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Steam: its Generation and Use
Table of Contents Previous Chapter
[Pg 173]
THE DETERMINATION OF HEATING VALUES OF FUELS
The heating value of a fuel may be determined either by a calculation from a chemical
analysis or by burning a sample in a calorimeter.
In the former method the calculation should be based on an ultimate analysis, which
reduces the fuel to its elementary constituents of carbon, hydrogen, oxygen, nitrogen,
sulphur, ash and moisture, to secure a reasonable degree of accuracy. A proximate
analysis, which determines only the percentage of moisture, fixed carbon, volatile matter
and ash, without determining the ultimate composition of the volatile matter, cannot be
used for computing the heat of combustion with the same degree of accuracy as an
ultimate analysis, but estimates may be based on the ultimate analysis that are fairly
correct.
An ultimate analysis requires the services of a competent chemist, and the methods to be
employed in such a determination will be found in any standard book on engineering
chemistry. An ultimate analysis, while resolving the fuel into its elementary constituents,
does not reveal how these may have been combined in the fuel. The manner of their
combination undoubtedly has a direct effect upon their calorific value, as fuels havingalmost identical ultimate analyses show a difference in heating value when tested in a
calorimeter. Such a difference, however, is slight, and very close approximations may be
computed from the ultimate analysis.
Ultimate analyses are given on both a moist and a dry fuel basis. Inasmuch as the latter is
the basis generally accepted for the comparison of data, it would appear that it is the best
basis on which to report such an analysis. When an analysis is given on a moist fuel basis it
may be readily converted to a dry basis by dividing the percentages of the various
constituents by one minus the percentage of moisture, reporting the moisture content
separately.
Moist Fuel Dry Fuel
C 83.95 84.45
H 4.23 4.25
O 3.02 3.04
N 1.27 1.28
S .91 .91
Ash 6.03 6.07–––––––––––
100.00
Moisture .59 .59–––––––––––
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100.00
CALCULATIONS FROM AN ULTIMATE ANALYSIS—The first formula for the calculation of heating
values from the composition of a fuel as determined from an ultimate analysis is due to
Dulong, and this formula, slightly modified, is the most commonly used to-day. Other
formulae have been proposed, some of which are more accurate for certain specific classes
of fuel, but all have their basis in Dulong’s formula, the accepted modified form of which is:
Heat units in B. t. u. per pound of dry fuel =
14,600 C + 62,000( H -
O––––
8 ) + 4000 S (18)
[Pg 174]
where C, H, O and S are the proportionate parts by weight of carbon, hydrogen, oxygen and
sulphur.
Assume a coal of the composition given. Substituting in this formula (18),
Heating value per pound of dry coal
= 14,600 × .8445 + 62,000 ( .0425 -.0304–––––––––
8) + 4000 × .0091 = 14,765 B. t. u.
This coal, by a calorimetric test, showed 14,843 B. t. u., and from a comparison the degreeof accuracy of the formula will be noted.
The investigation of Lord and Haas in this country, Mabler in France, and Bunte in
Germany, all show that Dulong’s formula gives results nearly identical with those obtained
from calorimetric tests and may be safely applied to all solid fuels except cannel coal,
lignite, turf and wood, provided the ultimate analysis is correct. This practically limits its
use to coal. The limiting features are the presence of hydrogen and carbon united in the
form of hydrocarbons. Such hydrocarbons are present in coals in small quantities, but they
have positive and negative heats of combination, and in coals these appear to offset each
other, certainly sufficiently to apply the formula to such fuels.
HIGH AND LOW HEAT VALUE OF FUELS—In any fuel containing hydrogen the calorific value as
found by the calorimeter is higher than that obtainable under most working conditions in
boiler practice by an amount equal to the latent heat of the volatilization of water. This
heat would reappear when the vapor was condensed, though in ordinary practice the
vapor passes away uncondensed. This fact gives rise to a distinction in heat values into the
so-called “higher” and “lower” calorific values. The higher value, i. e., the one determined
by the calorimeter, is the only scientific unit, is the value which should be used in boiler
testing work, and is the one recommended by the American Society of MechanicalEngineers.
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There is no absolute measure of the lower heat of combustion, and in view of the wide
difference in opinion among physicists as to the deductions to be made from the higher or
absolute unit in this determination, the lower value must be considered an artificial unit.
The lower value entails the use of an ultimate analysis and involves assumptions that
would make the employment of such a unit impracticable for commercial work. The use of
the low value may also lead to error and is in no way to be recommended for boiler
practice.
An example of its illogical use may be shown by the consideration of a boiler operated in
connection with a special economizer where the vapor produced by hydrogen is partially
condensed by the economizer. If the low value were used in computing the boiler
efficiency, it is obvious that the total efficiency of the combined boiler and economizer
must be in error through crediting the combination with the heat imparted in condensing
the vapor and not charging such heat to the heat value of the coal.
HEATING VALUE OF GASEOUS FUELS—The method of computing calorific values from an
ultimate analysis is particularly adapted to solid fuels, with the exceptions already noted.The heating value of gaseous fuels may be calculated by Dulong’s formula provided
another term is added to provide for any carbon monoxide present. Such a method,
however, involves the separating of the constituent gases into their elementary gases,
which is oftentimes difficult and liable to simple arithmetical error. As the combustible
portion of gaseous fuels is ordinarily composed of hydrogen, carbon [Pg 175]monoxide and
certain hydrocarbons, a determination of the calorific value is much more readily obtained
by a separation into their constituent gases and a computation of the calorific value from a
table of such values of the constituents. Table 37 gives the calorific value of the more
common combustible gases, together with the theoretical amount of air required for their
combustion.
TABLE 37
WEIGHT AND CALORIFIC VALUE OF VARIOUS GASES
AT 32 DEGREES FAHRENHEIT AND ATMOSPHERIC PRESSURE
WITH THEORETICAL AMOUNT OF AIR REQUIRED FOR COMBUSTION
Gas Symbol
Cubic Feet of
Gas perPound
B. t. u.
perPound
B. t. u. per
CubicFoot
Cubic Feet of
Air
Requiredper Pound of
Gas
Cubic Feet of
Air Required
Per CubicFoot
of Gas
Hydrogen H 177.90 62000 349 428.25 2.41
Carbon
MonoxideCO 2.81 4450 347 30.60 2.39
Methane CH4 22.37 23550 1053 214.00 9.57
Acetylene C2H2 13.79 21465 1556 164.87 11.93
Olefiant Gas C2H4 12.80 21440 1675 183.60 14.33
Ethane C2H6 11.94 22230 1862 199.88 16.74
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In applying this table, as gas analyses may be reported either by weight or volume, there is
given in Table 33[36] a method of changing from volumetric analysis to analysis by weight.
