Reference calorimeter

In the case of an electrical calibration, at the beginning of the main period a potential V is applied to a resistance inside the calorimeter proper, causing a current of intensity / to flow over a period t. As a result, an amount of heat Q = Vlt is dissipated in the calorimeter proper, causing the observed temperature rise. If the calibration is carried out on the reference calorimeter proper (without contents ), then eci = ecf = 0 and the internal energy change of the calorimetric system during the main period is... 

Electrical calibration has the advantage of being more flexible. It can afford s0 through equation 7.23 ifitisdone on the reference calorimeter proper. Flowever, it can also be performed on the initial or final state of the actual experiment leading to (e0 + ecl) or (e0 + ecf), respectively. Twenty or 30 years ago the electrical calibration required very expensive instrumentation that was not readily available except in very specialized places, such as the national standards laboratories. Although the very accurate electronic instrumentation that is available today at moderate prices may change the situation, most users of combustion calorimetry still prefer to calibrate their apparatus with benzoic acid. 

The value of s (e, or sr) is usually determined by electrical calibration (note that contrary to combustion calorimetry, it is not common practice to separate the initial and final energy equivalents of the calorimeter into the contribution of the reference calorimeter, e0, and those of the contents present in the initial, C1, and, final, ecf, states see section 7.1). In the case of the calorimeter in figure 8.1, a current I is passed trough the resistance F for a known period of time t and the potential change V across F is measured. Then ... 

In a power-compensated DSC (Figure 3.1) the sample and reference calorimeters are provided with power necessary to maintain them at the same temperature while the polymer passes through a transition or undergoes a chemical reaction. The difference in power, AP, supplied to the sample and reference calorimeters is directly related to the heat-capacity difference at that temperature. As the temperature is scaimed, AP will be either positive or negative depending on whether there is an endotherm, or exotherm respectively. Then the direct conversion to heat flow from power means that... 

The main measured quantity discussed in this paper is the reversing heat flow. It is proportional to the temperature difference between reference calorimeter (empty) and sample calorimeter (AT T, Representing the instantaneous heat flow as a Fourio series with v representing an integer running from 1 to oo and p ... 

The heat-flow rate of the sample calorimeter, consisting of a pan and the sample, and the reference calorimeter, consisting usually of an empty pan, is governed by the rate of temperature change, q (in K min ), and the heat capacity, Cp (in 1K ). The heat capacity measured at constant pressure, p, and composition, n, can then be represented by Cp = (8H/8T)p , with H being the enthalpy and T, the temperature. The overall heat capacity of the sample calorimeter is written as = (mCp + Q), where m... 

Mathematically this simation without a AT loop is expressed by the upper three boxed equations in Fig. 4.60, where dQs/dt and dQs/dt are the heat-flow rates into the reference and sample calorimeters, respectively. The measured and true temperatures are represented by T and T. For simplicity, one can assume that the proportionality constant K is the same for the sample and reference calorimeters. Differences are assessed by calibration. Both bottom equations are then equal to the power input from the average temperature amplifier. Wav (ill W or J s ). 

The use of the upper, differential amplifier loop in Fig. 4.59 closes the AT loop. The temperature-difference signal is directly amplified and a corresponding power is used to compensate the imbalance between the sample and reference calorimeter temperatures so that only a small temperature difference remains, as indicated in Fig. 4.60. This differential-power signal is also sent to the computer as W, the... 

One additional point needs to be considered. The commercial DSC is constructed in a slightly different fashion. Instead of letting the differential amplifier correct only the temperature of the sample calorimeter by adding power, only half is added, and an equal amount of power is subtracted from the reference calorimeter. This is accomplished by properly phasing the power input of the two amplifiers. A check of the derivations shows that the result does not change with this modification. 

In the sketch A of Fig. A.l 1.2 the equivalent electrical circuit for a conventional DSC measurement is drawn. The heat-flow rate into the sample calorimeter (pan + sample) is represented by and is the heat-flow rate into the empty pan which is the reference calorimeter. The heat-flow rate into the sample itself should then be = and matches Eq. (3) of Fig. 4.69 when assuming the thermal resistances... 

Before the DSC experiment is started, the two calorimeters (i.e., the sample and reference pods, since they are separate calorimeters with one heater) are in equilibrium, they are at the same temperature Tu = T = where is the block temperature, is the sample temperature and T, is the reference temperature. When the operator starts the heating experiment, the block will be heated at a linear rate therefore the sample and the reference calorimeters will also be heated. They will lag behind the block temperature, but to a different extent since the heat capacity of the sample calorimeter is higher because of the additional mass of the sample as compared with an empty pan for the reference. The sample temperature will lag behind T,. Assuming the pan masses are identical, the Th - and Th - temperature differences will be proportional to the heat capacity of the sample and reference calorimeters, respectively. The temperatures Th, T, and T, are measured by thermocouples. 

The T4 mode, which uses all four terms in Eq. (2.6), including a correction for the different heating rates of the sample and reference calorimeters, due to their different heat capacities. 

The T4P mode, which also includes a correction for the differences in mass of the sample and reference pans, and a correction for thermal resistance of the pan material (aluminum, copper, etc.) in addition to the terms listed for the T4. One should correct for the difference in pan masses to account for their effects on the heat capacities of the sample and reference calorimeters. Only the QIOOO and now the Q2000 are capable of operating in the T4P mode. 

It has been shown that the measured temperature difference between the sample holder and the reference holder (AT) is proportional to the power necessary to establish an approximately equal temperature of the two holders (Perkin-Elmer 1970). The heat flow rate into the sample and the reference calorimeters can be expressed by the equations... 

Mathematically this situation is expressed by Eqs. (l)-(3). The heat flow into the reference calorimeter, dQj /dt, is equal to the thermal conductivity, K, multiplied by the difference between the measured reference temperature at the platinum thermometer, and the true temperature, Tr. A typical... 

One additional point needs to be considered. The commercial DSC is constructed in a slightly different fashion than that just described. Rather than letting the differential amplifier loop correct only the temperature of the sample, an equal amount of power is subtracted from or added to the power delivered to the reference by the average temperature amplifier. This is accomplished by proper phasing of the power input of the differential temperature amplifier. In reality, thus, one-half of is added to the sample calorimeter in addition to the full power from the average temperature loop, while one-half of IFp is at the same time subtracted from the power going into the reference calorimeter. This results in a total additional power to the sample that is equal to IV, as required by our calculations. The performance of the DSC is thus still described by Eqs. (1), (4), (5), (10), and (11). 

For simplicity it is assumed that Cp is also the heat capacity of the empty reference calorimeter (sample holder). The equality of the heat capacities of the sample and reference holders is best adjusted experimentally otherwise a minor complication in the mathematics is necessary, requiring knowledge of the different masses and the heat capacity of aluminum or other calorimeter material. Checking the precision of several analyses with sample holders of different masses, it was found that matching sample and reference sample pans gives higher precision than calculating the effect of the different masses. ... 

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