Heat capacity determination accuracy

The masses of the sample pans, the sample, and the standard should be determined to an accuracy of at least 0.1% in order to ensure a 1% accuracy of the heat capacity determined. In all of the three runs the temperature of the DSC cell has to be brought to T) (the starting temperature of the runs), at which it should be held for at least 10 min to achieve temperature equilibration. Then the actual runs start. There is an isothermal period at temperature Ti for a specific time (usually 2-5 min), and then heating begins at a constant rate and continues to temperature T2, where there is another isothermal period. All the run parameters in all three runs must be identical. The heat capacity can be calculated only at those temperatures where steady-state conditions exist. 

The accuracy of heat capacity determination with a traditional DSC can be better than 1% when the measurements are done carefully (Bares and Wunderlich 1973). 

After calibration, the measurement technique of specific heat of sample fluids composed of a double experiment performing two nearly identical runs-one with the two cells without sample and the other with the sample in one of the cells. In this way, any differences between the two crucibles are eliminated from the final signal to be used in equation (1). The uncertainty of the heat capacity determinations is found to be better than 1.5% at a 95% confidence level. It is noted that according to the ISO definition, a coverage factor k=2 is used and in order to obtain the accuracy value it must be divided by 2 (Sampaio Nieto de Castro, 1998). We have checked the accuracy of the measurements by measuring the heat capacity of certified reference material sapphire (NIST SRM-707), between room temperature and 430 K, and found deviations of less than 1.5 % with an average absolute deviation (AAD) of 0.68%. 

The temperature dependence of the open circuit voltage has been accurately determined (22) from heat capacity measurements (23). The temperature coefficients are given in Table 2. The accuracy of these temperature coefficients does not depend on the accuracy of the open circuit voltages at 25°C shown in Table 1. Using the data in Tables 1 and 2, the open circuit voltage can be calculated from 0 to 60°C at concentrations of sulfuric acid from 0.1 to 13.877 m. 

The versatility of the DSC method and the high speed of the experiments have costs in terms of accuracy. For example, the best accuracy in the determination of heat capacities of solids by DSC is typically 1% [3,248-250], at least one order of magnitude worse than the accuracy of the corresponding measurements by adiabatic calorimetry [251]. This accuracy loss may, however, be acceptable for many purposes, because DSC experiments are much faster and require much smaller samples than adiabatic calorimetry experiments. In addition, they can be performed at temperatures significantly above ambient, which are outside the normal operating range of most adiabatic calorimeters. 

Instead, a wide variety of spectroscopic and electrochemical titration methods are often employed to determine the equilibrium constants for a molecular recognition process at several different temperatures, which are then analyzed by the van t Hoff equation to give the thermodynamic parameters for the process. However, there is a critical tradeoff between the accuracy of the value obtained and the convenience of the measurement since the thermodynamic parameters, evaluated through the van t Hoff treatment, do not take into account the possible temperature dependence of the enthalpy change, i.e. heat capacity, and are less accurate in principle. In fact, it has been demonstrated with some supramolecular systems that the van t Hoff treatment leads to a curved plot and therefore the thermodynamic parameters deviated considerably from those determined by calorimetry.3132 Hence one should be cautious in handling thermodynamic parameters determined by spectroscopic titration and particularly in comparing the values for distinct systems determined by different methods. 

Use of the thermochemistry discussed above allows rough estimation of reaction enthalpy for a wide range of reactions involving resonance-stabilized radicals. Furthermore, reaction entropies and heat capacities may often be estimated to a good level of accuracy (+ 1-2 cal/mol K) (7b). Hence, equilibrium constants may be estimated to a level of accuracy determined primarily by the uncertainty in reaction enthalpy. 

The heat-capacity ratio 7 = CJOyOfa gas can be determined with good accuracy by measuring the speed of sound c. For an ideal gas. 

Heat capacities of activation have been determined for relatively few other reactions, probably because the necessary experimental accuracy is more easily reached in solvolytic studies. Unfortunately, some of the values reported in the literature cannot be accepted either because they are obviously spurious or because separate sets of workers studying the same or similar reactions obtained quite different results. Examples of investigations which appear to be free from such objections are given below but it must be pointed out that the findings are often surprising and that mechanistic conclusions cannot always be drawn from the information available so far. 

The accuracy of the results over the entire temperature range can be improved by transferring the uncalibrated data to a spreadsheet, and calibrating each temperature point separately with its own heat capacity constant. Artificial sapphire is often used as the standard because an equation (Equation 4.14) giving its change in heat capacity across a given temperature range has been determined. 

The third form (Fig. 7) differs only in detail from the second it was preferred for the experiments with liquid hydrogen, because it could be made of much smaller dimensions. The platinum wire was wound on the outside of the cylindrical silver vessel and covered, to avoid thermal losses, with silver foil which was soldered at the edges to give a better thermal contact this form has the advantage that the platinum wire docs not have to be introduced vacuum-tight into the inside of the silver vessel. In a small size and at low temperatures this form of calorimeter proved to be excellent. The heat capacity of the silver vessel could be calculated with good accuracy, but it was also directly determined by a series of... 

Because the equations used to evaluate both the Reynolds number and the Mach number are functions of the heat transport capacity, it is necessary to first assume the conditions of the vapor flow. Using these assumptions, the maximum heat capacity qc m can be determined by substituting the values of the individual pressure drops into Eq. 12.1 and solving for qc m. Once the value of qc m is known, it can then be substituted into the expressions for the vapor Reynolds number and Mach number to determine the accuracy of the original assumption. Using this iterative approach, which is covered in more detail by Chi [9], accurate values for the capillary limitation as a function of the operating temperature can be determined in units of watt-m or watts for (qL)c m and qc m, respectively. 

Often only a few pieces of information are missing from a complete data set. Thus, for example, the standard entropy and heat capacity of crystalline substances (particularly of intermetallic compounds and oxides with several cations) can be determined with sufficient accuracy by estimation [8]. 

It is seen that the calibration constant disappears, which assumes that it is constant over the experimental conditions. The calculation is carried out using dedicated software. In some circumstances the crucible used for the sample may have to be different from that used for the calibrant. This means that a correction will be required to take into account the difference between the heat capacity of the two crucibles - readily calculated with sufficient accuracy. Measurements can be made at a series of temperatures but are meaningful only within the quasi-steady-state region of the experiment. The specific heat capacity of sapphire has been listed by ASTM in connection with the standard test method E 1269 (1999) for determining specific heat capacity by differential scanning calorimetry. 

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