Examples:
1st. Assume a blast furnace gas, the analysis of which in percentages by weight is, oxygen =
2.7, carbon monoxide = 19.5, carbon dioxide = 18.7, nitrogen = 59.1. Here the only
combustible gas is the carbon monoxide, and the heat value will be,
0.195 × 4450 = 867.75 B. t. u. per pound.
The net volume of air required to burn one pound of this gas will be,
0.195 × 30.6 = 5.967 cubic feet.
2nd. Assume a natural gas, the analysis of which in percentages by volume is oxygen =
0.40, carbon monoxide = 0.95, carbon dioxide = 0.34, olefiant gas (C2H4) = 0.66, ethane
(C2H6) = 3.55, marsh gas (CH4) = 72.15 and hydrogen = 21.95. All but the oxygen and thecarbon dioxide are combustibles, and the heat per cubic foot will be,
From CO = 0.0095 × 347 = 3.30
C2H4 = 0.0066 × 1675 = 11.05
C2H6 = 0.0355 × 1862 = 66.10
CH4 = 0.7215 × 1050 = 757.58
H = 0.2195 × 349 = 76.61–––––––––––
B. t. u. per cubic foot = 914.64
[Pg 176]
The net air required for combustion of one cubic foot of the gas will be,
CO = 0.0095 × 2.39 = 0.02
C2H4 = 0.0066 × 14.33 = 0.09
C2H6 = 0.0355 × 16.74 = 0.59
CH4 = 0.7215 × 9.57 = 6.90
H = 0.2195 × 2.41 = 0.53–––––––
Total net air per cubic foot = 8.13
PROXIMATE ANALYSIS—The proximate analysis of a fuel gives its proportions by weight of
fixed carbon, volatile combustible matter, moisture and ash. A method of making such an
analysis which has been found to give eminently satisfactory results is described below.
From the coal sample obtained on the boiler trial, an average sample of approximately 40
grams is broken up and weighed. A good means of reducing such a sample is passing it
through an ordinary coffee mill. This sample should be placed in a double-walled air bath,
which should be kept at an approximately constant temperature of 105 degreescentigrade, the sample being weighed at intervals until a minimum is reached. The
percentage of moisture can be calculated from the loss in such a drying.
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For the determination of the remainder of the analysis, and the heating value of the fuel, a
portion of this dried sample should be thoroughly pulverized, and if it is to be kept, should
be placed in an air-tight receptacle. One gram of the pulverized sample should be weighed
into a porcelain crucible equipped with a well fitting lid. This crucible should be supported
on a platinum triangle and heated for seven minutes over the full flame of a Bunsen
burner. At the end of such time the sample should be placed in a desiccator containing
calcium chloride, and when cooled should be weighed. From the loss the percentage of
volatile combustible matter may be readily calculated.
The same sample from which the volatile matter has been driven should be used in the
determination of the percentage of ash. This percentage is obtained by burning the fixed
carbon over a Bunsen burner or in a muffle furnace. The burning should be kept up until a
constant weight is secured, and it may be assisted by stirring with a platinum rod. The
weight of the residue determines the percentage of ash, and the percentage of fixed carbon
is easily calculated from the loss during the determination of ash after the volatile matter
has been driven off.
Proximate analyses may be made and reported on a moist or dry basis. The dry basis is
that ordinarily accepted, and this is the basis adopted throughout this book. The method of
converting from a moist to a dry basis is the same as described in the case of an ultimate
analysis. A proximate analysis is easily made, gives information as to the general
characteristics of a fuel and of its relative heating value.
Table 38 gives the proximate analysis and calorific value of a number of representative
coals found in the United States. [Pg 177]
TABLE 38
APPROXIMATE COMPOSITION AND CALORIFIC VALUE OF CERTAIN TYPICAL AMERICAN COALS
State CountyField, Bed
or VeinMine Size
Proximate Analysis (Dry Coal) B. t. u.
Per
Pound
Dry
Coal
AuthorityMoisture
Volatile
Matter
Fixed
Carbon Ash
ANTHRACITES
Pa. Carbon Lehigh Beaver Meadow 1.50 2.41 90.30 7.29 Gale
Pa. Dauphin Schuylkill Buckwheat 2.15 12.88 78.23 8.89 13137 Whitham
Pa. Lackawanna Wyoming Belleview No. 2 Buck. 8.29 7.81 77.19 15.00 12341 Sadtler
Pa. Lackawanna Wyoming Johnson Culm. 13.90 11.16 65.96 22.88 10591 B. & W. Co.
Pa. Luzerne Wyoming Pittston No. 2 Buck. 3.66 4.40 78.96 16.64 12865 B. & W. Co.
Pa. Luzerne Wyoming Mammoth Large 4.00 3.44 90.59 5.97 13720 Carpenter
Pa. Luzerne Wyoming Exeter Rice 0.25 8.18 79.61 12.21 12400 B. & W. Co.
Pa. Northumberland Schuylkill Treverton 0.84 6.73 86.39 6.88 Isherwood
Pa. Schuylkill Schuylkill Buck Mountain 3.17 92.41 4.42 14220 Carpenter
Pa. Schuylkill York Farm Buckwheat 0.81 5.51 75.90 18.59 11430
Pa. Victoria Buckwheat 4.30 0.55 86.73 12.72 12642 B. & W. Co.
Pa. Carbon LehighLehigh & Wilkes
C. Co.Buck. & Pea 1.57 6.27 66.53 27.20 12848 B. & W. Co.
Pa. Carbon Lehigh Buckwheat 5.00 81.00 14.00 11800 Carpenter
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Pa. Lackawanna Del. & Hud. Co. No. 1 Buck. 6.20 11.60 12100 Denton
SEMI-ANTHRACITES
Pa. Lycoming Loyalsock 1.30 8.72 84.44 6.84
Pa. Sullivan Lopez 5.48 7.53 81.00 11.47 13547 B. & W. Co.
Pa. Sullivan Bernice 1.29 8.21 84.43 7.36
SEMI-BITUMINOUS
Md. AlleghanyBig Vein,
George's Crk. 3.50 21.33 72.47 6.20 14682 B. & W. Co.
Md. Alleghany George's Creek 3.63 16.27 76.93 6.80 14695 B. & W. Co.
Md. Alleghany George's Creek 2.28 19.43 77.44 6.13 14793 B. & W. Co.
Md. Alleghany George's Creek Ocean No. 7 Mine run 1.13 14451 B. & W. Co.
Md. Alleghany Cumberland 1.50 17.26 76.65 6.09 14700
Md. Garrett Washington No.
3Mine run 2.33 14.38 74.93 10.49 14033 U. S. Geo. S.[37]
Pa. Bradford Long Valley 1.55 20.33 68.38 11.29 12965
Pa. Tioga Antrim 2.19 18.43 71.87 9.70 13500
Pa. Cambria "B" or MillerSoriman Shaft C.
Co. 3.40 20.70 71.84 7.46 14484 N. Y. Ed. Co.
Pa. Cambria "B" or Miller Henrietta 1.23 18.37 75.28 6.45 14770 So. Eng. Co.
