Heat Conduction, Viscosity, and Diffusion

In this appendix we shall give a combined account of three phenomena by means of which the mean free path in a gas can be determined experimentally. These phenomena are heat conduction, viscosity, and diffusion. In all these phenomena there is a variation in some physical property of the molecules of the gas from point to point, which, however, tends to disappear as a result of the movements of the molecules. 

The amount of the property A transferred is therefore proportional to the gradient of A , and also to the number of molecules per cubic centimetre, their mean velocity, and their mean free path. This equation is known as the transport equation. 

We note that M A) is independent of the pressure, provided that A itself denotes a property of the gas molecules which is independent of the pressure (Maxwell). For the pressure of a gas is given by p = nhT, i.e. at constant temperature depends only on the number of molecules per cubic centimetre. It is true that n appears as a factor in the transport equation but this factor is compensated by the occurrence in the formula of the mean free path, which is inversely proportional to n and to the cross-section of the molecule. This independence of the pressure accordingly results from the fact that though more molecules take part in the transference of A at the higher pressures, they do not on the average travel so far. 

We shall now make particular application of the transport equation to the three phenomena mentioned above. We begin with heat conduction. Here A stands for the kinetic energy of a molecule, i.e. idn = const. -f where c m is the specific heat of the gas at 

We see that it is proportional to the temperature gradient the factor of proportionality k nvlc m is called the thermal conductivity. 

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It is well known that Truesdell is of the view that Onsager s relations do not apply to phenomena like heat conduction, viscosity and diffusion since there is no unambiguous way of selecting the fluxes and forces. It would appear therefore that there may be some doubts as to the validity of Parodi s relation. Available data indicate that (3.1.39) is satisfied within experimental limits, but, in any case, the relation has been tadtly assumed to be true in most discussions. 

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