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HeatingValue-of-Fuels-Determination.pdf
9/24/2014
Steam—chapter_value
Steam: its Generation and Use
Table of Contents
Previous Chapter
THE DETERMINATION OF HEATING VALUES OF
FUELS
[Pg 173]
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 having
almost 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.
C
H
O
N
S
Ash
Moist Fuel
83.95
4.23
3.02
1.27
.91
6.03
Dry Fuel
84.45
4.25
3.04
1.28
.91
6.07
–––––––––––
Moisture
.59
100.00
.59
–––––––––––
100.00
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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)
where C, H, O and S are the proportionate parts by weight of carbon, hydrogen, oxygen
and sulphur.
[Pg 174]
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
degree of 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
Mechanical Engineers.
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.
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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
[Pg 175]
portion of gaseous fuels is ordinarily composed of hydrogen, carbon 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
Cubic
Cubic Feet
Feet of
of
Cubic Feet
B. t. u.
B. t. u.
Air
Air
of
per
Gas
Symbol
per
Required Required
Gas per
Cubic
Pound
per Pound Per Cubic
Pound
Foot
of
Foot
Gas
of Gas
Hydrogen
H
177.90
62000
349
428.25
2.41
Carbon
Monoxide
CO
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
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,
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Steam—chapter_value
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
the carbon dioxide are combustibles, and the heat per cubic foot will be,
From CO
C2H4
C2H6
CH4
H
=
=
=
=
=
0.0095
0.0066
0.0355
0.7215
0.2195
×
×
×
×
×
347
1675
1862
1050
349
=
=
=
=
=
3.30
11.05
66.10
757.58
76.61
–––––––––––
B. t. u. per cubic foot = 914.64
The net air required for combustion of one cubic foot of the gas will be,
CO
C2H4
C2H6
CH4
H
=
=
=
=
=
0.0095
0.0066
0.0355
0.7215
0.2195
[Pg 176]
× 2.39 = 0.02
× 14.33 = 0.09
× 16.74 = 0.59
× 9.57 = 6.90
× 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 degrees
centigrade, 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.
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
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Steam—chapter_value
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
B. t. u.
Per
Pound
Volatile Fixed
Moisture
Ash
Dry
Matter Carbon
Coal
Proximate Analysis (Dry Coal)
State
County
Field, Bed
or Vein
Mine
Size
Authority
ANTHRACITES
Pa.
Carbon
Lehigh
Pa.
Dauphin
Schuylkill
Pa.
Lackawanna
Wyoming
Pa.
Lackawanna
Pa.
Beaver
Meadow
1.50
2.41
90.30
7.29
Buckwheat
2.15
12.88
78.23
8.89 13137
Whitham
Belleview
No. 2
Buck.
8.29
7.81
77.19
15.00 12341
Sadtler
Wyoming
Johnson
Culm.
13.90
11.16
65.96
22.88 10591 B. & W. Co.
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
Pa.
Luzerne
Wyoming
Exeter
Rice
0.25
8.18
79.61
Pa.
Northumberland Schuylkill
Treverton
0.84
6.73
86.39
6.88
Isherwood
Pa.
Schuylkill
Buck
Mountain
3.17
92.41
4.42 14220
Carpenter
Pa.
Schuylkill
Schuylkill
Pa.
Pa.
Carbon
Lehigh
Pa.
Carbon
Lehigh
Pa.
Lackawanna
Gale
5.97 13720
Carpenter
12.21 12400 B. & W. Co.
York Farm
Buckwheat
0.81
5.51
75.90
18.59 11430
Victoria
Buckwheat
4.30
0.55
86.73
12.72 12642 B. & W. Co.
Buck. &
Pea
1.57
6.27
66.53
27.20 12848 B. & W. Co.
5.00
81.00
14.00 11800
Carpenter
11.60 12100
Denton
Lehigh &
Wilkes C. Co.
Buckwheat
Del. & Hud.
