Abstract

The thermodynamics of irreversible processes, based on the O n s a g e r reciprocal relations, is applied to a system consisting of a mixture of two substances, of which one can go over into the other. The mixture is enclosed in two communicating reservoirs at different temperatures T
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and T + ΔT. The situations, in which systems arrive, when one, two or more differences between the values of state parameters in the two reservoirs are kept fixed, are called “stationary states of first, second etc. order”. For the stationary state of the first order with fixed ?T the corresponding pressure difference ?P is calculated. This gives the thermomolecular pressure effect
ΔP/ΔT = —Q*/v T = (h — U*)/v T,
where h and v. are the mean specific enthalpy and volume. This equation shows the connection with the mechano-caloric effect Q*, since application of the O n s a g e r relations shows that Q* is the “heat of transfer” i.e. the heat supplied per unit of time from the surroundings to the reservoir at temperature T, when one unit of mass is transferred from one reservoir to the other in the stationary state of the second order with fixed ΔP and ΔT = 0 (uniform temperature). Similarly U* is the “energy of transfer”. The influence of ΔT on the relative separation (thermal effusion) and the “chemical affinity” of the two components is also calculated. The heat conduction can be split into an “abnormal” part due to the coupling of diffusion and chemical reaction between the components and a “normal” part also present when no reaction takes place.
The results can be applied to liquid helium II, considered in the two-fluid theory as a mixture of “normal” (1) and “superfluid” (2) atoms, capable of the “chemical reaction” 1 ⇔ 2. When it is supposed that chemical equilibrium is immediately established and that only superfluid atoms can pass through a sufficiently narrow capillary, the above mentioned equation leads . to G o r t e r's formula
v ΔP/ΔT = χ1 ∂s/∂χ1,
where χ1 is the fraction of normal atoms and s the mean specific entropy of the mixture. Under the same circumstances only the “normal” part of the heat conduction subsists.
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