Heat capacity per unit volume

A general method of estimating the temperature distribution in a body of any shape consists of replacing the heat flow problem by the analogous electrical situation and measuring the electrical potentials at various points. The heat capacity per unit volume C.,p is represented by an electrical capacitance, and the thermal conductivity k by an... 

Special correlations have also been developed for liquid metals, used in recent years in the nuclear industry with the aim of reducing the volume of fluid in the heat transfer circuits. Such fluids have high thermal conductivities, though in terms of heat capacity per unit volume, liquid sodium, for example, which finds relatively widespread application, has a value of Cpp of only 1275 k.l/ni1 K. 

Fig. 12.16. Heat capacity per unit volume of the two neutron transmutation doped (NTD) Ge wafers.

Let us first consider data from the first and second measurements on the non-metallized sample (see Fig. 12.16). Data can be well represented by a linear fit which crosses the origin within the experimental errors. The heat capacity per unit volume of the wafer... 

Let us examine the data of the third measurement on the metallized wafer. There are two contributions to the heat capacity, a linear contribution and a spurious one. The spurious contribution may be interpreted as the high temperature side of a Schottky anomaly. In this hypothesis, the heat capacity per unit volume of the metallized wafer may be... 

The heat transfer characteristics of liquid-solid fluidised systems, in which the heat capacity per unit volume of the solids is of the same order as that of the fluid are of considerable interest. The first investigation into such a system was carried out by Lemlich and Caldas193, although most of their results were obtained in the transitional region between streamline and turbulent flow and are therefore difficult to assess. Mitson194 and Smith(20) measured heat transfer coefficients for systems in which a number of different solids were fluidised by water in a 50 mm diameter brass tube, fitted with an annular heating jacket. 

Although the parameters in equation 6.58 were varied over a wide range, the heat capacities per unit volume and the thermal conductivities of the liquids were almost constant, as they are for most organic liquids, and the dimensions of the surface and of the tube were not varied. Nevertheless, for the purposes of comparison with other results, it is useful to work in terms of dimensionless groups. 

The Nusselt number with respect to the tube Nu(= hdt/k) is expressed as a function of four dimensionless groups the ratio of tube diameter to length, the ratio of tube to particle diameter, the ratio of the heat capacity per unit volume of the solid to that of the fluid, and the tube Reynolds number, Rec = (ucdtp/p,). However, equation 6.59 and other equations quoted in the literature should be used with extreme caution, as the value of the heat transfer coefficient will be highly dependent on the flow patterns of gas and solid and the precise geometry of the system. 

For liquid water and for aqueous solutions we wiU assume Cp = 1 cal/g K, and, since the density p of water is -1 g/cm, we have pCp = 1 cal/cm K or pCp =1000 cal/Uter K. To estimate the heat capacity of gases, we will usually assume that the molar heat capacity Cp is j R cal/mole K. There are thus three types of heat capacity, the heat capacity per unit mass Cp, the heat capacity per unit volume pCp, and the heat capacity per mole Cp. However, we will use heat capacity per unit volume for much of the next two chapters, and we use the symbol pCp for most of the equations. 

The original densities, heat capacities per unit volume and enthalpies of mixing from which the various thermodynamic functions are calculated for the ternary systems are given elsewhere. ... 

Standard heat capacities of transfer can be derived from the temperature dependence of standard enthalpies of solution (8). While this technique can give general trends in the transfer functions from water to mixed solvents (9), it is not always sufficiently precise to detect the differences between similar cosolvents, and the technique is rather laborious. Direct measurements of the difference between heat capacities per unit volume of a solution and of the solvent a — gq can be obtained with a flow microcalorimeter (10) to 7 X 10 5 JK 1 cm-3 on samples of the order of 10 cm3. A commercial version of this instrument (Picker dynamic flow calorimeter, Techneurop Inc.) has a sensitivity improved by a factor oi about two. 

Now (dhj(T)ldT) = cpj is the heat capacity per mole of Aj, and the second term on the left-hand side of this equation could be written 0Cp(dTldt), where Cp is the total heat capacity per unit volume. Also, by multiplying each of the equations in (57) by the corresponding hj and subtracting from (59), we have... 

Equality of the thermal diffusivity (the ratio of thermal conductivity to heat capacity per unit volume) and the diffusion coefficients of the substances. 

Regenerators quite frequently are chosen for applications where the heat-transfer effectiveness, defined as G actual/2ideal, must approach values of 0.98 to 0.99. It is clear that a high regenerator effectiveness requires a high heat capacity per unit volume and a large surface area per unit volume. 

The heat-loss terms describe both the loss via the flow of gases leaving the reactor and via Newtonian cooling through the walls where f es is taken to be the average residence time of the reactor. is the ambient temperature, V the volume, 5 the reactor surface area and x the heat transfer coefficient. Cp is the heat capacity per unit volume which is assumed to be independent of temperature, and qj the exothermicity of the yth reaction step. 

In the second part of the chapter, we have examined the spread of vibrational energy through coordinate space in systems that are large on the molecular scale—in particular, clusters of hundreds of water molecules and proteins—and computed thermal transport coefficients for these systems. The coefficient of thermal conductivity is given by the product of the heat capacity per unit volume and the energy diffusion coefficient summed over all vibrational modes. For the water clusters, the frequency-dependent energy diffusion coefficient was... 

The calculation of sound intensity requires a knowledge of the acoustic absorption coefficient of the imbedding material and its heat capacity per unit volume at the temperature at which measurements are made, according to,... 

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