Co.
No. 1
Buck.
6.20
SEMI-ANTHRACITES
Pa.
Lycoming
Pa.
Sullivan
Pa.
Sullivan
Loyalsock
Lopez
Bernice
1.30
8.72
84.44
5.48
7.53
81.00
6.84
1.29
8.21
84.43
7.36
11.47 13547 B. & W. Co.
SEMI-BITUMINOUS
Md.
Alleghany
Big 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
Md.
Alleghany
Cumberland
Ocean No. 7
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Mine run
1.13
1.50
14451 B. & W. Co.
17.26
76.65
6.09 14700
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Steam—chapter_value
Md.
Garrett
Washington
No. 3
2.33
14.38
74.93
Geo. S.
10.49 14033 U. 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 Miller
Soriman Shaft
C. Co.
3.40
20.70
71.84
7.46 14484
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.
Cambria
Lower
Kittanning
Penn. C. & C.
Co. No. 3
Mine run
3.51
17.43
75.69
6.88 14279 U. S. Geo. S.
Pa.
Cambria
Upper
Kittanning
Valley
Mine run
3.40
14.89
75.03
10.08 14152 B. & W. Co.
Pa.
Clearfield
Lower
Kittanning
Eureka
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.
Clearfield
AtlanticClearfield
Mine run
1.55
23.36
71.15
5.94 13963
Pa.
Huntington
Barnet &
Fulton
Carbon
Mine run
4.50
18.34
73.06
8.60 13770 B. & W. Co.
Pa.
Huntington
Mine run
N. Y. Ed.
Co.
Whitham
Rock Hill
Mine run
5.91
17.58
73.44
8.99 14105 B. & W. Co.
Kimmelton
Mine run
3.09
17.84
70.47
11.69 13424 U. S. Geo. S.
Pa.
Somerset
Lower
Kittanning
Pa.
Somerset
"C" Prime
Vein
Jenner
Mine run
9.37
16.47
75.76
7.77 14507
W. Va. Fayette
New River
Rush Run
Mine run
2.14
22.87
71.56
5.57 14959
W. Va. Fayette
New River
Loup Creek
W. Va. Fayette
New River
W. Va. Fayette
New River
W. Va. Fayette
New River
Rush Run
W. Va. McDowell
Pocahontas
No. 3
W. Va. McDowell
P. R. R.
U. S. Geo.
S. [Pg 178]
0.55
19.36
78.48
2.16 14975
Slack
6.66
20.94
73.16
5.90 14412 B. & W. Co.
Mine run
2.16
17.82
75.66
6.52 14786 B. & W. Co.
Mine run
0.94
22.16
75.85
1.99 15007 B. & W. Co.
Zenith
Mine run
4.85
17.14
76.54
6.32 14480 U. S. Geo. S.
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.
B. t. u.
Per
Pound
Volatile Fixed
Moisture
Ash
Dry
Matter Carbon
Coal
Hill
Proximate Analysis (Dry Coal)
State
County
Field, Bed
or Vein
Mine
Size
Authority
BITUMINOUS
Ala.
Bibb
Cahaba
Hill Creek
Ala.
Jefferson
Pratt
Pratt No. 13
Ala.
Jefferson
Pratt
Warner
Ala.
Jefferson
Coalburg
Ala.
Walker
Horse Creek
Ivy C. & I.
Co. No. 8
Ala.
Walker
Jagger
Galloway C.
Co. No. 5
Ark.
Franklin
Denning
Western No. 4
Ark.
Sebastian
Jenny Lind
Mine No. 12
Ark.
Sebastian
Huntington
Cherokee
Col.
Boulder
South Platte
Lafayette
Mine run
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Mine run
6.19
28.58
55.60
15.82 12576 B. & W. Co.
4.29
25.78
67.68
6.54 14482 B. & W. Co.
Mine run
2.51
27.80
61.50
10.70 13628 U. S. Geo. S.