Pa. Cambria "B" or Miller Penker 3.64 21.34 70.48 8.18 14401 B. & W. Co.
Pa. Cambria "B" or Miller Lancashire 4.38 21.20 70.27 8.53 14453 B. & W. Co.
Pa. CambriaLower
Kittanning
Penn. C. & C. Co.
No. 3Mine run 3.51 17.43 75.69 6.88 14279 U. S. Geo. S.
Pa. CambriaUpper
KittanningValley Mine run 3.40 14.89 75.03 10.08 14152 B. & W. Co.
Pa. ClearfieldLower
KittanningEureka Mine run 5.90 16.71 77.22 6.07 14843 U. S. Geo. S.
Pa. Clearfield Ghem Mine run 3.43 17.53 69.67 12.80 13744 B. & W. Co.Pa. Clearfield Osceola 1.24 25.43 68.56 6.01 13589 B. & W. Co.
Pa. Clearfield Reynoldsville 2.91 21.55 69.03 9.42 14685 B. & W. Co.
Pa. ClearfieldAtlantic-
ClearfieldMine run 1.55 23.36 71.15 5.94 13963 Whitham
Pa. Huntington Barnet & Fulton Carbon Mine run 4.50 18.34 73.06 8.60 13770 B. & W. Co.
Pa. Huntington Rock Hill Mine run 5.91 17.58 73.44 8.99 14105 B. & W. Co.
Pa. Somerset Lower
KittanningKimmelton Mine run 3.09 17.84 70.47 11.69 13424 U. S. Geo. S.
Pa. Somerset "C" Prime Vein Jenner Mine run 9.37 16.47 75.76 7.77 14507 P. R. R.
W. Va. Fayette New River Rush Run Mine run 2.14 22.87 71.56 5.57 14959 U. S. Geo. S.[Pg178]
W. Va. Fayette New River Loup Creek 0.55 19.36 78.48 2.16 14975 Hill
W. Va. Fayette New River Slack 6.66 20.94 73.16 5.90 14412 B. & W. Co.
W. Va. Fayette New River Mine run 2.16 17.82 75.66 6.52 14786 B. & W. Co.
W. Va. Fayette New River Rush Run Mine run 0.94 22.16 75.85 1.99 15007 B. & W. Co.
W. Va. McDowellPocahontas No.
3Zenith Mine run 4.85 17.14 76.54 6.32 14480 U. S. Geo. S.
W. Va. McDowell Tug River Big Sandy Mine run 1.58 18.55 76.44 4.91 15170 U. S. Geo. S.
W. Va. Mercer Pocahontas Mora Lump 1.74 18.55 75.15 6.30 15015 U. S. Geo. S.
W. Va. Mineral Elk Garden 2.10 15.70 75.40 8.90 14195 B. & W. Co.
W. Va. McDowell Pocahontas Flat Top Mine run 0.52 24.02 74.59 1.39 14490 B. & W. Co.
W. Va. McDowell Pocahontas Flat Top Slack 3.24 15.33 77.60 7.07 14653 B. & W. Co.
W. Va. McDowell Pocahontas Flat Top Lump 3.63 16.03 78.04 5.93 14956 B. & W. Co.
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State CountyField, Bed
or VeinMine Size
Proximate Analysis (Dry Coal) B. t. u.
Per
Pound
Dry
Coal
AuthorityMoisture
Volatile
Matter
Fixed
Carbon Ash
BITUMINOUS
Ala. Bibb Cahaba Hill Creek Mine run 6.19 28.58 55.60 15.82 12576 B. & W. Co.
Ala. Jefferson Pratt Pratt No. 13 4.29 25.78 67.68 6.54 14482 B. & W. Co.
Ala. Jefferson Pratt Warner Mine run 2.51 27.80 61.50 10.70 13628 U. S. Geo. S.
Ala. Jefferson Coalburg Mine run 0.94 31.34 65.65 3.01 14513 B. & W. Co.
Ala. Walker Horse Creek Ivy C. & I. Co. No.
8Nut 2.56 31.82 53.89 14.29 12937 U. S. Geo. S.
Ala. Walker JaggerGalloway C. Co.
No. 5Mine run 4.83 34.65 51.12 14.03 12976 U. S. Geo. S.
Ark. Franklin Denning Western No. 4 Nut 2.22 12.83 75.35 11.82 U. S. Geo. S.
Ark. Sebastian Jenny Lind Mine No. 12 Lump 1.07 17.04 74.45 8.51 14252 U. S. Geo. S.
Ark. Sebastian Huntington Cherokee Mine run 0.97 19.87 70.30 9.83 14159 U. S. Geo. S.
Col. Boulder South Platte Lafayette Mine run 19.48 38.80 49.00 12.20 11939 B. & W. Co.
Col. Boulder Laramie Simson Mine run 19.78 44.69 48.62 6.69 12577 U. S. Geo. S.
Col. Fremont Canon City ChandlerNut and
Slack 9.37 38.10 51.75 10.15 11850 B. & W. Co.
Col. Las Animas Trinidad Hastings Nut 2.15 31.07 53.40 15.53 12547 B. & W. Co.
Col. Las Animas Trinidad Moreley Slack 1.88 28.47 55.58 15.95 12703 B. & W. Co.
Col. Routt Yampa Oak Creek 6.67 42.91 55.64 1.45 Hill
Ill. Christian Pana Penwell Col. Lump 8.05 43.67 49.97 6.36 10900 Jones
Ill. Franklin No. 6 Benton Egg 8.31 34.52 54.05 11.43 11727 U. S. Geo. S.
Ill. Franklin Big Muddy Zeigler ¾ inch 13.28 31.97 57.37 10.66 12857 U. S. Geo. S.
Ill. Jackson Big Muddy 4.85 31.55 62.19 6.26 11466 Breckenridge
Ill. La Salle Streator 8.40 41.76 51.42 6.82 11727 Breckenridge
Ill. La Salle Streator Marseilles Mine run 12.98 43.73 49.13 7.14 10899 B. & W. Co.
Ill. Macoupin Nilwood Mine No. 2 Screenings 13.34 34.75 44.55 20.70 10781 B. & W. Co.
Ill. Macoupin Mt. Olive Mine No. 2 Mine run 13.54 41.28 46.30 12.42 10807 U. S. Geo. S.
Ill. Madison Belleville Donk Bros. Lump 13.47 38.69 48.07 13.24 12427 U. S. Geo. S.
Ill. Madison Glen Carbon Mine run 9.78 38.18 51.52 10.30 11672 Bryan
Ill. Marion Odin Lump 6.20 42.91 49.06 8.03 11880 Breckenridge
Ill. Mercer Gilchrist Screenings 8.50 36.17 41.64 22.19 10497 Breckenridge
Ill. Montgomery Pana or No. 5 Coffeen Mine run 11.93 34.05 49.85 16.10 10303 U. S. Geo. S.
