ │ │ │
(7) Improved │ │ │ │
engines │ │ │ │
with │ │ │ │
expansion │ │ │ │
cylinders, │ │ │ │
consuming │ │ │ │
an │ 495,000│ 70,710│ 114.4│ 26
equivalent │ │ │ │
to 4 lbs. │ │ │ │
of best │ │ │ │
coal per │ │ │ │
horse-power│ │ │ │
per hour │ │ │ │
─────────────────┴─────────────┴──────────────┴─────────────┴──────────
TABLE B.
VARIOUS ENGINES IN WHICH THE TEMPERATURE OF THE BOILER IS 121° C.[74]
AND THAT OF THE CONDENSER 30° C.
_Theoretical Duty for each Unit of Heat transmitted, 371 foot-pounds._
─────────────────┬─────────────┬──────────────┬─────────────┬──────────
CASES. │Work produced│Work produced │Work produced│Percentage
│for each lb. │ for each lb. │for each unit│ of
│ of coal │ of water │ of heat │theoretical
│ consumed. │ evaporated. │transmitted. │ duty.
─────────────────┼─────────────┼──────────────┼─────────────┼──────────
│ Ft.-lbs. │ Ft.-lbs. │ Ft.-lbs. │
(3) French │ │ │ │
engines, │ │ 98,427│ 160.3│ 43.2
according │ │ │ │
to contract│ │ │ │
(4) English │ │ │ │
engines, │ 565,700│⁶¹⁴⁄₆₁₈×80,814│ 130.8│ 35
according │ │ │ │
to contract│ │ │ │
(6) Common │ │ │ │
engines, │ │ │ │
consuming │ │ │ │
12 lbs. of │ 165,000│⁶¹⁴⁄₆₁₈×23,571│ 38.1│ 10.3
coal per │ │ │ │
horse-power│ │ │ │
per hour │ │ │ │
(7) Improved │ │ │ │
engines │ │ │ │
with │ │ │ │
expansion │ │ │ │
cylinders, │ │ │ │
consuming │ │ │ │
an │ 495,000│⁶¹⁴⁄₆₁₈×70,710│ 114.4│ 30.7
equivalent │ │ │ │
to 4 lbs. │ │ │ │
best coal │ │ │ │
per │ │ │ │
horse-power│ │ │ │
per hour │ │ │ │
─────────────────┴─────────────┴──────────────┴─────────────┴──────────
APPENDIX A.
EXTRACTS FROM UNPUBLISHED WRITINGS OF CARNOT.