Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Heat capacity discussion

Furthermore, this type of simulation provides a convenient route to the calculation of key quantities such as the entropies and heat capacities discussed throughout this book. Since S = -(dAJdT)v, and Cy = (dU/dT)v it follows that... [Pg.349]

The melting point of Ta is chosen as 3258 10 K based on the subsecond pulse heating technique of Cezairliyan (X). This choice is made so as to have a T consistent with Cp data at temperatures near T (see heat capacity discussion). Other T values covering the range 3053-3273 K are referenced by Charlesworth (9) while additional references are found in Gmelin (8). Hultgren et al. (1 ) recommends a T value of 3287 K. [Pg.1812]

Enthalpies are referred to the ideal vapor. The enthalpy of the real vapor is found from zero-pressure heat capacities and from the virial equation of state for non-associated species or, for vapors containing highly dimerized vapors (e.g. organic acids), from the chemical theory of vapor imperfections, as discussed in Chapter 3. For pure components, liquid-phase enthalpies (relative to the ideal vapor) are found from differentiation of the zero-pressure standard-state fugacities these, in turn, are determined from vapor-pressure data, from vapor-phase corrections and liquid-phase densities. If good experimental data are used to determine the standard-state fugacity, the derivative gives enthalpies of liquids to nearly the same precision as that obtained with calorimetric data, and provides reliable heats of vaporization. [Pg.82]

Heat carriers. If adiabatic operation produces an unacceptable rise or fall in temperature, then the option discussed in Chap. 2 is to introduce a heat carrier. The operation is still adiabatic, but an inert material is introduced with the reactor feed as a heat carrier. The heat integration characteristics are as before. The reactor feed is a cold stream and the reactor efiluent a hot stream. The heat carrier serves to increase the heat capacity fiow rate of both streams. [Pg.325]

Brunauer and co-workers [129, 130] found values of of 1310, 1180, and 386 ergs/cm for CaO, Ca(OH)2 and tobermorite (a calcium silicate hydrate). Jura and Garland [131] reported a value of 1040 ergs/cm for magnesium oxide. Patterson and coworkers [132] used fractionated sodium chloride particles prepared by a volatilization method to find that the surface contribution to the low-temperature heat capacity varied approximately in proportion to the area determined by gas adsorption. Questions of equilibrium arise in these and adsorption studies on finely divided surfaces as discussed in Section X-3. [Pg.280]

Although the previous paragraphs hint at the serious failure of the van der Waals equation to fit the shape of the coexistence curve or the heat capacity, failures to be discussed explicitly in later sections, it is important to recognize that many of tlie other predictions of analytic theories are reasonably accurate. For example, analytic equations of state, even ones as approximate as that of van der Waals, yield reasonable values (or at least ball park estmiates ) of the critical constants p, T, and V. Moreover, in two-component systems... [Pg.622]

Physical Properties. Sulfur dioxide [7446-09-5] SO2, is a colorless gas with a characteristic pungent, choking odor. Its physical and thermodynamic properties ate Hsted in Table 8. Heat capacity, vapor pressure, heat of vaporization, density, surface tension, viscosity, thermal conductivity, heat of formation, and free energy of formation as functions of temperature ate available (213), as is a detailed discussion of the sulfur dioxide—water system (215). [Pg.143]

These heat capacity approximations take no account of the quantal nature of atomic vibrations as discussed by Einstein and Debye. The Debye equation proposed a relationship for the heat capacity, the temperature dependence of which is related to a characteristic temperature, Oy, by a universal expression by making a simplified approximation to the vibrational spectimii of die... [Pg.164]

The STM postulated tunneling matrix element distribution P(A) oc 1 /A implies a weakly (logarithmically) time-dependent heat capacity. This was pointed out early on by Anderson et al. [8], while the first specific estimate appeared soon afterwards [93]. The heat capacity did indeed turn out time dependent however, its experimental measures are indirect, and so a detailed comparison with theory is difficult. Reviews on the subject can be found in Nittke et al. [99] and Pohl [95]. Here we discuss the A distribution dictated by the present theory, in the semiclassical limit, and evaluate the resulting time dependence of the specific heat. While this limit is adequate at long times, quantum effects are important at short times (this concerns the heat condictivity as well). The latter are discussed in Section VA. [Pg.138]

As is clear from the previous discussion, the long-time power law behavior of the heat capacity is determined by the slow two-level systems corresponding to the higher barrier end of the tunneling amplitude distribution, argued to be of the form shown in Eq. (24). If one assumes that this distribution is valid for the... [Pg.141]

Section V, other quantum effects are indeed present in the theory and we will discuss how these contribute both to the deviation of the conductivity from the law and to the way the heat capacity differs from the strict linear dependence, both contributions being in the direction observed in experiment. Finally, when there is significant time dependence of cy, the kinematics of the thermal conductivity experiments are more complex and in need of attention. When the time-dependent effects are included, both phonons and two-level systems should ideally be treated by coupled kinetic equations. Such kinetic analysis, in the context of the time-dependent heat capacity, has been conducted before by other workers [102]. [Pg.142]

