By James Jeans
This booklet could be defined as a student's variation of the author's Dynamical conception of Gases. it really is written, in spite of the fact that, with the wishes of the scholar of physics and actual chemistry in brain, and people components of which the curiosity was once often mathematical were discarded. this doesn't suggest that the e-book comprises no critical mathematical dialogue; the dialogue particularly of the distribution legislations is sort of precise; yet typically the maths is worried with the dialogue of specific phenomena instead of with the dialogue of basics.
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Extra info for An Introduction to the Kinetic Theory of Gases (Cambridge Science Classics)
As we shall see later (§ 189), a gas in which abundant collisions are occurring behaves exactly like the fluid of hydrodynamical theory; at every point there is a pressure of the amount given by equation (3) or (19), namely pRT m If the gas is in a steady state at a uniform temperature T, variations in this pressure hold the gas at rest against the forces exerted by the external field. ), p. 364. 40 A PRELIMINARY SURVEY These three equations have the common integral, well known in hydrodynamical theory, BTlogp = — x + a constant, or p = Be~*IRTy (39) where B is a constant.
The pressure needed to create the new momentum after impact can be calculated in precisely the same way. We enumerate the molecules which have impinged on dS within an interval dt, and find that their momentum would be produced by a steady pressure Zmv^^dS, where the summation is now over all showers for which u is negative. Combining these two contributions, we find that the total pressure pdS on the area dS is given by (52) pdS = Zmv&ldS, where the summation is over all the showers of molecules.
In a similar way, the ' 2hm m mean value of the velocity *J(u2 + v2 + w2)} which we shall denote by 2 c, is found to be -7—=—r, which is 0-921 times C. so that C= l-086c. ^(nhm) 25. If two gases are mixed, and the mixture has attained its steady state, the temperature must be the same for both, so that h, which is equal to 1/2RT, must be the same for both. Thus the laws of distribution for the two gases will be of the form ^ e-hm(u2-'rv2iw2)^ (42) A PRELIMINARY SURVEY A' 2 e-hmXu'*+v' +w'*)9 43 (43) where m' and u',v\w' denote the mass and components of velocity of a molecule of the second gas.