Theory heat flow calorimeter

No theory can possibly take into account the arrangement of a real heat-flow calorimeter in all its details. Theoretical models of heat-flow calorimeters, which are necessarily simplified versions of the actual instruments, will therefore be used in the following calculations. It must be remarked that because of the limitations of the theory, no absolute measurements can be made with a heat-flow calorimeter, nor with any calorimeter. It is possible, however, to compare successive measurements with precision. A calorimetric study necessarily involves the calibration of the calorimeter and, upon this operation, depends the accuracy of the whole series of measurements. 

The development of the theory of heat-flow calorimetry (Section VI) has demonstrated that the response of a calorimeter of this type is, because of the thermal inertia of the instrument, a distorted representation of the time-dependence of the evolution of heat produced, in the calorimeter cell, by the phenomenon under investigation. This is evidently the basic feature of heat-flow calorimetry. It is therefore particularly important to profit from this characteristic and to correct the calorimetric data in order to gain information on the thermokinetics of the process taking place in a heat-flow calorimeter. 

A mathematical treatment of heat flow calorimeters can be made at almost any level of complexity. Owing to the intricacy of the non-steady states involved, the matter can hardly be covered in a comprehensive manner. Even with regard to a steady or quasi-steady state, a thorough treatment of the matter may turn out to be too complex, extensive, and in the final analysis of little practical value. A relatively simple theory can be formulated for the Calvet calorimeter, which is widely used in practice and allows slow scanning of the surroundings, too (see Section 7.9.2.3). 

An apparatus with high sensitivity is the heat-flow microcalorimeter originally developed by Calvet and Prat [139] based on the design of Tian [140]. Several Tian-Calvet type microcalorimeters have been designed [141-144]. In the Calvet microcalorimeter, heat flow is measured between the system and the heat block itself. The principles and theory of heat-flow microcalorimetry, the analysis of calorimetric data, as well as the merits and limitations of the various applications of adsorption calorimetry to the study of heterogeneous catalysis have been discussed in several reviews [61,118,134,135,141,145]. The Tian-Calvet type calorimeters are preferred because they have been shown to be reliable, can be used with a wide variety of solids, can follow both slow and fast processes, and can be operated over a reasonably broad temperature range [118,135]. The apparatus is composed by an experimental vessel, where the system is located, which is contained into a calorimetric block (Figure 13.3 [146]). 

Calculate the heat transfer, Q, from a bomb calorimeter (constant volume) or a steady flow calorimeter (constant pressure), Qp, from theory or experimental data. 

Although the fundamental function principle of nanocalorimeters is not changed, the theory of such calorimeters and the mathematics for the deconvolution of the sample properties from the measurements are much more complicated than for common calorimeters. The pathway of the heat flow cannot be approximated by a one-dimensional model, and the heat capacity of the sample is often in the same order of magnitude as the heat capacity of the calorimeter system, which in many chips consists only of a very thin silicon membrane. In classical calorimeters, the calorimeter system is much larger in mass and heat capacity than the sample. This is desirable to avoid an influence of the sample on the sensitivity of the calorimeter and to keep the calibration factor a device property and free it from sample properties. 

Most commonly used are heat-flow microcalorimeters of the Han-Calvet type [5, 8]. The detailed theory and operation of this calorimeter can be found elsewhere [11]. The apparatus is composed of an experimental vessel, where the studied system is located, which is placed into a calorimetric block (Fig. 3.1). The temperature of the block, which functions as heat sink, is controlled very precisely. The heat generated in the system flows to the heat sink and is accurately measured by means of detector. This is made of a large numbers of identical thermocouples (a thermopile) that surrounds the vessel and connected to the block (Fig. 3.2) in such a way that vessel and block temperature are always close to each other. A signal is generated by the detector that is proportional to the heat transfer per unit time. Undesired signals due to the external temperature fluctuations in the calorimetric block are minimized by connecting in opposition two heat flow detectors from two identical vessels, one of which is used to perform the experiment, the other being used as a reference. Heat related to the introduction of the probe and other parasitic phenomena are thus compensated. 

The present theory of calorimetry is concerned mostly with the instruments whose principle of operation is assumed to involve the transfer of heat in the system. This is true for most of the existing calorimeters, whether those with a constant or those with a variable temperature of the shield. It includes calorimeters in which the flow of heat between the calorimeter proper and its surroundings is quite intense, and also those in which this flow of heat is very low. On the other hand, the present theory is concerned to only a minor degree with calorimeters whose principle of operation is based on the assumption that there is no heat transfer (adiabatic calorimeters) or that, by definition, the heat transfer process is stationary (the generated heat effect is compensated). 

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