Measured curve calorimeter

If the calorimeter could respond instantaneously to the heat effects associated with the addition of titrant, then the measured curve would coincide with the dashed lines in figure 11.5. The deviation of the data from this ideal behavior corresponds to periods in which the isothermal condition is not observed. When necessary, however, it is possible to use deconvolution techniques to generate the input function represented by the dashed line from the observed experimental curve. 

Calorimeter. A differential calorimeter, operating at 25.0 °C under near-isothermal conditions, was used for all heat measurements. Similar calorimeters, designed for determining heats of ion exchange in zeolites, have been described previously (5, 6, 14, 15). The calorimeter was calibrated by measuring the heat of solution of potassium chloride in water. The ratio of the area under the curve traced by the recorder pen to the heat produced was 1.50 dz 0.04 cm per calorie. No heat could be detected when an empty evacuated bulb was broken under water. 

To achieve these objectives, we have written all the chapters and sections in such a way as to emphasize principles and problems. The measuring examples and instruments described were selected in accordance with this view. Crucial items, such as the evaluation of measuring curves, are treated in detail and with reference to particular commercial calorimeters. Readers are instructed about criteria for the... 

Figure 6.7 Exothermic process involving constant heat generation with the corresponding measured curve obtained with an ideal adiabatic calorimeter.

Figure 6.13 Measured curve of an isoperibol calorimeter for a constant heat flow of finite...

Figure 6.19 Measured curve of a differential scanning calorimeter for an endothermic process (dashed baseline dotted extrapolated from steady-state regions).

The fluctuations of the apparatus function / result, of course, in a fluctuation Ah of the halfwidth (Figure 6.24). It can be shown that the haUwidth of the steeper arm of the apparatus function measures the resolution of the instmment along the abscissa (usually the time see Theory of Calvet s Calorimeter in Section 7.9.2.3). Accordingly, the fluctuation of the halfwidth provides a measure of the resolution of the desmeared measured curve along the abscissa. 

Every chemical reaction involves an exchange of heat. The respective heat flow rate is proportional to the reaction rate. Thus, the course of the reaction can be followed from the measured heat flow rate function. In the case of quick reactions, where the reaction heat is released within time intervals of the order of magnitude of the time constant of the calorimeter, the measured curve desmeared according to Section 6.3 must be taken as a basis for further evaluations. In reactions that proceed much more slowly than the time constant of the calorimeter, the... 

The calibration factor can therefore be calculated from the quotient of the exchanged heat and the area under the measured curve. The reliability of a calorimeter depends essentially on the repeatability of this factor in case of a variation of other experimental parameters such as type and amount of sample and the nature and pressure of the gas used. 

To sum up, the Calvet calorimeter has a very simple exponential apparatus function based on the above assumptions (namely, a very small Rthi and a rapid heat relaxation inside the sample and sample container (calorimeter vessel)). The measured curve can then be desmeared in a simple and accurate maimer according to Eq. (7.9). The assumptions are complied with to some extent if Rth2 is made suitably large by an appropriate design (see Figure 7.16). The large time... 

At the times when the classical calorimeters were built, no computers existed and all evaluation was done by hand. Therefore, there was a need for simple formulas to calculate the quantities of interest from the measured curves. The construction of the calorimeters was such to give a signal strictly proportional to the heat flow rate into the sample itself with a calibration factor almost not influenced by the heat transfer to the sample and its heat capacity. The price to be paid for this comfort was a rather low sensitivity of the calorimeter with a need for large samples and large time constants in the range from some seconds up to many minutes in the case of very sensitive microcalorimeters (see Section 7.9.2). 

The time constant limits the accuracy of the desmearrng of the measured curve with regard to time (or temperature). To bring the desmeared measured curve to an accuracy much larger than that corresponding to half of the time constant, one has to make a thorough analysis of the possible errors - a task that usually necessitates a very extensive test program and a theoretical mastery of the behavior of the calorimeter (see Section 6.3.5). 

The output of a differential scanning calorimeter is a measure of the power (the rate of energy supply) supplied to the sample cell. The thermogram in the third illustration shows a peak that signals a phase change. The thermogram does not look much like a heating curve, but it contains all the necessary information and is easily transformed into the familiar shape. 

Adiabatic calorimetry. Dewar tests are carried out at atmospheric and elevated pressure. Sealed ampoules, Dewars with mixing, isothermal calorimeters, etc. can be used. Temperature and pressure are measured as a function of time. From these data rates of temperature and pressure rises as well as the adiabatic temperature ri.se may be determined. If the log p versus UT graph is a straight line, this is likely to be the vapour pressure. If the graph is curved, decomposition reactions should be considered. Typical temperature-time curves obtained from Dewar flask experiments are shown in Fig. 5.4-60. The adiabatic induction time can be evaluated as a function of the initial temperature and as a function of the temperature at which the induction time, tmi, exceeds a specified value. 

As already indicated (Section IV.A), the quantity of heat evolved in the calorimeter cell is measured, in the case of usual heat evolutions, by the area limited by the thermogram. The integration of the calorimetric curves is, therefore, often needed. This may be achieved by means of integrating devices which may be added to the recorder. From our experience, however,... 

The determination of these curves requires not only the measurement of small amounts of heat in a microcalorimeter, but also the simultaneous determination of the corresponding quantity of adsorbed gas. Volumetric measurements are to be preferred to gravimetric measurements for these determinations because it would be very difficult indeed to ensure a good, and reproducible, thermal contact between a sample of adsorbent, hanging from a balance beam, and the inner cell of a heat-flow calorimeter. 