Mine run
0.94
31.34
65.65
3.01 14513 B. & W. Co.
Nut
2.56
31.82
53.89
14.29 12937 U. S. Geo. S.
Mine run
4.83
34.65
51.12
14.03 12976 U. S. Geo. S.
Nut
2.22
12.83
75.35
11.82
Lump
1.07
17.04
74.45
8.51 14252 U. S. Geo. S.
Mine run
0.97
19.87
70.30
9.83 14159 U. S. Geo. S.
19.48
38.80
49.00
12.20 11939 B. & W. Co.
U. S. Geo. S.
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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
Chandler
Nut 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
Ill.
Christian
Pana
Penwell Col.
8.05
43.67
49.97
6.36 10900
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.
Ill.
Madison
Glen Carbon
Ill.
Marion
Ill.
Mercer
Gilchrist
Ill.
Montgomery
Pana or No. 5
Coffeen
Ill.
Peoria
No. 5
Empire
Ill.
Perry
Du Quoin
Number 1
Ill.
Perry
Du Quoin
Willis
Ill.
Sangamon
Ill.
St. Glair
Ill.
Ill.
Odin
Lump
Hill
Jones
Lump
13.47
38.69
48.07
13.24 12427 U. S. Geo. S.
Mine run
9.78
38.18
51.52
10.30 11672
Bryan
Lump
6.20
42.91
49.06
8.03 11880 Breckenridge
Screenings
8.50
36.17
41.64
22.19 10497 Breckenridge
Mine run
11.93
34.05
49.85
16.10 10303 U. S. Geo. S.
17.64
31.91
46.17
21.92 10705 B. & W. Co.
Screenings
9.81
33.67
48.36
17.97 11229 B. & W. Co.
Mine run
7.22
33.06
53.97
12.97 11352
Pawnee
Slack
4.81
41.53
39.62
18.85 10220
Standard
Nigger
Hollow
Mine run
14.39
32.90
44.84
22.26 11059 B. & W. Co.
St. Clair
Standard
Maryville
Mine run
15.71
38.10
41.10
20.80 10999 B. & W. Co.
Williamson
Big Muddy
Daws
Mine run
8.17
34.33
52.50
13.17 12643 U. S. Geo. S.
Ill.
Williamson
Carterville or
No. 7
Carterville
4.66
35.65
56.86
Ill.
Williamson
Carterville or
No. 7
Burr
Nut, Pea
and Slack
11.91
33.70
55.90
Ind.
Brazil
Brazil
Gartside
Block
2.83
40.03
51.97
Ind.
Clay
Ind.
Green
Island City
Ind.
Knox
Vein No. 5
Ind.
Parke
Vein No. 6
Ind.
Sullivan
Ind.
Vigo
Louise
7.49 12286
U. S. Geo.
S. [Pg 179]
Jones
Univ. of Ill.
10.40 12932 B. & W. Co.
8.00 13375
Stillman
Block
0.83
39.70
52.28
8.02 13248
Jones
Mine run
6.17
35.42
53.55
11.03 11916
Dearborn
Tecumseh
Mine run
10.73
35.75
54.46
9.79 12911 B. & W. Co.
Parke Coal
Co.
Lump
10.72
44.02
46.33
9.65 11767 U. S. Geo. S.
Sullivan No. 6 Mildred
Washed
16.59
42.17
48.44
9.59 13377 U. S. Geo. S.
Number 6
Mine run
2.28
34.95
50.50
Fontanet
14.55 11920
Dearborn
B. t. u.
Per
Pound
Volatile Fixed
Moisture
Ash
Dry
Matter Carbon
Coal
Authority
Proximate Analysis (Dry Coal)
State
County
Field, Bed
or Vein
Mine
Ind.
Vigo
Number 7
Red Bird
Iowa
Appanoose
Mystic
Iowa
Lucas
Lucas
Iowa
Marion
Iowa
Polk
Iowa
Wapello
Wapello
Kan.
