A Convenient Multiple-Unit Calorimeter Installation Page: 42
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42 CONVENIENT MULTIPLE-UNIT CALORIMETER INSTALLATION.
The sum of the- initial rate, r1, and the final rate, r2, given as
0.0179, represents the total change of rate for the combustion period.
Now, assuming Newton's law to hold, then
rl+r2 X
A -T
Where T is any temperature interval during the combustion period
and x is the corresponding rate change at that time
Then r +(r,2-x) r +(r-x2) r+ ) x( cooling correction.
The first two terms are for half-minute interval observations,
The reader should note that r1 and r2 are not strictly the rates at the
beginning and end of the combustion period represented; however,
the error introduced by considering them as such is less than the
experimental error of their determination.
Applying Dickinson'sa method to the calculation of this curve
where
C=a tm(n- o)dt+a t2(2._ -0o)dt
or
C=r (tm-to)+r2(t2-tm)
where tm is taken as to at the point of 77 per cent of the total rise
instead of 60 per cent, giving 0.0118 (0.77) -0.0061 (4.23) =0.0091-
0.0258=0.0167, which agrees well with the figures found above.
Now, it has been noted that there is quite a little variation in the
cooling correction obtained for different combustions with the same
amount of heat liberated, even when the initial and final tempera-
tures of the combustion period are the same, because of the difficulty
of getting exact temperature readings during the first part of the
combustion period. Accordingly, the average correction obtained
for 5 to 8 combustions (the beginning temperature always remaining
the same) of the same weight of standard has been taken as the cor-
rection corresponding to that rise. A table of corrections may be
obtained from the results of combustion of different weights of
standard corresponding to different resistance differences (rises).
Such a table for bomb 3 is given below.
Since the amount of heat liberated in the bomb and the rate of
combustion of various coals will not vary greatly, the error involved
by assuming the time constant for the period is slight, and it becomes
necessary to make only two observations, the initial and final, for a
determination, the cooling correction being noted from the table.
a Dickinson, H. C., Combustion calorimetry and the heats of combustion of cane sugar,
benzoic acid, and naphthalene: Bureau of Standards, Bull. 2, vol. 11, Mar. 1, 1915,
pp. 189-257.
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Davis, J. D. & Wallace, E. L. A Convenient Multiple-Unit Calorimeter Installation, report, 1918; Washington D.C.. (https://digital.library.unt.edu/ark:/67531/metadc66440/m1/54/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.