Linear theory applied to a calorimeter during quasi-isothermal operation

Abstract

The first law of thermodynamics is applied to a calorimeter model in which the reaction domain is surrounded by a heat-conducting domain through which heat is exchanged linearly with constant-temperature surroundings. Equations describing the quasi-isothermal operation of the calorimeter are derived. It proves possible to represent the temperature change of the reaction domain or the wall of the reaction domain for any thermal reaction in terms of the rate of enthalpy change and temperature response caused by impulse or step power input. The proportionality relation between the change in the enthalpy and the time integral of the deviation of the temperature from the convergence temperature is obtained. The proportionality constant is shown to depend only on the geometrical structure and the physical nature of the heat-conducting domain and to be independent of those of the reaction domain. It is also shown that when the temperature and the concentrations of the reactants in the reaction domain are uniform, the thermodynamic state of the reaction domain can be represented by two variables, the extent of reaction and the temperature, thus providing theoretical bases for the deconvolution methods used in thermokinetics. Equations describing a twin calorimeter system are also derived and shown to have the same forms as those for the single calorimeter system. Some problems in the recent treatment of a time-varying calorimeter system are discussed, and the advantages of an isothermal calorimeter with regulation of power are illustrated.