parr 6775 - Example Calculations; Calculation of the Radiation Correction and the Corrected Temperature Rise (T)

Digital Thermometer
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9
n =
the number of temperature read-
ings in the combustion period
after fi ring
=
average temperature during the
preliminary period
=
average temperature during the
fi nal period
t
1
, t
2
, . . .
t
n
=
successive temperatures recorded
during the combustion period
after fi ring at equal time intervals
(e.g. one minute)
=
the sum of t
1
, t
2
, t
3
… t
c-1
The remaining symbols are the same as defi ned
in the Dickinson formula. In general, the results
obtained by the two methods are in practical agree-
ment.
The corrected temperature rise is given by the fol-
lowing formula: t = t
c
– t
a
+ C
r
Example Calculations
Observed Calorimeter Temperature Readings
Time / minutes Temperature / C
0 (start) 22.439
t
start
1 22.447
2 22.454
3 22.462
4 22.469
5 (a) 22.477
t
a
6 (b) 23.896
7 24.555
8 24.714
9 24.770
10 24.792
11 24.802
12 24.806
13 24.809
14 24.812
15 (c) 24.814
t
c
16 24.816
17 24.818
18 24.820
19 24.821
20 (end) 24.823
t
end
Calculation of the Radiation Correction and the Corrected Temperature Rise (t)
r
1
= (t
a
– t
start
) / (a – start)
= (22.477 – 22.439) / 5 = 0.0076
r
2
= (t
end
– t
c
) / (end – c)
= (24.823 – 24.814) / 5 = 0.002
= (t
a
+ t
start
) / 2
= (22.477 + 22.439) / 2 = 22.458
= (t
end
+ tc) / 2
= (24.823+ 24.814) / 2 = 24.818
k = (r
1
– r
2
) / ( - )
= 0.0024
t
m
= 1/n ( + (t
a
+ t
c
) / 2)
= 1/10 (221.956 + 23.646) = 24.560
C
r
(Dickinson) = - r
1
(b – a) – r
2
(c – b)
= - 0.0076 (1) – 0.002 (9) = - 0.026
C
r
(Regnault-Pfaundler) = (c – a) (k (t
m
- ) – r
1
)
= (15 – 5) ((0.0024) (24.560 – 22.458) – 0.0076) = - 0.026
t
Dickinson
= t
c
– t
a
+ Cr
= (24.814 – 22.477) – 0.026 = 2.311
t
Regnault-Pfaundler
= t
c
– t
a
+ C
r
= (24.814 – 22.477) – 0.026 = 2.311