Ill. Peoria No. 5 Empire 17.64 31.91 46.17 21.92 10705 B. & W. Co.
Ill. Perry Du Quoin Number 1 Screenings 9.81 33.67 48.36 17.97 11229 B. & W. Co.
Ill. Perry Du Quoin Willis Mine run 7.22 33.06 53.97 12.97 11352U. S. Geo. S.[Pg
179]
Ill. Sangamon Pawnee Slack 4.81 41.53 39.62 18.85 10220 Jones
Ill. St. Glair Standard Nigger Hollow Mine run 14.39 32.90 44.84 22.26 11059 B. & W. Co.
Ill. St. Clair Standard Maryville Mine run 15.71 38.10 41.10 20.80 10999 B. & W. Co.
Ill. Williamson Big Muddy Daws Mine run 8.17 34.33 52.50 13.17 12643 U. S. Geo. S.
Ill. WilliamsonCarterville or
No. 7Carterville 4.66 35.65 56.86 7.49 12286 Univ. of Ill.
Ill. WilliamsonCarterville or
No. 7Burr
Nut, Pea and
Slack 11.91 33.70 55.90 10.40 12932 B. & W. Co.
Ind. Brazil Brazil Gartside Block 2.83 40.03 51.97 8.00 13375 Stillman
Ind. Clay Louise Block 0.83 39.70 52.28 8.02 13248 Jones
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Ind. Green Island City Mine run 6.17 35.42 53.55 11.03 11916 Dearborn
Ind. Knox Vein No. 5 Tecumseh Mine run 10.73 35.75 54.46 9.79 12911 B. & W. Co.
Ind. Parke Vein No. 6 Parke Coal Co. Lump 10.72 44.02 46.33 9.65 11767 U. S. Geo. S.
Ind. Sullivan Sullivan No. 6 Mildred Washed 16.59 42.17 48.44 9.59 13377 U. S. Geo. S.
Ind. Vigo Number 6 Fontanet Mine run 2.28 34.95 50.50 14.55 11920 Dearborn
State CountyField, Bed
or Vein Mine Size
Proximate Analysis (Dry Coal) B. t. u.
Per
PoundDry
Coal
AuthorityMoisture VolatileMatter
FixedCarbon
Ash
Ind. Vigo Number 7 Red Bird Mine run 11.62 41.17 46.76 12.07 12740 U. S. Geo. S.
Iowa Appanoose Mystic Mine No. 3 Lump 13.48 39.40 43.09 17.51 11678 U. S. Geo. S.
Iowa Lucas Lucas Inland No. 1 Mine run 16.01 37.82 46.24 15.94 11963 U. S. Geo. S.
Iowa Marion Big Vein Liberty No. 5 Mine run 14.88 41.53 39.63 18.84 11443 U. S. Geo. S.
Iowa Polk Third Seam Altoona No. 4 Lump 12.44 41.27 40.86 17.87 11671 U. S. Geo. S.
Iowa Wapello Wapello Lump 8.69 36.23 43.68 20.09 11443 U. S. Geo. S.
Kan. Cherokee Weir PittsburghSouthwestern
Dev. Co.Lump 4.31 33.88 53.67 12.45 13144 U. S. Geo. S.
Kan. Cherokee Cherokee Screenings 6.16 35.56 46.90 17.54 10175 Jones
Kan. Cherokee Cherokee Lump 1.81 34.77 52.77 12.46 12557 Jones
Kan. Linn Boicourt Lump 4.74 36.59 47.07 16.34 10392 Jones
Ky. Bell Straight Creek Str. Ck. C. & C.
Co.Mine run 2.89 36.67 57.24 6.09 14362 U. S. Geo. S.
Ky. Hopkins Bed No. 9 Earlington Lump 6.89 40.30 55.16 4.54 13381 St. Col. Ky.
Ky. Hopkins Bed No. 9 Barnsley Mine run 7.92 40.53 48.70 10.77 13036 U. S. Geo. S.
Ky. Hopkins Vein No. 14 NeboPea and
Slack 8.02 31.91 54.02 14.07 12448 B. & W. Co.
Ky. Johnson Vein No. 1 Miller's Creek Mine run 5.12 38.46 58.63 2.91 13743 U. S. Geo. S.
Ky. Mulenburg Bed No. 9 PiercePea and
Slack 9.22 33.94 52.18 13.88 12229 B. & W. Co.
Ky. Pulaski Greensburg 2.80 26.54 63.58 9.88 14095 N. Y. Ed. Co.
Ky. Webster Bed No. 9Pea and
Slack 7.30 31.08 60.72 8.20 13600 B. & W. Co.
Ky. Whitley JellicoNut and
Slack 3.82 31.82 58.78 9.40 13175 B. & W. Co.
Mo. Adair Danforth Mine run 9.00 30.55 46.26 23.19 9889 B. & W. Co.
Mo. Bates Rich Hill New Home Mine run 7.28 37.62 43.83 18.55 12109 U. S. Geo. S.
Mo. Clay Lexington Mo. City Coal Co. 12.45 39.39 48.47 12.14 12875 Univ. of Mo.
Mo. Lafayette Waverly Buckthorn 8.58 41.78 45.99 12.23 12735 Univ. of Mo.
Mo. Lafayette Waverly Higbee 10.84 31.72 55.29 12.99 12500 Univ. of Mo.
Mo. Linn Bevier Marceline 9.45 36.72 52.20 11.08 13180 Univ. of Mo.
Mo. Macon BevierNorthwest Coal
Co.13.09 37.83 42.95 19.22 11500 U. S. Geo. S.
Mo. Morgan Morgan Co.Morgan Co. Coal
Co.Mine run 12.24 45.69 47.98 6.33 14197 U. S. Geo. S.
Mo. Putnam Mendotta Mendotta No. 8 20.78 39.36 50.00 10.64 12602 U. S. Geo. S.
N.Mex. McKinley Gallup GibsonPea and
Slack 12.17 36.31 51.17 12.52 12126 B. & W. Co.
Ohio Athens Hocking Valley Sunday Creek Slack 12.16 34.64 53.10 12.26 12214
[Pg 180] Ohio Belmont Pittsburgh No. 8 Neff Coal Co. Mine run 5.31 38.78 52.22 9.00 12843 U. S. Geo. S.
Ohio ColumbianaMiddle
KittanningPalestine 2.15 37.57 51.80 10.63 13370 Lord & Haas
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Ohio CoshoctonMiddle
KittanningMorgan Run Mine run 41.76 45.24 13.00 13239 B. & W. Co.
Ohio Guernsey Vein No. 7 Little Kate 6.19 33.02 59.96 7.02 13634 B. & W. Co.
Ohio Hocking Hocking Valley Lump 6.45 39.12 50.08 10.80 12700 Lord & Haas
Ohio Hocking Hocking Valley 2.60 40.80 47.60 11.60 12175 Jones
Ohio Jackson BrookvilleSuperior Coal
Co.Mine run 7.59 38.45 43.99 17.56 11704 U. S. Geo. S.
