Heat capacity, mixture

The two steady-state heat-transfer coefficients, hr and hj, could be further described in terms of the physical properties of the system. The solution-to-wall coefficient for heat transfer, hT in Equation 8.8, is strongly dependent on the physical properties of the reaction mixture (heat capacity, density, viscosity and thermal conductivity) as well as on the fluid dynamics inside the reactor. Similarly, the wall-to-jacket coefficient for heat transfer, hj, depends on the properties and on the fluid dynamics of the chosen cooling liquid. Thus, U generally varies during measurements on a chemical reaction mainly for the following two reasons. 

Process simulation software can also be used to help build simple energy balances in spreadsheet models, for example, by entering stream data to calculate mixture heat capacities, to calculate stream enthalpies, or to estimate heats of reaction. 

Assuming constant thermodynamic properties, determine the length of a 2-in inner-diameter (ID) tubular reactor that operates adiabatically and provides 93% conversion of B. The heat of reaction is AHr -48,000 Btu/lbmo and the mixture heat capacity is Cp = 110 Btu/lbmo °R. 

Table 6.6 Parameter values for Example 6.6 heat of reaction and mixture heat capacity assumed constant.

The mixture enthalpy H and the mixture heat capacity Cp are calculated as ... 

The enthalpy of a vapor mixture is obtained first, from zero-pressure heat capacities of the pure components and second, from corrections for the effects of mixing and pressure. 

This chapter presents quantitative methods for calculation of enthalpies of vapor-phase and liquid-phase mixtures. These methods rely primarily on pure-component data, in particular ideal-vapor heat capacities and vapor-pressure data, both as functions of temperature. Vapor-phase corrections for nonideality are usually relatively small. Liquid-phase excess enthalpies are also usually not important. As indicated in Chapter 4, for mixtures containing noncondensable components, we restrict attention to liquid solutions which are dilute with respect to all noncondensable components. 

Sengers and coworkers (1999) have made calculations for the coexistence curve and the heat capacity of the real fluid SF and the real mixture 3-methylpentane + nitroethane and the agreement with experiment is excellent their comparison for the mixture [28] is shown in figure A2.5.28. 

Figure A2.5.28. The coexistence curve and the heat capacity of the binary mixture 3-methylpentane + nitroethane. The circles are the experimental points, and the lines are calculated from the two-tenn crossover model. Reproduced from [28], 2000 Supercritical Fluids—Fundamentals and Applications ed E Kiran, P G Debenedetti and C J Peters (Dordrecht Kluwer) Anisimov M A and Sengers J V Critical and crossover phenomena in fluids and fluid mixtures, p 16, figure 3, by kind pemiission from Kluwer Academic Publishers.

Solution calorimetry covers the measurement of the energy changes that occur when a compound or a mixture (solid, liquid or gas) is mixed, dissolved or adsorbed in a solvent or a solution. In addition it includes the measurement of the heat capacity of the resultant solution. Solution calorimeters are usually subdivided by the method in which the components are mixed, namely, batch, titration and flow. 

Fig. 12. Correlatioa of AT. The three lines represeat the best fit of a mathematical expressioa obtaiaed by multidimensional nonlinear regressioa techniques for 99, 95, and 90% recovery the poiats are for 99% recovery. = mean molar heat capacity of Hquid mixture, average over tower AY = VA2 slope of equiHbrium line for solute, to be taken at Hquid feed temperature mg = slope of equilibrium line for solvent.

Fig. 3. Temperature—enthalpy representation of stream where A represents a pure component that is condensiag, eg, steam B and C represent streams having constant heat capacity, that are to be heated or cooled, respectively and D represents a multicomponent mixture that changes phase as it is...

