Heat capacity relative

Robinson G. R. Jr. and Haas I L. Jr. (1983). Heat capacity, relative enthalpy and calorimetric entropy of silicate minerals An empirical method of prediction. Amer. Mineral, 68 541-553. 

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. 

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. 

The question as to whether a flame retardant operates mainly by a condensed-phase mechanism or mainly by a vapor-phase mechanism is especially comphcated in the case of the haloalkyl phosphoms esters. A number of these compounds can volatilize undecomposed or undergo some thermal degradation to release volatile halogenated hydrocarbons (37). The intact compounds or these halogenated hydrocarbons are plausible flame inhibitors. At the same time, thek phosphoms content may remain at least in part as relatively nonvolatile phosphoms acids which are plausible condensed-phase flame retardants (38). There is no evidence for the occasionally postulated formation of phosphoms haUdes. Some evidence has been presented that the endothermic vaporization and heat capacity of the intact chloroalkyl phosphates may be a main part of thek action (39,40). 

Because of its small size and portabiHty, the hot-wire anemometer is ideally suited to measure gas velocities either continuously or on a troubleshooting basis in systems where excess pressure drop cannot be tolerated. Furnaces, smokestacks, electrostatic precipitators, and air ducts are typical areas of appHcation. Its fast response to velocity or temperature fluctuations in the surrounding gas makes it particularly useful in studying the turbulence characteristics and rapidity of mixing in gas streams. The constant current mode of operation has a wide frequency response and relatively lower noise level, provided a sufficiently small wire can be used. Where a more mgged wire is required, the constant temperature mode is employed because of its insensitivity to sensor heat capacity. In Hquids, hot-film sensors are employed instead of wires. The sensor consists of a thin metallic film mounted on the surface of a thermally and electrically insulated probe. 

Thermodynamic and physical properties of water vapor, Hquid water, and ice I are given ia Tables 3—5. The extremely high heat of vaporization, relatively low heat of fusion, and the unusual values of the other thermodynamic properties, including melting poiat, boiling poiat, and heat capacity, can be explained by the presence of hydrogen bonding (2,7). 

A relatively simple example of a group contribution technique is the method for estimating Hquid and soHd heat capacities (159). This method is a modification of Kopp s rule (160,161) which was originally proposed in 1864. Kopp s rule states that, at room temperature, the heat capacity of a soHd compound is approximately equal to a stoichiometric summation of the heat capacities of its atoms (elements). The Hurst-Harrison modified equation is as follows ... 

Liquid mole fraction Vapor mole fraction Temper- ature, R Relative volatifity Pressure activity coefficient Endialpy, Btu/ (Ib-mol) Heat capacity, Btu/(lb-mol- R)... 

There are a number of reliable estimating techniques for obtaining pure-component hq uid heat capacity as a function of tem )erature, including Ruzicka and Dolmalsld, Tarakad and Danner, " and Lee and Kesler. These methods are somewhat compheated. The relatively single atomic group contribution approach of Chueh and Swanson for liquid heat capacity at 29.3.15 K is presented here ... 

Heat capacity (specific heat) of petroleum liqiiids between 0 and 205°C (32 and400°F), having a relative density of 0.75 to 0.96 at 15°C (60°F), can be calculated within 2 to 4 percent of the experimental values from the following equations ... 

Different areas of the earth s surface react quite differently to heating by the sun. For example, although a sandy surface reaches fairly high temperatures on a sunny day, the heat capacity and conductivity of Scmd are relatively low the heat does not penetrate more than about 0.2-0.3 m and little heat is stored. In contrast, in a body of water, the sun s rays penetrate several meters and slowly heat a fairly deep layer. In addition, the water can move readily and convection can spread the heat through a deeper layer. The heat capacity of water is considerably greater than that of sand. All these factors combine to allow considerable storage of heat in water bodies. 

Consider the heat balance of the cell. However, as opposed to the GC column, the heat capacity of the liquid mobile phase in an in LC column is relatively large. Consequently, heat convected from the cell by the mobile phase must also be taken into account. It follows that... 

The behavior of the internal energy, heat capacity, Euler characteristic, and its variance ( x ) x) ) the microemulsion-lamellar transition is shown in Fig. 12. Both U and (x) jump at the transition, and the heat capacity, and (x ) - (x) have a peak at the transition. The relative jump in the Euler characteristic is larger than the one in the internal energy. Also, the relative height of the peak in x ) - x) is bigger than in the heat capacity. Conclude both quantities x) and x ) - can be used to locate the phase transition in systems with internal surfaces. 

Thus curvature in an Arrhenius plot is sometimes ascribed to a nonzero value of ACp, the heat capacity of activation. As can be imagined, the experimental problem is very difficult, requiring rate constant measurements of high accuracy and precision. Figure 6-2 shows a curved Arrhenius plot for the neutral hydrolysis of methyl trifluoroacetate in aqueous dimethysulfoxide. The rate constants were measured by conductometry, their relative standard deviations being 0.014 to 0.076%. The value of ACp was estimated to be about — 200 J mol K, with an uncertainty of less than 10 J moE K. ... 

Convective heat transmission occurs within a fluid, and between a fluid and a surface, by virtue of relative movement of the fluid particles (that is, by mass transfer). Heat exchange between fluid particles in mixing and between fluid particles and a surface is by conduction. The overall rate of heat transfer in convection is, however, also dependent on the capacity of the fluid for energy storage and on its resistance to flow in mixing. The fluid properties which characterize convective heat transfer are thus thermal conductivity, specific heat capacity and dynamic viscosity. 

Whereas heat capacity is a measure of energy, thermal diffusivity is a measure of the rate at which energy is transmitted through a given plastic. It relates directly to processability. In contrast, metals have values hundreds of times larger than those of plastics. Thermal diffusivity determines plastics rate of change with time. Although this function depends on thermal conductivity, specific heat at constant pressure, and density, all of which vary with temperature, thermal diffusivity is relatively constant. 

The specific heat of a substance must always be defined relatively to a particular set of conditions under which heat is imparted, and it is here that the fluid analogy is very liable to lead to error. The number of heat units required to produce unit rise of temperature in a body depends in fact on the manner in which the heat is communicated. In particular, it is different according as the volume or the pressure is kept constant during the rise of temperature, and we have to distinguish between specific heats (and also heat capacities) at constant volume and those at constant pressure, as well as other kinds to be considered later. 

Boilers are heat-transfer devices, wherein water, in the form of either liquid water or gaseous steam, is commonly employed as a medium for the transport of heat to some distant point of use. Although other heat-transfer mediums are sometimes utilized, water is particularly suitable because of its relative abundance, low cost, and high heat capacity. It is generally the medium of choice in most boiler applications, whether for domestic, commercial, institutional, or industrial purposes. 

Differentiation of equation (7.65) with respect to temperature gives an equation for Ji, the relative partial molar heat capacity, given by... 

The difference Cp. -C°pi is the relative partial molar heat capacity Jt. Thus... 

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