Response of the calorimeter

Since electronic devices such as DSC instruments have a limited response time the intrinsic C -signal may be distorted by the response behaviour of the calorimeter. In general the output signal g t) is the convolution of the ideal input signal f t) and the response function k t) of the calorimeter  

The factor a equals 1 and is only required for a simulation of a distortion according to equations 84 and 85, if the time difference between two sample points is large compared to the instrumental relaxation time b. A convenient method to recover f t) from g[t) is provided by the use of Laplace transforms. The Laplace transform K s) of fc( ) is 

According to the rules of Laplace transformation [56] the time derivative of equation 84 is given by 

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For special attention to the heat transfer and response of the calorimeter Zielenkiewicz (2005)... 

The response of the calorimeter depends on the instrumental time constant, as given in (13). In general, useful kinetic information can be gained only when the rate of a reaction is significantly slower than the time constant. However, a mathematical correction can be made for reactions that are slightly faster than the instrument time constant. ... 

The least squares method for determination of the transmittance parameters was proposed by Rodriguez et al. [69]. This method allows the time constants r,- and the zeros r of the transmittance nominator to be obtained by approximation of the pulse response of the calorimeter by the least squares nonhnear curve-fitting procedure described by Marquardt [70]. 

Reading et al. [216, 217] proposed a method in which a DSC is used. In this case, the response of the calorimeter as a Mnear system would be a superposition oftwo input functions 1) the ramp function [Eq. (2.49)] generated in the calorimetric shield and 2) the periodic function generated in the sample. When the periodic function is sinusoidal [Eq. (2.53],... 

In the multidomains method and in the numerical methods, in accordance with the detailed solution of Fourier s heat conduction equation, it was assumed that the impulse response of the calorimeter is described by an infinite sum of exponential functions [Eq. (2.57)] ... 

Figure 4.8. Plots of pulse responses of the calorimeter with a concentric configuration.

We can demonstrate this on examples of 1) the pulse response of the calorimeter and 2) the temperature changes of the calorimeter as a thermally inert object. 

A calorimeter Is a device used to measure heat flows that accompany chemical processes. The basic features of a calorimeter include an Insulated container and a thermometer that monitors the temperature of the calorimeter. A block diagram of a calorimeter appears in Figure 6-15. In a calorimetry experiment, a chemical reaction takes place within the calorimeter, resulting in a heat flow between the chemicals and the calorimeter. The temperature of the calorimeter rises or falls in response to this heat flow. 

The proportionality constant g includes such parameters as the number of thermoelectric couples in the pile, their thermoelectric power, and the gain of the amplification device. It is supposed, moreover, that the response of the recording line is considerably faster than the thermal lag in the calorimeter. The Tian equation may also be written therefore ... 

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. 

From Tian s equation [Eq. (30)3, it appears that in order to transform the calorimeter response g(t) into a curve proportional to the thermal input f(t), it is sufficient to add, algebraically, to the ordinate of each point on the thermogram g(t), a correction term which is the product of the calorimeter time constant n, by the slope of the tangent to the thermogram at this particular point. This may be achieved manually by the geometrical construction presented on Fig. 10. 

In order to get an overall idea of the effects of the above-mentioned phenomena on the response of a non-ideal calorimeter, let us now considerer a simplified model of one of the calorimeter of COURICINO (Fig. 15.7) experiment (see Section 16.6). 

A typical reaction calorimeter consists of a jacketed reactor, addition device, temperature transducer(s) and calibration heaters. There are a number of devices within Dow ranging from the commercially available Mettler RC-1 (1-2 L volume) to smaller, in-house reactors (10-50 ml). While each of these devices has their unique attributes (e.g., in-situ spectrometry, quick turn-around, ability to reflux, etc.), all of the calorimeters will produce a signal of heat flow vs. time. The heat flow is usually produced in response to the addition of a reagent or an increase in temperature. Volume of gas or pressure generated may also be measured. 

Some care should be exercised when using coated thermocouples since the response of the probe strongly depends on the coating. Although a calorimeter is important for the basic calibration of transducers, the calorimeter itself of little interest for sonochemical studies, unless it is used as the reactor. 

The response of the detector for hadrons from 15 to 350 GeV is depicted in Fig. 2 (left), where the energy deposition in the ionization chambers is plotted as function of the depth in the calorimeter, measured in hadronic interaction lengths i. To guide the eye, the measurements are parameterized according to... 

A sensitive Moseley strip-chart recorder was used to measure the voltage output of the thermocouple. This recorder has a full scale response time of 0.5 sec. A typical trace is shown in Figure 3. Peak 1 is the instantaneous temperature registered by the thermocouple. This is not the equilibrium temperature of the calorimeter. The thermocouple... 

The primary purpose of the new standards was to measure the linearity of calorimeter response over its entire range from 800 to 1200 Btu/SCF. Preliminary tests on three calorimeters show that there may be a bias of+1.5 Btu at the midrange of the calorimeter. That means that when standard B (certified heating value of 813.3 Btu/SCF) or standard C (certified heating value of 1186.1 Btu/SCF) are used to calibrate the calorimeter and the other two standards are used as a test gas, only standard A (certified heating value of 996.6 Btu/SCF) reads high by 1.5 Btu/SCF. This study will continue for other points within the 800-1200 Btu range in order to develop an accurate calibration curve for future use. 

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