Cherokee
Weir
Pittsburgh
Kan.
Cherokee
Kan.
Cherokee
Kan.
Linn
Size
Mine run
11.62
41.17
46.76
12.07 12740 U. S. Geo. S.
Mine No. 3
Lump
13.48
39.40
43.09
17.51 11678 U. S. Geo. S.
Inland No. 1
Mine run
16.01
37.82
46.24
15.94 11963 U. S. Geo. S.
Big Vein
Liberty No. 5
Mine run
14.88
41.53
39.63
18.84 11443 U. S. Geo. S.
Third Seam
Altoona No. 4
Lump
12.44
41.27
40.86
17.87 11671 U. S. Geo. S.
Lump
8.69
36.23
43.68
20.09 11443 U. S. Geo. S.
Lump
4.31
33.88
53.67
12.45 13144 U. S. Geo. S.
Cherokee
Screenings
6.16
35.56
46.90
17.54 10175
Jones
Cherokee
Lump
1.81
34.77
52.77
12.46 12557
Jones
Boicourt
Lump
4.74
36.59
47.07
16.34 10392
Jones
Southwestern
Dev. Co.
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7/19
9/24/2014
Steam—chapter_value
Ky.
Bell
Straight Creek
Str. Ck. C. &
C. Co.
Ky.
Hopkins
Bed No. 9
Earlington
Ky.
Hopkins
Bed No. 9
Barnsley
Ky.
Hopkins
Vein No. 14
Nebo
Ky.
Johnson
Vein No. 1
Ky.
Mulenburg
Bed No. 9
Ky.
Pulaski
Ky.
Webster
Ky.
Whitley
Mo.
Adair
Mo.
Bates
Rich Hill
Mo.
Clay
Lexington
Mo. City Coal
Co.
Mo.
Lafayette
Waverly
Buckthorn
Mo.
Lafayette
Waverly
Higbee
Mo.
Linn
Bevier
Mo.
Macon
Mo.
Mo.
Mine run
2.89
36.67
57.24
Lump
6.89
40.30
55.16
Mine run
7.92
40.53
48.70
10.77 13036 U. S. Geo. S.
Pea and
Slack
8.02
31.91
54.02
14.07 12448 B. & W. Co.
Miller's Creek
Mine run
5.12
38.46
58.63
2.91 13743 U. S. Geo. S.
Pierce
Pea and
Slack
9.22
33.94
52.18
13.88 12229 B. & W. Co.
2.80
26.54
63.58
9.88 14095
Pea and
Slack
7.30
31.08
60.72
8.20 13600 B. & W. Co.
Jellico
Nut and
Slack
3.82
31.82
58.78
9.40 13175 B. & W. Co.
Danforth
Mine run
9.00
30.55
46.26
23.19
New Home
Mine run
7.28
37.62
43.83
18.55 12109 U. S. Geo. S.
12.45
39.39
48.47
12.14 12875 Univ. of Mo.
Greensburg
Bed No. 9
6.09 14362 U. S. Geo. S.
4.54 13381
St. Col. Ky.
N. Y. Ed.
Co.
9889 B. & W. Co.
8.58
41.78
45.99
12.23 12735 Univ. of Mo.
10.84
31.72
55.29
12.99 12500 Univ. of Mo.
Marceline
9.45
36.72
52.20
11.08 13180 Univ. of Mo.
Bevier
Northwest
Coal Co.
13.09
37.83
42.95
19.22 11500 U. S. Geo. S.
Morgan
Morgan Co.
Morgan Co.
Coal Co.
12.24
45.69
47.98
6.33 14197 U. S. Geo. S.
Putnam
Mendotta
Mendotta No.
8
20.78
39.36
50.00
10.64 12602 U. S. Geo. S.
N.Mex. McKinley
Gallup
Gibson
Pea 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
Ohio
Belmont
Pittsburgh No.
Neff Coal Co.
