Calorimetric Approximations

Although Fleischmann preferred to use the full calorimetric equation [Equation (13.2)] in order to measure the excess power as accurately as possible, he also provided useful approximations that greatly simplify the mathematics. A lower bound heat transfer coefficient, k n or k c, should first be calculated by assuming Px = 0. For the Dewar calorimeter with heat transfer mainly by radiation, Equation (13.2) becomes 

Similarly, for a calorimeter with heat transfer mainly by conduction 

---

Further to our preliminary studies at 225°C subsequent wet oxidation experiments have been carried out at temperatures of 250 and 285°C. Partial pressures of oxygen were varied from 19 to 289 kPa whilst the partial pressure of water vapor in the calorimetric system was maintained at approximately 15 kPa. 

It is found that the rate of burning increases approximately linearly with the calorimetric value and lies in the range 0-4—1-3 cm s I at 7 MPa, although higher rates can be achieved. 

Calvet and Persoz (29) have discussed at length the question of the sensitivity of the Calvet calorimeter in terms of the number of thermocouples used, the cross section and the length of the wires, and the thermoelectric power of the couples. On the basis of this analysis, the micro-calorimetric elements are designed to operate near maximum sensitivity. The present-day version of a Tian-Calvet microcalorimetric element, which has been presented in Fig. 2, contains approximately 500 chromel-to-constantan thermocouples. The microcalorimeter, now commercially available, in which two of these elements are placed (Fig. 3) may be used from room temperature up to 200°C. 

The calculation of the enthalpy of formation of a given compound depends on the determination of the enthalpy of at least one reaction of this substance. Frequently, it is desirable to estimate the enthalpy of a chemical reaction involving a hitherto unsynthesized compound, or one that has been synthesized but has not been characterized calorimetrically. For the solution of problems of this type, a system of average bond enthalpies has been established such that, if the molecular structure of the compound is known, it is possible to approximate the enthalpy of formation by adding the appropriate average bond enthalpies. 

Among the purposes of this paper is to report the results of calorimetric measurements of the heats of micellar mixing in some nonideal surfactant systems. Here, attention is focused on interactions of alkyl ethoxylate nonionics with alkyl sulfate and alkyl ethoxylate sulfate surfactants. The use of calorimetry as an alternative technique for the determination of the cmc s of mixed surfactant systems is also demonstrated. Besides providing a direct measurement of the effect of the surfactant structure on the heats of micellar mixing, calorimetric results can also be compared with nonideal mixing theory. This allows the appropriateness of the regular solution approximation used in models of mixed micellization to be assessed. 

If a calorimetric bomb is not available and if the products of explosion are not determined by analysis, the heats of explosion can be approximately estimated from the equation of explosion... 

Seki and Tirrell [436] studied the pH-dependent complexation of poly(acrylic acid) derivatives with phospholipid vesicle membranes. These authors found that polyfacrylic acid), poly(methacrylic arid) and poly(ethacrylic acid) modify the properties of a phospholipid vesicle membrane. At or below a critical pH the polymers complex with the membrane, resulting in broadening of the melting transition. The value of the critical pH depends on the chemical structure and tacticity of the polymer and increases with polymer hydro-phobicity from approximately 4.6 for poly(acrylic acid) to approximately 8 for poly(ethacrylic acid). Subsequent photophysical and calorimetric experiments [437] and kinetic studies [398] support the hypothesis that these transitions are caused by pH dependent adsorption of hydrophobic polymeric carboxylic acids... 

If ruby s (C02/CO) ratios come near to being correct, Arbitrary 1 (Table I) approximates the detonation condition for high-density explosives at the C-J point while, from the correspondence with usual types of calorimetric measurements,5 it is likely that Arbitrary 2 represents a condition after the gases have expanded to several (possibly 2-20) charge diameters. Arbitrary 3 might correspond to a situation much farther down the isentrope. 

DEP, and DOP etc. have high negative calorimetric values or heats of combustion (-6280 to -840 Jg-1) whereas BDNPA/F have high positive calorimetric values approximately +2930 Jg-1. 

Calorimetric measurements permit the determination of (AH ), the value of AH averaged over the helix-coil transition region (19-21). An approximate... 

It has been shown that the two-phase pressure variation for palladium-hydrogen yields values of ASa— and AHa—/ , and that these values are closely temperature independent. The temperature independence results because the value of the integral in Equation 21 can be approximated closely by the corresponding relative partial value at the critical composition. Variations of ASg o and AHh—o with temperature (see Figure 6) are apparently too small to be detected in the plot of In /22(two-phase) against T ly but can be detected by the more sensitive plot of RT In P /2 against T or possibly could be detected by calorimetric determinations of AHa—over a wide temperature range. 

---