# Modelling

3

##### Modelling of the Calorimeters

The temperature-time variations of the calorimeters have been shown to be determined by the differential equation In equation  the term allows for the change of the water equivalent with time;
the term β was introduced to allow for a more rapid decrease than would be given by electrolysis
alone (exposure of the solid components of the cell contents, D2O vapour carried off in the gas
stream). As expected, the effects of β on Qf and K0R can be neglected if the cells are operated below 60°C. Furthermore, significant changes in the enthalpy contents of the calorimeters are normally only observed following the refilling of the cells with D2O (to make up for losses due to electrolysis and evaporation) so that it is usually sufficient to use the approximation The term allows for the decrease of the radiant surface area with time but, as we have already noted, this term may be neglected for calorimeters silvered in the top portion
(however, this term is significant for measurements made in unsilvered Dewars (1); see also (7)). Similarly, the effects of conductive heat transfer are small. We have therefore set Φ = 0 and have made a small increase in the radiative heat transfer coefficient k0R to k’R to allow for this
assumption. We have shown (see Appendix 2 of (1)) that this leads to a small underestimate of Qf (t); at the same time the random errors of the estimations are decreased because the number of parameters to be determined is reduced by one.

We have also throughout used the temperature of the water bath as the reference value and
arrive at the simpler equation which we have used extensively in our work:

4 ##### GLOSSARY OF SYMBOLS USED

CP,O2,g Heat capacity of O2, JK-1mol-1.
CP,D2,g Heat capacity of D2, JK-1 mol-1.
CP,D2O,l Heat capacity of liquid D2O, JK-1mol-1.
CP,D2O,g Heat capacity of D2O vapour, JK-1mol-1.
Ecell Measured cell potential, V
Ecell,t=0 Measured cell potential at the time when the initial values of the parameters are evaluated, V
Ethermoneutral bath Potential equivalent of the enthalpy of reaction for the dissociation of heavy water at the bath temperature, V
F Faraday constant, 96484.56 C mol-1.
H Heaviside unity function.
I Cell current, A.
k0R Heat transfer coefficient due to radiation at a chosen time origin, WK-4
(k’REffective heat transfer coefficient due to radiation, WK-4 Symbol for liquid phase.
L Enthalpy of evaporation, JK1mol-1.
M0 Heavy water equivalent of the calorimeter at a chosen time origin, mols.
P Partial pressure, Pa; product species. P* Atmospheric pressure
P* Rate of generation of excess enthalpy, W.
Qf(t) Time dependent rate of generation of excess enthalpy, W.
T Time, s.
Ν Symbol for vapour phase.
Q Rate of heat dissipation of calibration heater, W.
Δθ Difference in cell and bath temperature, K.
Θ Absolute temperature, K.
θbath Bath temperature, K.
Λ Slope of the change in the heat transfer coefficient with time.
Φ Proportionality constant relating conductive heat transfer to the radiative heat transfer term.