Formula For Thermal Conductivity Research Articles

Perturbation Expansion for Lattice Thermal Conductivity

A method is given for obtaining a perturbation expansion for the correlation function formula for thermal conductivity. The problem is reduced to the determination of the matrix elements of the products of resolvent operators Xll′ and Yll′ to different orders in the perturbation λH′. The coefficients in the general equations for Xll′ and Yll′ derived by Van Hove, Janner, and Swenson are iterated, and the resulting approximate equations are used to deduce the formulas for the contributions to the lattice thermal conductivity proportional to λ−2 (lowest order) and to λ−1.

Frequency-Dependent Transport Coefficients in Fluid Mechanics

Exact time-correlation formulas for frequency-dependent shear viscosity, bulk viscosity, and thermal conductivity are presented. These formulas are evaluated for a fluid composed of molecules with internal degrees of freedom, in the limit of very weak coupling of internal and translational motions. In this limit, the shear viscosity is unaffected by internal modes. The bulk viscosity consists of two parts, one due to translational motions, and the other due to relaxation of the energy contained in internal modes. The thermal conductivity consists of two parts, one due to translational motions, and the other due to diffusion of energy in internal modes (the Eucken correction). The resulting excess sound absorption is in complete agreement with the predictions of the thermodynamic theory of relaxation in fluids.

Interaction Energies and Transport Coefficients of Li+H and O+H Gas Mixtures at High Temperatures

Accurate potential energy curves for the X 1Σg+, A 1Σu+, B 1Πu, and C 1Πu states of the Li2 molecule are calculated from observed spectroscopic data by the method of Rydberg—Klein—Rees (RKR), and compared with previous quantum-mechanical calculations, Long-range attractive potentials are estimated by extrapolation of functions fitted to the RKR ground-state curves of Li2, LiH, and OH. From these, the repulsive potentials derivable from interacting ground-state atoms are estimated semiempirically. Collision integrals are computed from the potentials, and transport coefficients of the gaseous systems Li+Li, Li+H, and O+H are calculated for temperatures of 1000° to 10 000°K. A surprising result is the extraordinarily large values of the collision inregrals for Li+Li (and Li+H) interactions, which result in unexpectedly small values of diffusion coefficient, viscosity, and thermal conductivity. For traces of Li in Li+H mixtures at low temperature, the thermal diffusion factor is very large. Various approximate formulas for viscosity and thermal conductivity of mixtures are seen to give poor agreement with exact calculations for the systems considered.

Thermal Conductivity of a System of Interacting Electrons

Kubo's formula for thermal conductivity is evaluated for the case of an interacting electron gas and random, fixed, impurities. As in previous work, the theorems proved are exact to all orders in the electron-electron interactions and to lowest order in the concentration of impurities. The heat flux is examined in some detail and a Ward's identity is derived for the associated vertex function. Although the heat flux contains contributions from the interaction energy of pairs (or larger clusters) of correlated quasi-particles, it is found that these contributions enter the thermal conductivity only to higher orders in the impurity concentration. In a normal system where the many-body correlations are sufficiently weak, the Wiedemann-Franz law remains valid.

An Investigation on the Thermal Conductivity of Porous Materials and its Application to Porous Rook

The thermal conductivity of porous materials, particularly the effect of porosity and of temperature on thermal conductivity, has been investigated. A" comparison method " was used for measurement and the experiment was carried out with three types of models. A generalized formula for thermal conductivity is derived empirically. This formula can represent other formulas on the thermal conductivity of porous materials, and the formula can be applied to sandstones having different porosity as a typical example of porous materials.

High-Temperature Thermal Conductivity of Insulating Crystals: Relationship to the Melting Point

The Lindemann melting rule is used to eliminate the elastic constant from the thermal conductivity formula proposed by Lawson. The thermal conductivity is thus obtained as a function of density, atomic weight, and melting temperature. The introduction of a dependence on bond character allows a major fraction of the available high-temperature thermal conductivity data to be reproduced within a factor of two. A dependence of thermal conductivity on mass ratio of the type found theoretically by Blackman for diatomic crystals is observed.