8
Mine run
5.31
38.78
52.22
9.00 12843 U. S. Geo. S.
Ohio
Columbiana
Middle
Kittanning
Palestine
2.15
37.57
51.80
10.63 13370 Lord & Haas
Ohio
Coshocton
Middle
Kittanning
Morgan 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
6.45
39.12
50.08
10.80 12700 Lord & Haas
Ohio
Hocking
Hocking
Valley
2.60
40.80
47.60
11.60 12175
Ohio
Jackson
Brookville
Superior Coal
Co.
Mine run
7.59
38.45
43.99
17.56 11704 U. S. Geo. S.
Ohio
Jackson
Lower
Kittanning
Superior Coal
Co.
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
Ohio
Jefferson
Pittsburgh or
No. 8
Crow Hollow
¾ inch
4.04
40.08
52.27
9.65 13374 U. S. Geo. S.
Ohio
Jefferson
Pittsburgh or
No. 8
Rush Run No.
1
¾ inch
4.74
36.08
54.81
9.11 13532 U. S. Geo. S.
Ohio
Perry
Hocking
Congo
Ohio
Stark
Massillon
Ohio
Vinton
Brookville or
No. 4
Mine run
Mine run
Lump
Clarion
[Pg 180]
Jones
Hill
6 41
38.33
46.71
14.96 12284 B. & W. Co.
Slack
6.67
40.02
46.46
13.52 11860 B. & W. Co.
Nut and
Slack
2.47
42.38
50.39
6.23 13421 U. S. Geo. S.
B. t. u.
Per
Pound
Volatile Fixed
Moisture
Ash
Dry
Matter Carbon
Coal
Proximate Analysis (Dry Coal)
State
County
Field, Bed
or Vein
Mine
http://www.gutenberg.org/files/22657/22657-h/chapters/value.html
Size
Authority
8/19
9/24/2014
Steam—chapter_value
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
Henrietta
Lump and
Slack
7.65
36.77
50.14
13.09 12834 U. S. Geo. S.
Pa.
Allegheny
Pittsburgh 3rd
Pool
Slack
1.77
32.06
57.11
10.83 13205
Pa.
Allegheny
Monongahela
Turtle Creek
1.75
36.85
53.94
Pa.
Allegheny
Pittsburgh
Bertha
Pa.
Cambria
Beach Creek
¾ inch
2.61
35.86
57.81
6.33 13997 U. S. Geo. S.
Slack
3.01
32.87
55.86
11.27 13755 B. & W. Co.
Pa.
Cambria
Miller
Pa.
Clarion
Lower
Freeport
Mine run
5.39
30.83
61.05
8.12 13600 B. & W. Co.
0.54
35.93
57.66
6.41 13547
Pa.
Fayette
Connellsville
1.85
28.73
63.22
7.95 13775
Pa.
Greene
Youghiogheny
Pa.
Greene
Westmoreland
Lump
1.25
32.60
54.70
12.70 13100 B. & W. Co.
Screenings
11.12
31.67
55.61
Pa.
Indiana
Iselin
12.72 13100
Mine run
2.70
29.33
63.56
7.11 14220 B. & W. Co.
Pa.
Jefferson
Punxsutawney
Mine run
Lincoln
Slack
Carpenter
9.21 13480 Lord & Haas
Whitham
P. R. R.
3.38
29.33
64.93
5.73 14781 B. & W. Co.
0.70
37.06
56.24
6.70 13840 Lord & Haas
4.18
32.19
55.55
12.26 12820 B. & W. Co.
Pa.
Lawrence
Middle
Kittanning
Pa.
Mercer
Taylor
Pa.
Washington
Pittsburgh
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
Pa.
Westmoreland
Pittsburgh
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
Tenn.
Claiborne
Mingo
4.40
34.31
59.22
6.47
Tenn.
Marion
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
1.53
40.80
56.78
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.
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 13939
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
Va.
