Global Journal of Science Frontier Research, A: Physics and Space Science, Volume 23 Issue 1

obtain such results via the Onsager diffusion equation J k = - Σ i D ki µ i [1]. As another example, consider an inhomogeneous system divided into two parts by a porous partition. If a temperature difference ( ∆ T ≠ 0) is created in it, then a gas or liquid flux J k =D k ( s k * ∇ T - υ k * ∇ p ) occurs through the partition, leading, under conditions of incomplete equilibrium ( J k = 0), to the occurrence of a pressure difference on both sides of the partition (Feddersen effect, 1873) : ( ∆ p/ ∆ T ) st =- q k ∗ /T υ k * , (16) where q k ∗ =Ts k * represents the heat transfer of the k th substance. This phenomenon is now called thermo- osmosis. The opposite phenomenon has also been seen: the appearance of a temperature difference on both sides of the partition when air or other gas is forced through it. Both of these effects are of the same nature as the Knudsen effect (1910) - the appearance of a pressure difference in vessels connected by a capillary or a narrow slit and filled with gas of different temperatures. They are also of the same effect as the Allen and Jones “fountain effect” (1938), consisting of liquid helium II flowing out, at the slightest heating, from a vessel closed with a porous stopper. The opposite phenomenon - the occurrence of a temperature difference when a pressure difference is created on both sides of the partition - is called the mechanocaloric effect (Daunt-Mendelssohn). In the case of systems that initially have the same pressure on both sides of the porous partition (∆ p = 0) and initially the same concentration of the k th substance (∆ c k = 0), when a temperature difference ∆ T is created, a concentration difference occurs on both sides of it (the Soret effect , 1881): ( ∆ c k / ∆ T ) ст = - q k ∗ /T µ kk . (17) The opposite phenomenon, the appearance of temperature gradients during diffusion mixing of components, was discovered by Dufour in 1872 and bears his name. In isothermal systems ( ∆ T =0) for creating pressure differential across the membrane ∆ p occurs via reverse osmosis, i.e., the separation of a binary solution with separation from the k th component (usually a solvent). This phenomenon is widely used in water treatment plants. This occurs when the concentration difference k th part is given by the expression: ( ∆ c k / ∆ p ) st =- υ k / µ kk . (18) These results are consistent with those obtained in the framework of TIP [6,8]. However, for this it was not necessary to assume the linearity of phenomenological laws, postulate the constancy of the phenomenological coefficients L i or D k and resort to Onsager's reciprocity relations. At the same time, it becomes clear that these effects arise due to the onset of states of partial (incomplete) equilibrium; any multivariable system passes through such states on its way to full equilibrium. In this case, the "effects of superposition" are the result of superposition not of fluxes J i, but rather of forces F j in full accordance with the principles of mechanics. The advantages of this method consist not only in the further number of phenomenological coefficients from n ( n+ 1) / 2 in TIP to n [14], but also in the possibility of finding superposition effects in nonlinear systems far from equilibrium. In this case, the TIP itself becomes free from any postulates expressing the coefficients L i as a function of the parameters of the system. V. E stablishing the F undamental D ifference between the L aws of R elaxation and E nergy C onversion Consider an isolated system ( dU / dt = 0; J i = 0)in which energy is converted from one form to another. For such a system, from (6) at once follows: Σ k X k · J k = 0 . (19) For the process of converting some i th form of energy into j th , this expression can be given the form: J i / X j = -J j / X i . (20) According to this expression, the direction of the internal flux J i of the i th energy carrier, induced by the "exterior" force X j , is opposed to the direction of the "exterior" flux J j , induced by the driving force X i. If we denote the ratio J i / X j by L ij, and the ratio J j / X i by L i , then we come to the antisymmetric Onsager-Casimir reciprocity relations[6, 8]: L jj =-L ji . (21) This provision keeps the opposing direction of diverse forces; fluxes in the processes of energy conversion and possesses a general physical status. In particular, Faraday's law of induction follows from it, if by J i we mean the flux of magnetic coupling (expressed by the number of lines of force), and by X j , the resulting voltage. However, these conditions of anti symmetric matrices with “phenomenological” coefficients indicates also that for the processes of intercom version of ordered forms of energy, in the law (9) of Onsager, the coefficients L ij and L ji must be modified by the opposite signs: J i = L ij X i – L ji X j . (22) © 2023 Global Journals 1 Year 2023 12 Global Journal of Science Frontier Research Volume XXIII Issue ersion I VI ( A ) New Applications of Non-Equilibrium Thermodynamics