parr 6775 - Appendix 1; Calculating the Corrected Temperature Rise for a Calorimetric Test; Dickinson Formula; Regnault-Pfaundler Formula

Digital Thermometer
Parr Instrument Company
8
Appendix 1
Calculating the Corrected Temperature Rise
for a Calorimetric Test
There are two generally accepted methods for cal-
culating the correction for heat gain or loss from a
non-adiabiatic oxygen bomb calorimeter. The fi rst
method for calculating the correction is based upon
the work of Dr. H.C. Dickinson at the National Bureau
of Standards who showed that the amount of heat
leak during a test could be approximated by assum-
ing that the calorimeter is heated by its surround-
ings during the fi rst 63 percent of the temperature
rise at a rate equal to that measured during the
5-minute preperiod. The method then assumes that
the cooling (or heating) rate during the remaining 37
percent of the rise is the same as the rate observed
during the 5-minute postperiod. For most experi-
mental work the dividing point between these two
periods is taken as that point in time, b, when the
temperature has reached six-tenths (instead of 63%)
of the total rise. This method is given by the follow-
ing formula.
Dickinson Formula
C
r
= - r
1
(b – a) – r
2
(c – b)
where:
C
r
= radiation correction
r
1
= rate of rise in temperature in the
preliminary period. If temperature is
falling, r
1
is negative
r
2
= rate of rise of temperature in the fi nal
period. If temperature is falling, r
2
is
negative
t
a
= fi ring temperature
t
c
= fi nal temperature, being the fi rst
temperature after which the rate of
change is constant
a =
time at temperature t
a
b =
time at temperature t
a
+ 0.60 (t
c
— t
a
)
c =
time at temperature t
c
The second technique of making such correction is
by the use of a method originally developed by the
French chemist and physicist Henri Victor Regnault
and later modifi ed by Leopold Pfaundler otherwise
known as the Regnault-Pfaundler method. This
method assumes that starting with an initial rate
of heat exchange in the preperiod and ending with
a fi nal rate in the postperiod that the rate of heat
exchange during the main period is proportional to
the initial and fi nal rates. That is, the rate of heat ex-
change at a point halfway through the main period
will be the mean of the initial and fi nal rates. This
halfway point is achieved when the calorimeter tem-
perature equals the integrated mean temperature
during the main period. This method is given by the
following formula.
Regnault-Pfaundler Formula
C
r
= (c – a) (k (t
m
- ) – r
1
) = (c – a) (k ( - t
m
) – r
2
)
where:
C
r
= radiation correction;
k =
(r
1
– r
2
) / ( – )
The above quantity is often referred to as the spe-
cifi c rate constant of the calorimeter.
t
m
= 1/n ( + (t
a
+ t
c
) / 2)
The above quantity is the integrated mean tempera-
ture during the main period. This value results from
the numerical integration of temperature values in
the main period using the trapezoidal rule.