Vinyl acetate is a colorless, flammable Hquid having an initially pleasant odor which quickly becomes sharp and irritating. Table 1 Hsts the physical properties of the monomer. Information on properties, safety, and handling of vinyl acetate has been pubUshed (5—9). The vapor pressure, heat of vaporization, vapor heat capacity, Hquid heat capacity, Hquid density, vapor viscosity, Hquid viscosity, surface tension, vapor thermal conductivity, and Hquid thermal conductivity profile over temperature ranges have also been pubHshed (10). Table 2 (11) Hsts the solubiHty information for vinyl acetate. Unlike monomers such as styrene, vinyl acetate has a significant level of solubiHty in water which contributes to unique polymerization behavior. Vinyl acetate forms azeotropic mixtures (Table 3) (12). 

The ideal-gas-state heat capacity Cf is a function of T but not of T. For a mixture, the heat capacity is simply the molar average X, Xi Cf. Empirical equations giving the temperature dependence of Cf are available for many pure gases, often taking the form... 

When the mixture can be characterized by an overall heat capacity,... 

The heat capacity of gases is essential for some process engineering design involving gas-phase chemical reactions. Here, tlie heat capacities, Cp, for gases are required to determine the heat necessary to bring the chemical compound increase to the reaction temperature. The heat capacity of a mixture of gases may he found from the heat capacities of the individual components contained in the mixtures. 

Assuming the density of the mixture is constant, then p = m/Vj, and with Cp taken as the average heat capacity of the reacting mixture. Equation 6-64 becomes... 

A wide variety of physical properties are important in the evaluation of ionic liquids (ILs) for potential use in industrial processes. These include pure component properties such as density, isothermal compressibility, volume expansivity, viscosity, heat capacity, and thermal conductivity. However, a wide variety of mixture properties are also important, the most vital of these being the phase behavior of ionic liquids with other compounds. Knowledge of the phase behavior of ionic liquids with gases, liquids, and solids is necessary to assess the feasibility of their use for reactions, separations, and materials processing. Even from the limited data currently available, it is clear that the cation, the substituents on the cation, and the anion can be chosen to enhance or suppress the solubility of ionic liquids in other compounds and the solubility of other compounds in the ionic liquids. For instance, an increase in allcyl chain length decreases the mutual solubility with water, but some anions ([BFJ , for example) can increase mutual solubility with water (compared to [PFg] , for instance) [1-3]. While many mixture properties and many types of phase behavior are important, we focus here on the solubility of gases in room temperature IFs. 

Specific Heats of Solid Mixtures.—The specific heat of a homogeneous solid mixture of solid components is not usually additively composed of the specific heats of the latter. W. Spring (1886) found that the total heat capacity of alloys of lead and tin was always greater than the sum of those of the components, but above the melting-point the two were equal. A. Bogojawlensky and N. Winogradoff (1908) find, however, that the heat capacities of the isomorphous mixtures ... 

Reduced heat capacity to the extent of the partial pressure of the steam-water mixture... 

A reaction mixture is heated in a vessel fitted with an agitator and a steam coil of area 10 m2 fed with steam at 393 K. The heat capacity of the system is equal to that of 500 kg of water. The overall coefficient of heat transfer from the vessel of area 5 m2 is 10 W/m2 K. It takes 1800 s to heat the contents from ambient temperature of 293 to 333 K. How long will it take to heat the system to 363 K and what is the maximum temperature which can be reached ... 

By using the simple Reynolds Analogy, obtain the relation between the heat transfer coefficient and the mass transfer coefficient for the gas phase for the absorption of a soluble component from a mixture of gases. If the heat transfer coefficient is 100 W/m2 K, what will the mass transfer coefficient be for a gas of specific heat capacity Cp of 1.5 kJ/kg K and density 1.5 kg/m- The concentration of the gas is sufficiently low for hulk flow effects to be negligible. 

Figure 1. Typical reactor temperature profile for continuous addition polymerization a plug-flow tubular reactor. Kinetic parameters for the initiator 1 = 10 ppm Ea = 32.921 kcal/mol In = 26.492 In sec f = 0.5. Reactor parameter [(4hT r)/ (DpCp)] = 5148.2. [(Cp) = heat capacity of the reaction mixture (p) = density of the reaction mixture (h) = overall heat-transfer coefficient (Tf) = reactor jacket temperature (r) = reactor residence time (D) = reactor diameter].

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