Ohio Jackson LowerKittanning
Superior CoalCo.
Mine run 8.99 41.43 50.06 8.51 13113 U. S. Geo. S.
Ohio Jackson Quakertown Wellston 3.38 35.26 54.18 7.56 12506 Hill
Ohio JeffersonPittsburgh or
No. 8Crow Hollow ¾ inch 4.04 40.08 52.27 9.65 13374 U. S. Geo. S.
Ohio JeffersonPittsburgh or
No. 8Rush Run No. 1 ¾ inch 4.74 36.08 54.81 9.11 13532 U. S. Geo. S.
Ohio Perry Hocking Congo 6 41 38.33 46.71 14.96 12284 B. & W. Co.
Ohio Stark Massillon Slack 6.67 40.02 46.46 13.52 11860 B. & W. Co.
Ohio VintonBrookville or No.
4Clarion
Nut and
Slack 2.47 42.38 50.39 6.23 13421 U. S. Geo. S.
State CountyField, Bed
or VeinMine Size
Proximate Analysis (Dry Coal) B. t. u.Per
Pound
Dry
Coal
AuthorityMoisture
Volatile
Matter
Fixed
Carbon Ash
Okla. Choctaw McAlester Edwards No. 1 Mine run 4.79 39.18 49.97 10.85 13005 U. S. Geo. S.
Okla. Choctaw McAlester Adamson Slack 4.72 28.54 58.17 13.29 12105 B. & W. Co.
Okla. Creek HenriettaLump and
Slack 7.65 36.77 50.14 13.09 12834 U. S. Geo. S.
Pa. AlleghenyPittsburgh 3rd
PoolSlack 1.77 32.06 57.11 10.83 13205 Carpenter
Pa. Allegheny Monongahela Turtle Creek 1.75 36.85 53.94 9.21 13480 Lord & Haas
Pa. Allegheny Pittsburgh Bertha ¾ inch 2.61 35.86 57.81 6.33 13997 U. S. Geo. S.
Pa. Cambria Beach Creek Slack 3.01 32.87 55.86 11.27 13755 B. & W. Co.
Pa. Cambria Miller Lincoln Mine run 5.39 30.83 61.05 8.12 13600 B. & W. Co.
Pa. Clarion Lower Freeport 0.54 35.93 57.66 6.41 13547
Pa. Fayette Connellsville Slack 1.85 28.73 63.22 7.95 13775 Whitham
Pa. Greene Youghiogheny Lump 1.25 32.60 54.70 12.70 13100 B. & W. Co.
Pa. Greene Westmoreland Screenings 11.12 31.67 55.61 12.72 13100 P. R. R.
Pa. Indiana Iselin Mine run 2.70 29.33 63.56 7.11 14220 B. & W. Co.
Pa. Jefferson Punxsutawney Mine run 3.38 29.33 64.93 5.73 14781 B. & W. Co.
Pa. LawrenceMiddle
Kittanning0.70 37.06 56.24 6.70 13840 Lord & Haas
Pa. Mercer Taylor 4.18 32.19 55.55 12.26 12820 B. & W. Co.
Pa. Washington Pittsburgh Ellsworth 2.46 35.35 58.46 6.19 14013 U. S. Geo. S.
Pa. Washington Youghiogheny Anderson ¾ inch 1.00 39.29 54.80 5.91 13729 Jones
Pa. Westmoreland Pittsburgh Scott Haven Lump 4.06 32.91 59.78 7.31 13934 B. & W. Co.
Tenn. Campbell Jellico 1.80 37.76 62.12 1.12 13846 U. S. Navy
Tenn. Claiborne Mingo 4.40 34.31 59.22 6.47 U. S. Geo. S.
Tenn. Marion Etna 3.16 32.98 56.59 10.43
Tenn. Morgan Brushy Mt. 1.77 33.46 54.73 11.87 13824 B. & W. Co.
Tenn. Scott Glen Mary No. 4 Glen Mary 1.53 40.80 56.78 2.42 14625 Ky. State Col.
Tex. Maverick Eagle Pass 5.42 33.73 44.89 21.38 10945 B. & W. Co.
Tex. Paolo Pinto Thurber Mine run 1.90 36.01 49.09 14.90 12760 B. & W. Co.
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Tex. Paolo Pinto Strawn Mine run 4.19 35.40 52.98 11.62 13202 B. & W. Co.
Va. Henrico Gayton 0.82 17.14 74.92 7.94 14363 B. & W. Co.
Va. Lee Darby Darby 1½ inch 4.35 38.46 56.91 4.63 13939U. S. Geo. S.[Pg
181]
Va. Lee McConnel Wilson Mine run 3.35 36.35 57.88 5.77 13931 U. S. Geo. S.
Va. Wise Upper Banner Coburn 3½ inch 3.05 32.65 62.73 4.62 14470 U. S. Geo. S.
Va. Rockingham Clover Hill 31.77 57.98 10.25 13103Va. Russel Clinchfield 2.00 35.72 56.12 8.16 14200
Va. Monongahela Bernmont 32.00 59.90 8.10 13424 Carpenter
W. Va. Harrison Pittsburgh Ocean Mine run 2.47 39.35 52.78 7.87 14202 U. S. Geo. S.
W. Va. Harrison GirardNut, Pea and
Slack 36.66 57.49 5.85 14548 B. & W. Co.
W. Va. Kanawha Winifrede Winifrede 1.05 32.74 64.38 2.88 14111 Hill
W. Va. Kanawha Keystone Keystone Mine run 2.21 33.29 58.61 8.10 14202 U. S. Geo. S.
W. Va. Logan Island Creek Nut and
Slack 1.12 38.61 55.91 5.48 14273 Hill
W. Va. Marion Fairmont Kingmont 1.90 35.31 57.34 7.35 14198 U. S. Geo. S.W. Va. Mingo Thacker Maritime 0.68 31.89 63.48 4.63 14126 Hill
W. Va. Mingo Glen Alum Glen Alum Mine run 3.02 33.81 59.45 6.74 14414 U. S. Geo. S.
W. Va. Preston Bakerstown 4.14 29.09 63.50 7.41 14546 U. S. Geo. S.
W. Va. Putnam Pittsburgh Black Betsy Bug dust 7.41 32.84 53.96 13.20 12568 B. & W. Co.
W. Va. Randolph Upper Freeport CoaltonLump and
Nut 2.11 29.57 59.93 10.50 13854 U. S. Geo. S.
State CountyField, Bed
or VeinMine Size
Proximate Analysis (Dry Coal) B. t. u.
Per
Pound
Dry
Coal
AuthorityMoisture
Volatile
Matter
Fixed
Carbon Ash
LIGNITES AND LIGNITIC COALS
Col. Boulder Rex 16.05 42.12 47.97 9.91 10678 B. & W. Co.