Rockingham
31.77
57.98
10.25 13103
Va.
Russel
35.72
56.12
8.16 14200
32.00
59.90
8.10 13424
39.35
52.78
7.87 14202 U. S. Geo. S.
36.66
57.49
5.85 14548 B. & W. Co.
Ellsworth
Scott Haven
Etna
Glen Mary
Clover Hill
Clinchfield
2.00
Va.
Monongahela
Bernmont
W. Va. Harrison
Pittsburgh
Ocean
Mine run
Girard
Nut, Pea
and Slack
W. Va. Harrison
W. Va. Kanawha
Winifrede
Winifrede
W. Va. Kanawha
Keystone
Keystone
W. Va. Logan
Island Creek
W. Va. Marion
Fairmont
W. Va. Mingo
Thacker
W. Va. Mingo
Glen Alum
Glen Alum
Mine run
W. Va. Preston
Bakerstown
W. Va. Putnam
Pittsburgh
Black Betsy
Bug dust
W. Va. Randolph
Upper
Freeport
Coalton
Lump and
Nut
2.47
Jones
U. S. Navy
U. S. Geo. S.
2.42 14625
Ky. State
Col.
U. S. Geo.
S. [Pg 181]
4.62 14470 U. S. Geo. S.
Carpenter
1.05
32.74
64.38
2.88 14111
Mine run
2.21
33.29
58.61
8.10 14202 U. S. Geo. S.
Nut and
Slack
1.12
38.61
55.91
5.48 14273
Kingmont
1.90
35.31
57.34
7.35 14198 U. S. Geo. S.
Maritime
0.68
31.89
63.48
4.63 14126
3.02
33.81
59.45
6.74 14414 U. S. Geo. S.
4.14
29.09
63.50
7.41 14546 U. S. Geo. S.
7.41
32.84
53.96
13.20 12568 B. & W. Co.
2.11
29.57
59.93
10.50 13854 U. S. Geo. S.
Proximate Analysis (Dry Coal)
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B. t. u.
Per
Hill
Hill
Hill
9/19
9/24/2014
Steam—chapter_value
State
County
Per
Field, Bed
or Vein
Mine
Size
Pound
Volatile Fixed
Moisture
Ash
Dry
Matter Carbon
Coal
Authority
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
Mt. Carbon
20.38
46.38
47.50
6.12
Col.
Las Animas
Acme
16.74
47.90
44.60
7.50
18.30
45.29
44.67
10.04
Col.
South Platte
Lehigh
Col. Sc. of
M.
N.
Dak.
McLean
Eckland
Mine run
29.65
45.56
47.05
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
N.
Dak.
Stark
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
32.77
42.76
36.88
20.36
Tex.
Houston
Crockett
Lehigh
Glenham
7.39 10553
Lord
Lord
8958 B. & W. Co.
23.27
40.95
38.37
20.68 10886 U. S. Geo. S.
Houston C. &
C. Co.
31.48
46.93
34.40
18.87 10176 B. & W. Co.
Tex.
Houston
Tex.
Milam
Rockdale
Worley
32.48
43.04
41.14
15.82 10021 B. & W. Co.
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
3.71
48.72
46.56
4.72
Wyo.
Carbon
Hanna
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
7.70
38.57
56.99
4.44 12534 B. & W. Co.
Wyo.
Uinta
Adaville
19.15
45.50
48.11
6.39
Black
Diamond
Mine run
Screenings
Lazeart
Gale
9868 U. S. Geo. S.
[Pg 183]
[Pg 182] [Pl 182]
TABLE 39
SHOWING RELATION BETWEEN PROXIMATE AND ULTIMATE ANALYSES
OF COAL
State
Field or Bed
Mine
Proximate
Analysis
Common in
Proximate
& Ultimate
Analysis
Ultimate Analysis
Volatile Fixed
Carbon Hydrogen Oxygen Nitrogen Sulphur Ash Moisture
Matter Carbon
Ala. Horse Creek
Ark. Huntington
Icy Coal &
31.81
Iron Co., No. 8
Central C. & C.
