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d H =0 dT Tr in .NET Generating ANSI/AIM Code 39 in .NET d H =0 dT Tr




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d H =0 dT Tr using .net vs 2010 todisplay bar code 39 on asp.net web,windows application QR Code Standardiztion Therefore d d H HTr = H dT T dT T = CP = B + 2CT DT 2 CP = a + bT cT 2 (5.20). Getting data where a = B, b = 2C, and c = D Thus the Ma VS .NET barcode 3 of 9 ier Kelley coefficients for the muscovite data mentioned above are a = 97 65, b = 26 38 10 3 , and c = 25 44 105 , and these are the values for muscovite in Helgeson et al. (1978).

We have carried the superscript throughout this derivation, so clearly we intend standard conditions to include high temperatures at times. In this case, it means simply that we are measuring some pure compound, rather than any arbitrary mixture, for which H and CP would be more appropriate than H and CP ..

5.6.2 Differential scanning calorimetry Determinati .NET 3 of 9 barcode on of CP by differentiating an experimental curve introduces an uncertainty greater than the uncertainty of the measurements themselves. A differential scanning calorimeter (DSC) measures CP directly.

In this method, a sample and a reference material are slowly heated simultaneously with separate heating elements (Figure 5.9). Care is taken to keep the temperature of each sample exactly the same, but because the samples are of different materials, the power delivered to each heater is different, and the difference is a direct function of the difference in the heat capacity of the two materials.

Knowing the CP of the reference material, the CP of the sample may be determined. See H hne et al. (1996) for an overview of the many different variations of differential scanning calorimetry.

Results for the CP of muscovite from DSC measurements (Krupka et al., 1979) are compared to CP calculated from the Maier Kelley coefficients of Pankratz (1964) in Figure 5.10.

The slight difference may be due to the fact. Figure 5.9 Schematic cross-section of a power compensated differential scanning calorimeter (modi ed from Robie (1987)). R reference; S sample.

Under each sample pan is a platinum resistance thermometer and a platinum heater. The large metal block helps to keep the temperatures in the two chambers equal..

5.6 Data at higher temperatures Muscovite Krupka et al, 1979. 480 460. Pankratz, 1964. Figure 5.10 The heat capacity of muscovite, determined from drop calorimetry and from differential scanning calorimetry..

C P , J mol 1 K 1 440 420 400 380 360 400 500 600 700 Temperature, K 800 900 that the DS VS .NET USS Code 39 C measurements were corrected for the deviation of the sample composition from the stoichiometric formulas KAl2 AlSi3 O10 OH 2 , whereas the Pankratz measurements were not. The line through the data points of Krupka et al.

was calculated using equation (3.28), with the muscovite coefficients from Berman and Brown (1985)..

5.6.3 Entropies above 298 K For tempera USS Code 39 for .NET tures above 298 K, entropies can be calculated by combining STr and the HT HTr measurements previously described. Since we know STr , all we need are values of ST STr , which equals HT HTr /T .

Thus. d ST STr = dST (because STr is constant) =d HT HTr T T Tr dS = HT HTr T The right-hand side is integrated by parts, giving ST STr = HT HTr T + T Tr HT HTr T2 Getting data Since HT Code 39 Extended for .NET HTr and therefore HT HTr /T 2 is known as a function of T , the integral can be evaluated, and ST values calculated for elevated temperatures. As in the case of H values, an alternative and usually preferable method is to calculate ST values, or more likely r S values, at elevated temperatures by means of the Maier Kelley heat capacity coefficients.

In other words, since. d S dT = CP T then d dT r CP where r S r efers to the entropy change of a balanced chemical reaction. Integrating,. T Tr r CP (5.21). Combining this with the Maier Kelley equation CP = a + bT cT 2 (5.22). we have r ST r STr T Tr rb rc dT T3 r ST r STr T Tr T Tr + 1 1 T 2 Tr 2 (5.23). In this equ ation r ST refers to the entropy change of any balanced chemical reaction at temperature T . If the reaction is the formation of a compound from its elements, r ST becomes f ST . The apparent entropy of formation can be calculated from.

a ST f STr T Tr CP dT T where CP /T refers to the compound only. 5.6.4 Gibbs energies above 298 K Standard Gibbs energies of formation from the elements at 298 K are computed from f GTr f H Tr Tr f STr (5.24). 5.6 Data at higher temperatures and at higher temperatures from f GT f HT f ST Using the h eat capacity approach, for apparent Gibbs energies at higher temperatures for a compound i. a GT i = = = =. f GTr i + f GTr i + f GTr i + T Tr T Tr T Tr Gi / T dT Si dT STr i T Tr T Tr (5.25). CP i dT dT T T T Tr f GTr i STr i CP i dT dT T The integration in the last term is performed by parts. That is u dv = uv v du where T Tr CP i dT T This results in a GT i f GTr i STr i T Tr + T Tr CP i dT T T Tr CP i dT T (5.26). which, after substitution of T Tr CP dT = a T Tr + 1 b 2 1 T Tr2 + c 2 T Tr (5.27). T Tr CP T dT = a ln T Tr + b T Tr + 1 1 T 2 Tr2 (5.28). and collection of terms, results in a GT i f GTr i STr i T Tr T Tr (5.29). + ai T Tr T ln + + bi 2T Tr T 2 Tr 2 2 ci T 2 + Tr2 2T Tr 2TTr2 Getting data For a miner .net vs 2010 39 barcode al reaction, r G is obtained by substituting r STr for STr i and r a, r b, and r c for ai , bi , and ci , where r a, etc. are the usual product reactant terms.

Thus.
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