Total enthalpy method

The crystallinty of composites were calculated with the total enthalpy method [see eq. (1)] in all calculations, the heats of fusion at equilibrium melting temperature were 209 and 293 Jg"i, for PP and LDPE crystals, respectively (Brandrup Imergut, 2003)... 

In order to examine the effect of outdoor exposure on crystallinity of EVA, the degree of crystallinity was calculated via the total enthalpy method [20] according to Eq. (8) ... 

The first of these is now often referred to as the total enthalpy method (24,25). In one version, the crystallinty is determined as follows (25). At a temperature Ti below where melting begins, the total heat capacity can be written simply as... 

A calorimetric determination of crystallinity can be made by measurement of the heat of fusion using differential scanning calorimetry (DSC). The conversion from heat of fusion to mass crystallinity may be conducted by the total enthalpy method, which is illustrated in Fig. 7.42. It is assumed that only two components exist, and that each of them has a certain... 

The total enthalpy method yields crystallinity values in agreement with X-ray and density estimates. Significant deviation was found by Mandelkem (1965) for very high molar mass samples of linear polyethylene. The differences were attributed to the presence of a third, intermediate phase, with mobility in between that of the crystalline and the amorphous components. A problematic case is samples with low thermal stability. Polyvinylchloride is one example. An additional problem with this polymer is also its low crystallinity (5-10%). 

Figure 10.19 Schematic diagram of the DSC melting trace. Application of the total enthalpy method.

Results of the enthalpy balance for this test show that the method of calculation cannot account for 1.5% of the total enthalpy input. This difference is small and may arise from the accuracy of the individual measurements and by the approximation used to calculate some of the quantities, as described above. A preliminary error analysis indicates an uncertainty of +3.356 for the heat balance calculation. The two methods for calculating the efficiency will agree only if the heat balance closes exactly. In general, when the... 

This Stanton number is then used in Eq. (5-125), (5-126), or (5-127) to calculate the heat-transfer coefficient. When calculating the enthalpies for use in the above relations, the total enthalpy must be used i.e., chemical energy of dissociation as well as internal thermal energy must be included. The reference-enthalpy method has proved successful for calculating high-speed heat transfer with an accuracy of better than 10 percent. 

Replacing H-bonds by D-bonds has no effect on the electronic structure of H-bonds when nuclei are held at fixed positions. It nevertheless has a small, indirect effect on thermodynamic properties, because quantities such as enthalpies of formation of H- or D-bonds not only depend on their electronic structure, but also incorporate a significant vibrational component that is sensitive to this substitution. The result is a difference of enthalpies of formation of H- and D-bonds that amounts to only some percent of the total enthalpy of formation and remains consequently weak with respect to kT at room temperature for weak and intermediate strength H-bonds. It means that at room temperature this difference is not really apparent. Such a substitution consequently conveys almost no information for calorimetric methods. The geometry of the H-bond is also little affected by such a substitution that results in a small lengthening of the X- Y equilibrium distance in X-D- Y as compared to X-H---Y. It is an indirect, or second-order consequence of the strong and characteristic anharmonic modulation of the stretching vibration of the H-atom by the X- Y distance. It implies a weak effect with little information. 

Srinivasa and Edwards [215] analyzed the gaseous phase over InTe(l) by the isothermal total exhaustion method. They determined the enthalpy change... 

There are several ways of converting H29% to Af//29g and subsequently to Ahyd//298. The atomization method is illustrated in Fig. 3.9, which shows a thermochemical cycle for determination of Af//29g of a hydrocarbon. The top horizontal line represents the thermodynamic state of nuclei and electrons, the bottom horizontal line represents elements in their standard states and the verticals, of which there are six, represent enthalpy changes. Each of the three total enthalpy changes in the top half of the figure H29i represents a fall from the top state to the state of... 

Thus the integral is verihed to agree with the total enthalpy calculation. Although only is used in the integral method of calculation, information about Hp and the molar of the mixture are implied in and can be explicitly revealed by integrating to yield and subsequently adding the two partials to obtain the molar of the mixture. 

The change in state of a system produced by a specified chemical reaction is definite. The corresponding enthalpy change is definite, since the enthalpy is a function of the state. Thus, if we transform a specified set of reactants to a specified set of products by more than one sequence of reactions, the total enthalpy change must be the same for every sequence. This rule, which is a consequence of the first law of thermodynamics, was originally known as Hess s law of constant heat summation. Suppose that we compare two different methods of synthesizing sodium chloride from sodium and chlorine. 

