D O C . 3 3 9 A N I S O T R O P I C P R E S S U R E F O R C E S 2 6 9 components of the heat flow itself. That these really do exist and how they can be calculated in a simple way will be demonstrated in the following. A more detailed presentation can be found in the Zurich dissertation by Miss E. Einstein (1922).[3] We assume mechanical equilibrium of the flowing gas: If such isotropic pressure forces exist, then—as is gathered from purely formal considerations—they must be of the form , . . . (1) where p signifies the location-independent part of the gas pressure, the compo- nents of the heat flow (on the part appertaining to the molecule’s progressive mo- tion), or = 0, resp., depending on whether or z and are constants, depending on the state of the gas at the position under consideration. In the following we want to treat them as if they were independent of the coordi- nates, which however would imply an approximation. It is known that the heat flow fulfills both the relations . . . (2) . . . (3) Furthermore the equilibrium condition of the gas is . . . . (4) If one inserts in this in (1) the expressions (1), then one obtains with respect to (2) and (3), neglecting the spatial variability of the constants z and , the result , so that one obtains instead of (1): . . . . (1a) There now remains the solution of the main aim of finding out z from a consider- ation in gas theory. We ask about the most probable distribution of velocities at one location of the gas in which a heat flow occurs in the direction of the x axis without a current of the molecules (motion).[4] We look for an extremum of the Boltzmann integral,[5] pμν pδμν z z′( f α 2 )δμν + + = δμν 1= μ ν = μ ν z′ ∂fμ ∂xμ -------- μ 0= ∂fμ ∂xν ------- - ∂fν ∂xμ -------- 0. = ∂pμν ∂xν ----------- ν 0= μ 1 2 3) , , = ( z′ z′ 1 2 --z - –= pμν pδμν z 1 2 -–--δμν 2 α +=
Previous Page Next Page