Col. El Paso Curtis 23.25 42.11 49.38 8.51 11090 B. & W. Co.
Col. El Paso Pike View 23.77 48.70 41.47 9.83 10629 B. & W. Co.
Col. Gunnison South Platte Mt. Carbon 20.38 46.38 47.50 6.12
Col. Las Animas Acme 16.74 47.90 44.60 7.50 Col. Sc. of M.
Col. Lehigh 18.30 45.29 44.67 10.04
N.
Dak.McLean Eckland Mine run 29.65 45.56 47.05 7.39 10553 Lord
N.Dak.
McLean Wilton Lump 35.96 49.84 38.05 12.11 11036 U. S. Geo. S.
N.
Dak.McLean Casino 29.65 46.56 38.70 14.74 Lord
N.
Dak.Stark Lehigh Lehigh Mine run 35.84 43.84 39.59 16.57 10121 U. S. Geo. S.
N.
Dak.William Williston Mine run 41.76 39.37 48.09 12.54 10121 B. & W. Co.
N.
Dak.William Williston Mine run 42.74 40.83 47.79 11.38 10271 B. & W. Co.
Tex. Bastrop Bastrop Glenham 32.77 42.76 36.88 20.36 8958 B. & W. Co.
Tex. Houston Crockett 23.27 40.95 38.37 20.68 10886 U. S. Geo. S.
Tex. HoustonHouston C. & C.
Co.31.48 46.93 34.40 18.87 10176 B. & W. Co.
Tex. Milam Rockdale Worley 32.48 43.04 41.14 15.82 10021 B. & W. Co.
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Tex. Robertson Calvert Coaling No. 1 32.01 43.70 43.08 13.22 10753 B. & W. Co.
Tex. Wood Hoyt Consumer's Lig.
Co.33.98 46.97 41.40 11.63 10600 U. S. Geo. S.
Tex. Wood Hoyt 30.25 43.27 41.46 15.27 10597
Wash. King Black Diamond 3.71 48.72 46.56 4.72 Gale
Wyo. Carbon Hanna Mine run 6.44 51.32 43.00 5.68 11607 B. & W. Co.
Wyo. Crook Black Hills Stilwell Coal Co. 19.08 45.21 46.42 8.37 12641 U. S. Geo. S.
Wyo. Sheridan Sheridan Monarch 21.18 51.87 40.43 7.70 12316 U. S. Geo. S.
Wyo. Sweetwater Rock Spring Screenings 7.70 38.57 56.99 4.44 12534 B. & W. Co.
Wyo. Uinta Adaville Lazeart 19.15 45.50 48.11 6.39 9868
U. S. Geo. S.
[Pg
182] [Pl
182]
[Pg 183]
TABLE 39
SHOWING RELATION BETWEEN PROXIMATE AND ULTIMATE ANALYSES OF COAL
State Field or Bed Mine
Proximate
AnalysisUltimate Analysis
Common in
Proximate
& Ultimate
Analysis
Volatile
Matter
Fixed
CarbonCarbon Hydrogen Oxygen Nitrogen Sulphur Ash Moisture
Ala. Horse Creek Icy Coal & Iron Co., No.
831.81 53.90 72.02 4.78 6.45 1.66 .80 14.29 2.56
Ark. Huntington Central C. & C. Co., No. 3 18.99 67.71 76.37 3.90 3.71 1.49 1.23 13.30 1.99
Ill. Pana or No. 5 Clover Leaf, No. 1 37.22 45.64 63.04 4.49 10.04 1.28 4.01 17.14 13.19
Ind. No. 5, Warrick Co. Electric 41.85 44.45 68.08 4.78 7.56 1.35 4.53 13.70 9.11
Ky. No. 11, Hopkins Co. St. Bernard, No. 11 41.10 49.60 72.22 5.06 8.44 1.33 3.65 9.30 7.76
Pa."B" or Lower
KittanningEureka, No. 31 16.71 77.22 84.45 4.25 3.04 1.28 .91 6.07 .56
Pa. Indiana Co. 29.55 62.64 79.86 5.02 4.27 1.86 1.18 7.81 2.90
W.
Va.Fire Creek Rush Run 22.87 71.56 83.71 4.64 3.67 1.70 .71 5.57 2.14
Table 39 gives for comparison the ultimate and proximate analyses of certain of the coals
with which tests were made in the coal testing plant of the United States Geological Survey
at the Louisiana Purchase Exposition at St. Louis.
The heating value of a fuel cannot be directly computed from a proximate analysis, due to
the fact that the volatile content varies widely in different fuels in composition and in
heating value.
Some methods have been advanced for estimating the calorific value of coals from the
proximate analysis. William Kent [38] deducted from Mahler’s tests of European coals the
approximate heating value dependent upon the content of fixed carbon in the combustible.
The relation as deduced by Kent between the heat and value per pound of combustible andthe per cent of fixed carbon referred to combustible is represented graphically by Fig. 23.
Goutal gives another method of determining the heat value from a proximate analysis, in
which the carbon is given a fixed value and the heating value of the volatile matter is
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considered as a function of its percentage referred to combustible. Goutal’s method checks
closely with Kent’s determinations.
All the formulae, however, for computing the calorific value of coals from a proximate
analysis are ordinarily limited to certain classes of fuels. Mr. Kent, for instance, states that
his deductions are correct within a close limit for fuels containing more than 60 per cent of
fixed carbon in the combustible, while for those containing a lower percentage, the error
may be as great as 4 per cent, either high or low.
While the use of such computations will serve where approximate results only are
required, that they are approximate should be thoroughly understood.
CALORIMETRY—An ultimate or a proximate analysis of a fuel is useful in [Pg 184]determining
its general characteristics, and as described on page 183, may be used in the calculation of
the approximate heating value. Where the efficiency of a boiler is to be computed,
however, this heating value should in all instances be determined accurately by means of a
fuel calorimeter.
FIG. 23. GRAPHIC REPRESENTATION OF RELATION BETWEEN
HEAT V ALUE PER POUND OF COMBUSTIBLE AND
FIXED C ARBON IN COMBUSTIBLE AS DEDUCED BY WM. K ENT.
In such an apparatus the fuel is completely burned and the heat generated by such
combustion is absorbed by water, the amount of heat being calculated from the elevation
in the temperature of the water. A calorimeter which has been accepted as the best for
such work is one in which the fuel is burned in a steel bomb filled with compressed
oxygen. The function of the oxygen, which is ordinarily under a pressure of about 25
atmospheres, is to cause the rapid and complete combustion of the fuel sample. The fuel is
ignited by means of an electric current, allowance being made for the heat produced bysuch current, and by the burning of the fuse wire.
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A calorimeter of this type which will be found to give satisfactory results is that of M.
Pierre Mahler, illustrated in Fig. 24 and consisting of the following parts:
A water jacket A, which maintains constant conditions outside of the calorimeter proper,
and thus makes possible a more accurate computation of radiation losses.