To complete the discussion of the second-order interaction between tunneling centers, we note that the corresponding contribution to the heat capacity in the leading low T term comes from the ripplon-TLS term and scales as 7 +2 where a is the anomalous exponent of the specific law. Within the approximation adopted in this section, a = 0. However, it is easily seen that the magnitude of the interaction-induced specific heat is down from the two-level system value by a factor of 10(a/ ) ([Pg.188]

We have already discussed diffusion in solids to some degree. While bulk properties such as heat capacity are not sensitive to defect concentration, many other properties such as conductivity are. Thus, the method of preparation becomes important if one wishes to obtain a conductive or... [Pg.303]

The dependence of gas specific heats on temperature was discussed in Chapter 3, Section 3.5. For a gas in the ideal state the specific heat capacity at constant pressure is given by ... [Pg.325]

Others, like energetic and exergetic efficiency are discussed in Dincer et al. (2002). Basically we can distinguish between two kinds of heat transfer fluids with different ranges of heat capacities and heat transfer coefficients ... [Pg.294]

For reversible exothermic reactions, the situation is more complex. Figure 6.5a shows the behavior of an exothermic reaction as a plot of equilibrium conversion against temperature. Again, the plot can be obtained from values of AG° over a range of temperatures and the equilibrium conversion calculated as discussed previously. If it is assumed that the reactor is operated adiabatically, and the mean molar heat capacity of the reactants and products is constant, then for a given starting temperature for the reaction Tin, the temperature of the reaction mixture will be proportional to the reactor conversion X for adiabatic operation, Figure 6.5a. [Pg.105]

The energy involved in chemical reactions is often as important as the chemical products. For example, the fuel used in home furnaces and in automobiles is used solely for their energy content, and not for the chemical products of their combustion. The measurement of energy is discussed in Sec. 18.2, heat capacity is discussed in Sec. 18.3, the energy involved in changes of phase is treated in Sec. 18.4, and the energy involved in physical and chemical processes is taken up in Sec. 18.5. [Pg.270]

As has been the approach for most of the author s other reviews on organic thermochemistry, the current chapter will be primarily devoted to the relatively restricted scope of enthalpy of formation (more commonly and colloquially called heat of formation) and write this quantity as A//f, instead of the increasingly more commonly used and also proper A//f° and AfHm No discussion will be made in this chapter on other thermochemical properties such as Gibbs energy, entropy, heat capacity and excess enthalpy. Additionally (following thermochemical convention), the temperature and pressure are tacitly assumed to be 25 °C ( 298 K ) and 1 atmosphere (taken as either 101,325 or 100,000 Pa) respectively3 and the energy units are chosen to be kJmol-1 instead of kcalmol-1 (where 4.184 kJ = 1 kcal, 1 kJ = 0.2390 kcal). [Pg.69]

Quantitative estimates of E are obtained the same way as for the collision theory, from measurements, or from quantum mechanical calculations, or by comparison with known systems. Quantitative estimates of the A factor require the use of statistical mechanics, the subject that provides the link between thermodynamic properties, such as heat capacities and entropy, and molecular properties (bond lengths, vibrational frequencies, etc.). The transition state theory was originally formulated using statistical mechanics. The following treatment of this advanced subject indicates how such estimates of rate constants are made. For more detailed discussion, see Steinfeld et al. (1989). [Pg.143]

The absolute value of the entropy of a compound is obtained directly by integration of the heat capacity from 0 K. The main contributions to the heat capacity and thus to the entropy are discussed in this chapter. Microscopic descriptions of the heat capacity of solids, liquids and gases range from simple classical approaches to complex lattice dynamical treatments. The relatively simple models that have been around for some time will be described in some detail. These models are, because of their simplicity, very useful for estimating heat capacities and for relating the heat capacity to the physical and chemical... [Pg.229]

Entropies and heat capacities can thus now be calculated using more elaborate models for the vibrational densities of states than the Einstein and Debye models discussed in Chapter 8. We emphasize that the results are only valid in the quasiharmonic approximation and can only be as good as the accuracy of the underlying force-field calculation of such properties can thus be a very sensitive test of interatomic potentials. [Pg.350]

As discussed in Section 2.3.1.2, SEDEX [103,104] and SIKAREX [106] types of apparatus are also used in adiabatic calorimetric techniques. Compensation for the heat capacity of the sample containment is also a feature. Typical sensitivity of this type of equipment is 0.5 W/kg, the sample size is 10 to 30g, and the temperature range is 0 to 300°C. [Pg.69]


See other pages where Heat capacity discussion is mentioned: [Pg.1828]    [Pg.98]    [Pg.1828]    [Pg.98]    [Pg.644]    [Pg.1904]    [Pg.105]    [Pg.392]    [Pg.1510]    [Pg.223]    [Pg.169]    [Pg.125]    [Pg.102]    [Pg.136]    [Pg.139]    [Pg.139]    [Pg.142]    [Pg.187]    [Pg.192]    [Pg.350]    [Pg.592]    [Pg.105]    [Pg.84]    [Pg.19]    [Pg.230]    [Pg.262]    [Pg.89]    [Pg.8]   
See also in sourсe #XX -- [ Pg.14 ]




SEARCH



© 2024 chempedia.info