The stoichiometry of an interaction between gas molecules and preadsorbed species may thus be deduced from the modifications of the Q-6 curves for a given reactant which are produced by the presence of preadsorbed species on the solid. The results are, of course, particularly conclusive when the differential heats of adsorption of small doses of reactant are measured in a sensitive calorimeter. But, such a qualitative analysis of the calorimetric data, though very useful, does not allow definite conclusions. In the preceding example, for instance, a fraction of carbon dioxide may remain adsorbed on the solid ... 

In the various sections of this article, it has been attempted to show that heat-flow calorimetry does not present some of the theoretical or practical limitations which restrain the use of other calorimetric techniques in adsorption or heterogeneous catalysis studies. Provided that some relatively simple calibration tests and preliminary experiments, which have been described, are carefully made, the heat evolved during fast or slow adsorptions or surface interactions may be measured with precision in heat-flow calorimeters which are, moreover, particularly suitable for investigating surface phenomena on solids with a poor heat conductivity, as most industrial catalysts indeed are. The excellent stability of the zero reading, the high sensitivity level, and the remarkable fidelity which characterize many heat-flow microcalorimeters, and especially the Calvet microcalorimeters, permit, in most cases, the correct determination of the Q-0 curve—the energy spectrum of the adsorbent surface with respect to... 

Figure 11.5 Typical curve for a continuous titration calorimetry study of an exothermic reaction, using the calorimeter of Figure 11.1 in the heat flow isothermal mode of measurement./ is the frequency of the constant energy pulses supplied to the heater C in Figure 11.1 b. Adapted from [196,197],...

The idea of calorimetry is based on the chemical reaction characteristic of molecules. The calorimetry method does not allow absolute measurements, as is the case, for example, with volumetric methods. The results given by unknown compounds must be compared with the calibration curve prepared from known amounts of pure standard compounds under the same conditions. In practical laboratory work there are very different applications of this method, because there is no general rule for reporting results of calorimetric determinations. A conventional spectrophotometry is used with a calorimeter. The limitations of many calometric procedures lie in the chemical reactions upon which these procedures are based rather than upon the instruments available . This method was first adapted for quinolizidine alkaloid analysis in 1940 by Prudhomme, and subsequently used and developed by many authors. In particular, a calorimetric microdetermination of lupine and sparteine was developed in 1957. The micromethod depends upon the reaction between the alkaloid bases and methyl range in chloroform. 

Differential Scanning Calorimetry (DSC) This is by far the widest utilized technique to obtain the degree and reaction rate of cure as well as the specific heat of thermosetting resins. It is based on the measurement of the differential voltage (converted into heat flow) necessary to obtain the thermal equilibrium between a sample (resin) and an inert reference, both placed into a calorimeter [143,144], As a result, a thermogram, as shown in Figure 2.7, is obtained [145]. In this curve, the area under the whole curve represents the total heat of reaction, AHR, and the shadowed area represents the enthalpy at a specific time. From Equations 2.5 and 2.6, the degree and rate of cure can be calculated. The DSC can operate under isothermal or non-isothermal conditions [146]. In the former mode, two different methods can be used [1] ... 

The use of a filter determined by Eq. (3.15) allows the true form of the signal to be restored (Fig. 3.8, curve 1). In this case, both the magnitudes of the quantities measured and the qualitative shape of the experimental curve change. The use of this filtration method has enabled us to broaden the frequency range of the instrument by about an order of magnitude and to reduce the effective time constant of the calorimeter from 4 min to 30 sec. 

For thermally initiated reactions, is a function of time. Its course can be determined experimentally by measuring the thermal conversion as a function of time, while the reaction proceeds under normal operating conditions. These experiments can be carried out with DSC or, preferably with a Reaction Calorimeter. The Tcf curves can be obtained in the evaluation of the thermogram by using Equation 5.24. Its maximum (MTSR) can be searched from the TCf curve. 

A series of isothermal experiments are performed at different temperatures in a calorimeter, for example, in a DSC. On each curve, the maximum heat release rate, which represents the worst case, is measured (Figure 11.4). The experimental procedure must reach the desired temperature as fast as possible. For this purpose, in a DSC, the oven is preheated to the desired temperature with the reference cmcible in place. The sample cmcible is then placed into the oven and the measurement begins once thermal equilibrium is achieved, which usually takes approximately 2 minutes. During this time no measurement is possible, but 2 minutes is a very short time relative to the total experimental time of several hours. Thus, the achieved conversion before the measure really starts is negligible. It is left as an exercise for the reader to verify this point Moreover, the difference may be corrected graphically. 

In order to obtain the degree of cure and rate of curing, we must first measure the reaction. This is typically done using a differential scanning calorimeter (DSC) as explained in Chapter 2. Typically, several dynamic tests are performed, where the temperature is increased at a constant rate and heat release rate (Q) is measured until the conversion is finished. To obtain Qt we must calculate the area under the curve Q versus t. Figure 7.17 shows four dynamic tests for a liquid silicone rubber at heating rates of 10, 5, 2.5 and 1 K/min. The trapezoidal rule was used to integrate the four curves. As expected, the total heat Qt is the same (more or less) for all four tests. This is to be expected, since each curve was represented with approximately 400 data points. 

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