Specific heat pure component

The change in enthalpy with respect to temperature is not neghgible. It can be calculated for a pure component using the specific heat correlations like those in Table 7.1 ... 

The heat of fusion AHf (obtained from the area under the DSC melting curve) and percentage crystallinity calculated from AHf is found to be linearly dependent on butadiene content, and independent of the polymer architecture. This is shown in Figure 3. Also, the density of the block copolymers was found to be linearly dependent on butadiene content (see Figure 4). The linear additivity of density (specific volume) has been observed by other workers for incompatible block copolymers of styrene and butadiene indicating that very little change in density from that of pure components has occurred on forming the block copolymers.(32) While the above statement is somewhat plausible, these workers have utilized the small positive deviation from the linear additivity law to estimate the thickness of the boundary in SB block copolymers.(32)... 

When these reactants (both originally at the same temperature) are mixed, the temperature of the mixed solution is observed to increase. Thus the chemical reaction must be releasing energy as heat. This increases the random motions of the solution components, which in turn increases the temperature. The quantity of energy released can be determined from the temperature increase, the mass of the solution, and the specific heat capacity of the solution. For an approximate result we will assume that the calorimeter does not absorb or leak any heat and that the solution can be treated as if it were pure water with a density of 1.0 g/mL. 

An ideal mixture is one for which the heat of mixing or solution is negligible and so Hmixture 21 where n, is the amount of mixture component i and D, is the specific enthalpy of the pure component at the temperature and pressure of the mixture. Up to now in this text, we have assumed ideal mixture behavior for all mixtures and solutions. This assumption works well for nearly all gas mixtures and for liquid mixtures of similar compounds (such as mixtures of paraffins or of aromatics), but for other mixtures and solutions—such as aqueous solutions of strong acids or bases or certain gases (such as hydrogen chloride) or solids (such as sodium hydroxide)—heats of solution should be included in energy balance calculations. This section outlines the required procedures. 

The specific heats of liquid mixtures can be estimated, with sufficient accuracy for most technical calculations, by taking heat capacities as the mass (or mole) weighted sum of the pure component heat capacities. 

If both the substances have the same specific heat capacities, the term for mass transfer drops out of the equation. However in all other cases it does not assume a negligible value. In particular for substances such as water vapour and air, the specific heat capacities are so different that the mass transfer term cannot be removed. In addition it should be recognised that the energy equation agrees with that for pure substances when the specific heat capacities of the two components are equal and when no chemical reactions occur. 

Chemical reactions will not play any role in this discussion. The considerations here will be restricted to pure substances or binary mixtures which have components of approximately the same specific heat capacity. The energy equation (3.119) then agrees with that for pure substances (3.117). After introduction of the dimensionless quantities the continuity equation is... 

HUMIDITY CHARTS FOR SYSTEMS OTHER THAN AIR-WATER. A humidity chart may be constructed for any system at any desired total pressure. The data required are the vapor pressure and latent heat of vaporization of the condensable component as a function of temperature, the specific heats of pure gas and vapor, and the molecular weights of both components. If a chart on a mole basis is desired, all equations can easily be modified to the use of molal units. If a chart at a pressure other than 1 atm is wanted, obvious modificatioi in the above equations may be made. Charts for several common systems besides air-water have been published. ... 

The model based on the concept of pure limiting film resistance involves the steady-state concept of the heat transfer process and omits the essential unsteady nature of the heat transfer phenomena observed in many gas-solid suspension systems. The film model discounts the effects of thermophysical properties such as the specific heat of solids and hence would not be able to predict the particle convective component of heat transfer. For estimating the contribution of the particle convective component of heat transfer, the emulsion phase/packet model given in a subsequent section should be used to describe the temperature gradient from the heating surface to the bed. 

Thermal Properties of Nitration Acids. Heals of Solution. To determine the heat evolved during the actual process of nitration of a hydrocarbon by mixed acids, it is necessary to consider not only the heat of nitration but also various heats of solution. These may be obtained from the enthalpy chart developed by McKinley and Brown (Fig. 4-5). For each of the three components, the enthalpy is taken as zero at the standard state, consisting of the pure liquid component at a temperature of 32 F and a pressure of 1 atm. Plotted against the same abscissa but against different ordinates are the specific heat data for the system. From this figure, containing both 32 F relative enthalpies and specific heats, the enthalpy of any liquid mixtures of these components at ordinary temperatures can be readily calculated by reading the desired relative enthalpy at 32 F and the specific heat from the chart. 

In general, mole fractions are not linear functions of conversion because the total number of moles and the total molar flow rate are not constant when 5 = Vi 7 0. For this particular problem, 5 = —2. In summary, the easiest approach to performing a weighted average of heat capacities of all components in the mixture is to use a mass-fraction-weighted sum of the temperature-averaged specific heat of each pure component. Hence,... 

In practice, pure-component molar enthalpies are employed to approximate A/7rx. This approximation is exact for ideal solutions only, when partial molar properties reduce to pure-component molar properties. In general, one accounts for more than the making and breaking of chemical bonds in (3-35). Nonidealities such as heats of solution and ionic interactions are also accounted for when partial molar enthalpies are employed. Now, the first law of thermodynamics for open systems, which contains the total differential of specific enthalpy, is written in a form that allows one to calculate temperature profiles in a tubular reactor ... 

The heat of crystallization is the heat that has to be supplied or removed during crystallization at constant temperature. It is equal to the negative value of the heat of solution during the dissolution of crystals in an almost saturated solution. The heat of crystallization is accounted for in the enthalpy values. Processes in crystallizers can easily be tracked, if an enthalpy concentration diagram is available for the respective system. The pure component s enthalpy is zero at reference temperature, not the enthalpy of real mixtures however. In such diagrams, the lever rule is applicable. This is shown for the system calcium chloride/water in Fig. 8.3-5, where the specific enthalpy is plotted vs. the mass fractions. 

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