18.99
Co., No. 3
Clover Leaf,
37.22
No. 1
Ill.
Pana or No. 5
Ind.
No. 5, Warrick
Electric
Co.
41.85
http://www.gutenberg.org/files/22657/22657-h/chapters/value.html
53.90
72.02
4.78
6.45
1.66
.80
14.29
2.56
67.71
76.37
3.90
3.71
1.49
1.23
13.30
1.99
45.64
63.04
4.49
10.04
1.28
4.01
17.14
13.19
44.45
68.08
4.78
7.56
1.35
4.53
13.70
9.11
10/19
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Steam—chapter_value
Ky.
Pa.
Pa.
W.
Va.
No. 11,
Hopkins Co.
"B" or Lower
Kittanning
Indiana Co.
St. Bernard,
No. 11
41.10
49.60
72.22
5.06
8.44
1.33
3.65
9.30
7.76
Eureka, No. 31
16.71
77.22
84.45
4.25
3.04
1.28
.91
6.07
.56
29.55
62.64
79.86
5.02
4.27
1.86
1.18
7.81
2.90
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 and the 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
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.
[Pg 184]
CALORIMETRY—An ultimate or a proximate analysis of a fuel is useful in 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.
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 by
such current, and by the burning of the fuse wire.
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:
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11/19
9/24/2014
Steam—chapter_value
A water
jacket A,
which
maintains
constant
conditions
outside of
the
calorimeter
proper, and
thus makes
possible a
more
accurate
FIG. 23. GRAPHIC REPRESENTATION OF RELATION BETWEEN
HEAT VALUE PER POUND OF COMBUSTIBLE AND
FIXED CARBON IN COMBUSTIBLE AS DEDUCED BY WM. KENT.
computation of radiation losses.
The porcelain lined steel bomb B, in which the combustion of the fuel takes place in
compressed oxygen.
FIG. 24. MAHLER BOMB CALORIMETER
The platinum pan C, for holding the fuel.
[Pg 185]
The calorimeter proper D, surrounding the bomb and containing a definite weighed
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12/19
9/24/2014
Steam—chapter_value
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.
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
which have 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 broken
and 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 handled
wrench 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
[Pg 186]
weights and specific heats of the various parts of the apparatus. Such a determination is
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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. Another method 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 the
same 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
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 in all 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.
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FIG. 25. GRAPHIC METHOD OF RECORDING BOMB CALORIMETER RESULTS
After the bomb is placed in the calorimeter, and before the coal is ignited, readings of the
temperature 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 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 after ignition for five minutes, and for, say, [Pg 187]
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 method
suggested. 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.
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That is, the rate of radiation at a point midway between B and C will be the mean
between the initial and final rates; the rate of radiation at a point three-quarters of the
distance between B and C 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
Where C =
N=
R=
R' =
T=
T" =
T' =
(
R+
R' - R
––––––––––
T' - T
( T" - T )
)
(19)
correction in degree centigrade,
number of intervals over which correction is made,
initial radiation in degrees per interval,
final radiation in degrees per interval,
average temperature for period through which initial radiation is computed,
average temperature over period of combustion[39],
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
than that which would be indicated were readings to be taken at intervals of less than onehalf 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 combustion, and CD the time of final radiation. Therefore [Pg 188]
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,
20.29 + 22.54 + 22.84 + 22.88 + 22.87 + 22.86
T" = –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– = 22.36
6
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.
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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 minute before 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
––––
2
R + (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
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 results
within .003 degrees Fahrenheit for the limits within which its application holds 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.
[Pg 189]
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 calorimeter
together 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.
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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, or
22.3 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 the
corrected range and the amount equivalent to the calorimeter.
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.
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FOOTNOTES
[36] See page 161.
[37] U. S. Geological Survey.
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[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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