The Eldridge-Ferry method [2] gives the total enthalpy melting A//o of a junction by Anding the slope of Inc against /T through therelaAon... 

The method has been applied to absorbers (Khoury, 1980), where all heat duties, side draws, and all feeds except the liquid feed at the top of the column and the vapor feed at the bottom are set to zero. The rates of change of the component molar holdup and total enthalpy on a stage may be broken down into liquid and vapor contributions (subscripts j and i are dropped in the rates of change terms for simplicity) ... 

In general, the accuracy of enthalpy of fusion from vapor pressttre measrrrements depends on the accuracy of the vapor presstrre measrrrement from which it is determined and on the acctrracy of heat capacities of the compoimd in the gas, liquid, and sohd phases. The accuracy of enthalpy of fusion from vapor pressure is at least 5 percent and upto 50 percent, according to our analysis of the data collected in this book. In addition, the vapor pressure method can not separate the enthalpies of a sohd transition from that of fusion if the temperatures of the transition and fusion are close. For example, the enthalpies of fusion for the long-chain alcohols determined from vapor pressure by Davies and Kybett [65-dav/kyb] are actually the total enthalpies of fusion and transition for these compounds. 

Various thermometric assessments have been in the center of retailored techniques used to detect a wide variety of heat effects and properties. The traditional operation aims to measure, for example, heat capacities, total enthalpy changes, transitions and phase change heats, heats of adsorption, solution, mixing, and chemical reactions. The measured data can be used in a variety of clever ways to determine other quantities. Special role was executed by methods associated with enough adequate temperature measurements, which reveals an extensive history coming back to the first use of the word calorimeter introduced by the work Wilcke and later used by Laplace, Lavoisier as already discussed in the previous Chapter 4. 

The calculation of the thermal conductivity of gas hydrate using EMD and the Green-Kubo linear response theory was repeated recently. In that work, convergences of the relevant quantities were monitored carefully as a function of the model size. Subtleties in the numerical procedures were also carefully considered. The thermal conductivity of methane hydrate was found to converge within numerical accuracy for 3 x 3 x 3 and 4x4x4 supercells. In the calculation of the heat flux vector there is an interactive term that is a pairwise summation over the forces exerted by atomic sites on one another. The species (i.e., water and methane) enthalpy correction term requires that the total enthalpy of the system is decomposed into contributions from each species. Because of the partial transformation from pairwise, real-space treatment to a reciprocal space form in Ewald electrostatics, it is necessary to recast the diffusive and interactive terms in this expression in a form amenable for use with the Ewald method using the formulation of Petravic. ... 

The physical meanings of many thermodynamic parameters such as specific heat, enthalpy, entropy, and the Gibbs function were discussed, and several methods for determining their values for nonreacting and reacting liquid- and gas-phase mixtures were discussed. The heat of formation, sensible enthalpy, and latent heat of phase change make up the total enthalpy of a substance at a given temperature ... 

After you choose the computation method and options, you can use Start Log on the File menu to record results, such as total energies, orbital energies, dipole moments, atomic charges, enthalpies of formation (for the CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/I, and ZINDO/S methods), etc. 

The simplest method to measure gas solubilities is what we will call the stoichiometric technique. It can be done either at constant pressure or with a constant volume of gas. For the constant pressure technique, a given mass of IL is brought into contact with the gas at a fixed pressure. The liquid is stirred vigorously to enhance mass transfer and to allow approach to equilibrium. The total volume of gas delivered to the system (minus the vapor space) is used to determine the solubility. If the experiments are performed at pressures sufficiently high that the ideal gas law does not apply, then accurate equations of state can be employed to convert the volume of gas into moles. For the constant volume technique, a loiown volume of gas is brought into contact with the stirred ionic liquid sample. Once equilibrium is reached, the pressure is noted, and the solubility is determined as before. The effect of temperature (and thus enthalpies and entropies) can be determined by repetition of the experiment at multiple temperatures. 

Molecular mechanics (also known diS force-field calculations) is a method for the calculation of conformational geometries. It is used to calculate bond angles and distances, as well as total potential energies, for each conformation of a molecule. Steric enthalpy can be calculated as well. Molecular orbital calculations (p. 34) can also give such information, but molecular mechanics is generally easier, cheaper (requires less computer time), and/or more accurate. In MO calculations, positions of the nuclei of the atoms are assumed, and the wave equations take account only of... 

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