20.29 + 22.54 + 22.84 + 22.88 + 22.87 + 22.86
T" = --------------------------------------------- = 22.36
6
_ _
| .01 - 0 |
C = 6|0 + -------------(22.36 - 20.29)|
|_ 22.85 - 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
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,
2R + 2R'
C = ------- + (N - 2)R', or R + (N - 1)R' (20)
2
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
MR + MR' M M
C = ------- + (N - M)R' = - R + (N - -)R' (21)
2 2 2
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.
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.
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.