The porcelain lined steel bomb B, in which the combustion of the fuel takes place in
compressed oxygen.
FIG. 24. M AHLER BOMB C ALORIMETER
[Pg 185]
The platinum pan C , for holding the fuel.
The calorimeter proper D, surrounding the bomb and containing a definite weighed
amount of water.
An electrode E , connecting with the fuse wire F , for igniting the fuel placed in the pan C .
A support G, for a water agitator.
A thermometer I , for temperature determination of the water in the calorimeter. The
thermometer is best supported by a stand independent of the calorimeter, so that it may
not be moved by tremors in the parts of the calorimeter, which would render the making
of readings difficult. To obtain accuracy of readings, they should be made through a
telescope or eyeglass.
A spring and screw device for revolving the agitator.
A lever L, by the movement of which the agitator is revolved.
A pressure gauge M , for noting the amount of oxygen admitted to the bomb. Between 20
and 25 atmospheres are ordinarily employed.
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An oxygen tank O.
A battery or batteries P , the current from which heats the fuse wire used to ignite the fuel.
This or a similar calorimeter is used in the determination of the heat of combustion of solid
or liquid fuels. Whatever the fuel to be tested, too much importance cannot be given to the
securing of an average sample. Where coal is to be tested, tests should be made from a
portion of the dried and pulverized laboratory sample, the methods of obtaining whichhave been described. In considering the methods of calorimeter determination, the
remarks applied to coal are equally applicable to any solid fuel, and such changes in
methods as are necessary for liquid fuels will be self-evident from the same description.
Approximately one gram of the pulverized dried coal sample should be placed directly in
the pan of the calorimeter. There is some danger in the using of a pulverized sample from
the fact that some of it may be blown out of the pan when oxygen is admitted. This may be
at least partially overcome by forming about two grams into a briquette by the use of a
cylinder equipped with a plunger and a screw press. Such a briquette should be brokenand approximately one gram used. If a pulverized sample is used, care should be taken to
admit oxygen slowly to prevent blowing the coal out of the pan. The weight of the sample
is limited to approximately one gram since the calorimeter is proportioned for the
combustion of about this weight when under an oxygen pressure of about 25 atmospheres.
A piece of fine iron wire is connected to the lower end of the plunger to form a fuse for
igniting the sample. The weight of iron wire used is determined, and if after combustion a
portion has not been burned, the weight of such portion is determined. In placing the
sample in the pan, and in adjusting the fuse, the top of the calorimeter is removed. It is
then replaced and carefully screwed into place on the bomb by means of a long handledwrench furnished for the purpose.
The bomb is then placed in the calorimeter, which has been filled with a definite amount of
water. This weight is the “water equivalent” of the apparatus, i. e., the weight of water, the
temperature of which would be increased one degree for an equivalent increase in the
temperature of the combined apparatus. It may be determined by calculation from the
weights and specific heats of the various parts of [Pg 186]the apparatus. Such a
determination is liable to error, however, as the weight of the bomb lining can only be
approximated, and a considerable portion of the apparatus is not submerged. Anothermethod of making such a determination is by the adding of definite weights of warm water
to definite amounts of cooler water in the calorimeter and taking an average of a number
of experiments. The best method for the making of such a determination is probably the
burning of a definite amount of resublimed naphthaline whose heat of combustion is
known.
The temperature of the water in the water jacket of the calorimeter should be
approximately that of the surrounding atmosphere. The temperature of the weighed
amount of water in the calorimeter is made by some experimenters slightly greater than
that of the surrounding air in order that the initial correction for radiation will be in thesame direction as the final correction. Other experimenters start from a temperature the
same or slightly lower than the temperature of the room, on the basis that the temperature
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after combustion will be slightly higher than the room temperature and the radiation
correction be either a minimum or entirely eliminated.
While no experiments have been made to show conclusively which of these methods is the
better, the latter is generally used.
After the bomb has been placed in the calorimeter, it is filled with oxygen from a tank until
the pressure reaches from 20 to 25 atmospheres. The lower pressure will be sufficient inall but exceptional cases. Connection is then made to a current from the dry batteries in
series so arranged as to allow completion of the circuit with a switch. The current from a
lighting system should not be used for ignition, as there is danger from sparking in burning
the fuse, which may effect the results. The apparatus is then ready for the test.
Unquestionably the best method of taking data is by the use of co-ordinate paper and a
plotting of the data with temperatures and time intervals as ordinates and abscissae. Such
a graphic representation is shown in Fig. 25.
FIG. 25. GRAPHIC METHOD OF RECORDING BOMB C ALORIMETER RESULTS
After the bomb is placed in the calorimeter, and before the coal is ignited, readings of thetemperature of the water should be taken at one minute intervals for a period long enough
to insure a constant rate of change, and in this way determine the initial radiation. The coal
is then ignited by completing the circuit, the temperature at the instant the circuit is closed
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being considered the temperature at the beginning of the combustion. After ignition the
readings should be taken at one-half minute intervals, though because of the rapidity of
the mercury’s rise approximate readings only may be possible for at least a minute after
the firing, such readings, however, being sufficiently accurate for this period. The one-half
minute readings should be taken [Pg 187]after ignition for five minutes, and for, say, five
minutes longer at minute intervals to determine accurately the final rate of radiation.
Fig. 25 shows the results of such readings, plotted in accordance with the methodsuggested. It now remains to compute the results from this plotted data.
The radiation correction is first applied. Probably the most accurate manner of making
such correction is by the use of Pfaundler’s method, which is a modification of that of
Regnault. This assumes that in starting with an initial rate of radiation, as represented by
the inclination of the line AB, Fig. 25, and ending with a final radiation represented by the
inclination of the line CD, Fig. 25, that the rate of radiation for the intermediate
temperatures between the points B and C are proportional to the initial and final rates.
That is, the rate of radiation at a point midway between B and C will be the mean betweenthe initial and final rates; the rate of radiation at a point three-quarters of the distance
between B andC would be the rate at B plus three-quarters of the difference in rates
at B and C , etc. This method differs from Regnault’s in that the radiation was assumed by
Regnault to be in each case proportional to the difference in temperatures between the
water of the calorimeter and the surrounding air plus a constant found for each
experiment. Pfaundler’s method is more simple than that of Regnault, and the results by
the two methods are in practical agreement.