Formulas for Thermal Conductivity of Ternary Gas Mixtures

The thermal conductivities of ternary mixtures of neon, argon, and krypton have been recently reported by the authors. In the present paper these values have been compared with those calculated from the two simple generalized expressions for the thermal conductivity of a ternary mixture, one of which is obtained from an extension of the Enskog's expression for the binary thermal conductivity while the other from the Lindsay-Bromley formula. It is found that the latter generalization yields values which are in better agreement with the experiment, provided the two constants of the Lindsay-Bromley formula are determined experimentally from binary conductivity.

Illustrations of the Dual Theory of Metallic Conduction

The occurrence of a Peltier effect with change of direction within a metal crystal, which effect Bridgman has recently noted and which he has considered incapable of explanation by any of "our ordinary pictures of electrical conduction," is readily explained by the dual theory, through a formula published several years ago. Millikan's recent announcement that, according to experiments and reasoning of his own, most of the conductive electrons within metals do not share the energy of thermal agitation, while the "thermions," "presumably responsible for the Peltier and thermo-electric effects," do share this energy, tends to confirm views which the author has long held and repeatedly expressed. These facts seem to indicate that the time is opportune for a more continuous and better illustrated statement of the dual theory of metallic conduction than has yet been given. This statement reviews briefly what the theory has had to say concerning the Volta effect, Richardson's derivation of his formula for thermionic emission, and the thermo-electric pseudo equation $P=T$ $\frac{\mathrm{dV}}{\mathrm{dT}}$, applying everywhere the mass law of equilibrium between electrons, ions and atoms within a metal. It then undertakes to show how the Thomson effect, the Peltier effect, the electric conductivity and the thermal conductivity of a given metal may be rationally connected by means of a set of six equations containing six constants characteristic of the metal, the equations serving for the determination of the constants. It shows in particular how a theory of heat conduction, with a definite formula for thermal conductivity, grows out of the more fundamental conceptions of the dual theory. It applies the machinery of the dual theory to the results of Bridgman's experiments on changes of electrical, thermal and thermoelectric properties of metals under high pressure, showing explicitly how the corresponding changes of the "characteristic constants" can be found and what is the nature of these changes in particular instances. Two general results of importance appear from this discussion. The first, which was predicted, is that, as a rule, compression of a metal reduces the latent heat of the ionization process within it. The conception of thermal conductivity as the product, in a general way, of electric conductivity and heat of ionization, goes far to explain why the two conductivities, though so closely related, are so differently affected by certain changes of condition. The second general conclusion from the study of Bridgman's data is that, contrary to expectation, compression of a metal increases, as a rule, the ratio of free-electron conductivity to total electric conductivity. This evidence seems to give support to the idea, already familiar, that the free electrons may go through, not necessarily between, the atoms in their progress through a metal. This conception, taken with the consideration that latent heat of ionization diminishes with fall of temperature, suggests that the supraconductive state may be one in which the distinction between "free" electrons and "associated" electrons disappears, the metal being, as regards all the conductive electrons, in a state of flux.The theory here set forth, if it is to account for the whole of thermal conduction in metals, appears to require the heat of ionization within a metal to increase with increase of temperature, even when expansion is prevented by increase of pressure.The dual theory indicates that photo-electric emission should be nearly independent of temperature but suggests the following revision of Richardson's thermionic emission formula, $a$ being a constant: $i=A{T}^{\frac{1}{2}}{\ensuremath{\epsilon}}^{\frac{\ensuremath{-}{b}_{0}}{R}}=A{T}^{\frac{1}{2}}{\ensuremath{\epsilon}}^{\ensuremath{-}a}{\ensuremath{\epsilon}}^{\frac{\mathrm{aT}}{T}}{\ensuremath{\epsilon}}^{\frac{\ensuremath{-}{b}_{0}}{T}}={A}^{\ensuremath{'}}{T}^{\frac{1}{2}}{\ensuremath{\epsilon}}^{\frac{\ensuremath{-}({b}_{0}\ensuremath{-}aT)}{T}}$