Relative partial heat capacity

Differentiation of equation (7.65) with respect to temperature gives an equation for Ji, the relative partial molar heat capacity, given by... 

The difference Cp. -C°pi is the relative partial molar heat capacity Jt. Thus... 

We now show that equations analogous to Eq. (34) follow for the enthalpy and entropy of mixing, AHM and ASM, but that, in contrast to the chemical potentials, the partial molar enthalpies and entropies for the components differ from those for the species. Finally we show that the equation for the constant pressure relative heat capacity is of a slightly more complicated form than Eq. (34). Equation (34) and its analogs for and ASM are necessary for comparison of model predicted quantities with experiment. From basic thermodynamic equations we have... 

This, of course, is the difference between the heat capacity of the solution and the sum of those of the unmixed liquid elements. Using Eq. (38) and defining relative partial molar heat capacities of the components as... 

The values of (H2 — Hj ) for rounded molalities at 298.15° K were obtained from the plots of (H2 — H >) against ra1/2. The smooth curve was drawn through all the experimental points the average deviation from the smoothed curve was 15 calth mol-1 for 50 mass percent monoglyme. These values are presented in Table XIV and are higher than those found for hydrochloric acid in the same mixed solvents (1). The values of (H2 — H%) in aqueous medium at 298.15° K are given for direct comparison. The relative partial molal heat capacity (Cp — Cp) was calculated by the following formula ... 

Table XIV. Relative Partial Molal Enthalpy (//2 — H°) and Relative Partial Molal Heat Capacity (Cp — Cp°) of HBr in 50 Mass Percent Aqueous Monoglyme and in Water at 298.15°K (cal = 4.184/)...

Figure 17.5 Derived thermodynamic properties at T — 298.15 K and p = 0.1 MPa for (2Cic-CfiHi2 + X2n-CjHi4) (a) excess molar heat capacities obtained from the excess molar enthalpies (b) relative partial molar heat capacities obtained from the excess molar heat capacities (c) change of the excess molar volume with temperature obtained from the excess molar volumes and (d) change of the excess molar enthalpies with pressure obtained from the excess molar volumes.

Cp m of -1.4 J K-1 - mol-1 is again of moderate size. Figure 17.5b summarizes the relative partial molar heat capacity Jt = (CA m,- C t m,We note that the molar heat capacity of hexane in the infinitely dilute solution is 7.4 J-K 1 - mol-1 less than the molar heat capacity of pure hexane. 

The relative partial molar enthalpy and relative partial molar heat capacity are obtained from8... 

The relative partial molar heat contents (Li) in cal. mole and the relative, partial molar heat capacities ( pi — Cpi) in cal. deg. mole, of the water in hydrochloric acid solutions are as follows ... 

IR. Relative Partial Molar Heat Contents.—The partial molar thermal properties, namely, heat content and heat capacity, are of particular interest, as well as of practical importance, as will be seen from some of the examples to be given below. In accordance with the general definition ( 26a), the partial molar heat content of any constituent of a solution is represented by... 

The results obtained at 445 K and 525 K were recalculated to 298.15 K using the second and third laws and the heat capacities and entropies selected by this review. For the third law evaluation, relative ion intensities were taken from Figure 3 of the paper and combined with the total pressures reported by Niwa and Shibata [40NIW/SHI] for the lower and by Yamdagni and Porter [68YAM/POR] for the higher temperature range. A third law evaluation for Se2(g) and Seg(g) could not be made because of the lack of partial pressure data. 

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