Expressed as a formula, Pfaundler’s method is, though not in form given by him:
C = N( R +
R' - R––––––––––
T' - T( T" - T ))
(19)
Where C = correction in degree centigrade,
N = number of intervals over which correction is made,
R = initial radiation in degrees per interval,
R' = final radiation in degrees per interval,
T = average temperature for period through which initial radiation is computed,
T" = average temperature over period of combustion[39],
T' = average temperature over period through which final radiation is computed.[39]
The application of this formula to Fig. 25 is as follows:
As already stated, the temperature at the beginning of combustion is the reading just
before the current is turned on, or B in Fig. 25. The point C or the temperature at which
combustion is presumably completed, should be taken at a point which falls well within
the established final rate of radiation, and not at the maximum temperature that the
thermometer indicates in the test, unless it lies on the straight line determining the final
radiation. This is due to the fact that in certain instances local conditions will cause the
thermometer to read higher than it should during the time that the bomb is transmitting
heat to the water rapidly, and at other times the maximum temperature might be lower
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than that which would be indicated were readings to be taken at intervals of less than one-
half minute, i. e., the point of maximum temperature will fall below the line determined by
the final rate of radiation. With this understanding AB, Fig. 25, represents the time of initial
radiation, BC the time of [Pg 188]combustion, and CD the time of final radiation. Therefore
to apply Pfaundler’s correction, formula (19), to the data as represented by Fig. 25.
N = 6, R = 0, R' = .01, T = 20.29, T' = 22.83,
T" =20.29 + 22.54 + 22.84 + 22.88 + 22.87 + 22.86––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––
6= 22.36
C = 6( 0 +
.01 - 0–––––––––––––––––––––
22.85 - 20.29( 22.36 - 20.29 ))
= 6 × .008 = .048
Pfaundler’s formula while simple is rather long. Mr. E. H. Peabody has devised a simpler
formula with which, under proper conditions, the variation from correction as found by
Pfaundler’s method is negligible.
It was noted throughout an extended series of calorimeter tests that the maximum
temperature was reached by the thermometer slightly over one minute after the time of
firing. If this period between the time of firing and the maximum temperature reported
was exactly one minute, the radiation through this period would equal the radiation per
one-half minutebefore firing plus the radiation per one-half minute after the maximum
temperature is reached ; or, the radiation through the one minute interval would be the
average of the radiation per minute before firing and the radiation per minute after the
maximum. A plotted chart of temperatures would take the form of a curve of three straight lines (B, C' , D) in Fig. 25. Under such conditions, using the notation as in formula (19) the
correction would become,
C =2R + 2R'–––––––––––––––
2+ ( N - 2 ) R', or R + (N - 1)R' ( 20)
This formula may be generalized for conditions where the maximum temperature is
reached after a period of more than one minute as follows:
Let M = the number of intervals between the time of firing and the maximum temperature.
Then the radiation through this period will be an average of the radiation for M intervals
before firing and for M intervals after the maximum is recorded, or
C =MR + MR'–––––––––––––––––
2+ ( N - M ) R' =
M––––
2R + ( N -
M––––
2) R' ( 21)
In the case of Mr. Peabody’s deductions M was found to be approximately 2 and formula
( 21) becomes directly, C = R + (N - 1)R' or formula ( 20).
The corrections to be made, as secured by the use of this formula, are very close to those
secured by Pfaundler’s method, where the point of maximum temperature is not more
than five intervals later than the point of firing. Where a longer period than this is
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indicated in the chart of plotted temperatures, the approximate formula should not be
used. As the period between firing and the maximum temperature is increased, the plotted
results are further and further away from the theoretical straight line curve. Where this
period is not over five intervals, or two and a half minutes, an approximation of the
straight line curve may be plotted by eye, and ordinarily the radiation correction to be
applied may be determined very closely from such an approximated curve.
Peabody’s approximate formula has been found from a number of tests to give resultswithin .003 degrees Fahrenheit for the limits within which its application holds [Pg
189]good as described. The value of M, which is not necessarily a whole number, should be
determined for each test, though in all probability such a value is a constant for any
individual calorimeter which is properly operated.
The correction for radiation as found on page 188 is in all instances to be added to the
range of temperature between the firing point and the point chosen from which the final
radiation is calculated. This corrected range multiplied by the water equivalent of the
calorimeter gives the heat of combustion in calories of the coal burned in the calorimetertogether with that evolved by the burning of the fuse wire. The heat evolved by the
burning of the fuse wire is found from the determination of the actual weight of wire
burned and the heat of combustion of one milligram of the wire (1.7 calories), i. e., multiply
the weight of wire used by 1.7, the result being in gram calories or the heat required to
raise one gram of water one degree centigrade.
Other small corrections to be made are those for the formation of nitric acid and for the
combustion of sulphur to sulphuric acid instead of sulphur dioxide, due to the more
complete combustion in the presence of oxygen than would be possible in the atmosphere.
To make these corrections the bomb of the calorimeter is carefully washed out with water
after each test and the amount of acid determined from titrating this water with a standard
solution of ammonia or of caustic soda, all of the acid being assumed to be nitric acid. Each
cubic centimeter of the ammonia titrating solution used is equivalent to a correction of
2.65 calories.
As part of acidity is due to the formation of sulphuric acid, a further correction is
necessary. In burning sulphuric acid the heat evolved per gram of sulphur is 2230 calories
in excess of the heat which would be evolved if the sulphur burned to sulphur dioxide, or22.3 calories for each per cent of sulphur in the coal. One cubic centimeter of the ammonia
solution is equivalent to 0.00286 grams of sulphur as sulphuric acid, or to 0.286 × 22.3 =
6.38 calories. It is evident therefore that after multiplying the number of cubic centimeters
used in titrating by the heat factor for nitric acid (2.65) a further correction of 6.38 - 2.65 =
3.73 is necessary for each cubic centimeter used in titrating sulphuric instead of nitric acid.
This correction will be 3.73⁄0.297 = 13 units for each 0.01 gram of sulphur in the coal.
The total correction therefore for the aqueous nitric and sulphuric acid is found by
multiplying the ammonia by 2.65 and adding 13 calories for each 0.01 gram of sulphur in
the coal. This total correction is to be deducted from the heat value as found from thecorrected range and the amount equivalent to the calorimeter.
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After each test the pan in which the coal has been burned must be carefully examined to
make sure that all of the sample has undergone complete combustion. The presence of
black specks ordinarily indicates unburned coal, and often will be found where the coal
contains bone or slate. Where such specks are found the tests should be repeated. In
testing any fuel where it is found difficult to completely consume a sample, a weighed
amount of naphthaline may be added, the total weight of fuel and naphthaline being
approximately one gram. The naphthaline has a known heat of combustion, samples for
this purpose being obtainable from the United States Bureau of Standards, and from the
combined heat of combustion of the fuel and naphthaline that of the former may be readily
computed.
The heat evolved in burning of a definite weight of standard naphthaline may also be used
as a means of calibrating the calorimeter as a whole.
Table of Contents Next Chapter
FOOTNOTES
[36]See page 161.
[37]U. S. Geological Survey.
[38]See “Steam Boiler Economy”, page 47, First Edition.
[39]To agree with Pfaundler’s formula the end ordinates should be given half values in determining T", i. e., T" =((Temp. at B + Temp. at C) ÷ 2 + Temp. all other ordinates) ÷ N
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