By A. H. Beck
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35) where a = 1/(1 + //2a). This simple result is in agreement with the more rigorous calculations to within 2 per cent in the range FIG. 8. Flow in a short tube. 5. It fails completely, however, when l/a becomes large. It should be noted that in the free-molecule regime considered here (λ $> I or a) the gas-flows from A to B and from B to A in Fig. 8 occur quite independently. There is thus no loss of generality if we consider only the gas-flow in the direction A -> B. 35) is clearly the fraction of the molecules entering the tube from A which pass right through into B.
18): nc sin θ cos Θ dU . 4) that, on the average, the last collision a molecule makes before crossing dS will have occurred at a distance FIG. 3. Transport in gases at high pressures. λ from dS. 33) KINETIC THEORY OF GASES AND GASEOUS FLOW 245 The net transport across dS per second is thus: -dS dG Ί cos ΘΘ ! sin Θ cos Θ dö G +— — .. 35) where cv is the specific heat at constant volume. The heat transferred across dS per second is therefore: dT dT Δ β = a ncXmcv — = k — . dS dz dz where k is the coefficient of heat conduction.
Dcy . 25) where the direction of drift is assumed to be parallel to the x-axis. 9) if the distribution can be taken to be Maxwellian in a co-ordinate system moving in the x direction with velocity u. Since u is normally small compared with cx this becomes approximately: A e- c2 /« 2 . 1 + - j . 26) where c is the resultant velocity of a molecule. dO . dcf) 2 = A e^2/«2 1 + —^ . uc . sin Θ cos φc2 sin Θ dc . do . 27) The number of molecules striking an area dS of the wall in time dt having values of c, 0, φ in the given ranges is clearly: F(c) c .
Gases and Vacua. Handbook of Vacuum Physics by A. H. Beck