An Introduction to the Kinetic Theory of Gases (Cambridge by James Jeans

By James Jeans

This booklet will be defined as a student's variation of the author's Dynamical thought of Gases. it truly is written, in spite of the fact that, with the desires of the scholar of physics and actual chemistry in brain, and people components of which the curiosity was once quite often mathematical were discarded. this doesn't suggest that the e-book includes no severe mathematical dialogue; the dialogue specifically of the distribution legislations is kind of designated; yet usually the math is anxious with the dialogue of specific phenomena instead of with the dialogue of basics.

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22 A PRELIMINARY SURVEY Let the molecules have masses m, m\ and let their components of velocity before collision be u, v9 w and u\ v', wr. Since the impact occurs along the axis Ox, the components of velocity parallel to Oy and Oz are unaltered, so that we may suppose the velocities after the collision to be u,v,w and u',vryw'. Gas Wall Fig. 5 The equations of energy and momentum now take the simple forms mu + m'u' = or, by a slight transposition, m(u2 - u2) = - m'{u'2 - u'2)f (5) m(u-u) = -m'(u'-u').

Another illustration of the same dynamical principle can be found in astronomy, being provided by the motion of the stars in space. The stars move with very different speeds, but there is found to be a correlation between their speeds and masses, the lighter stars moving the faster, and this correlation is such that the average kinetic energy of stars of any specified mass is (with certain limitations) equal to that of the stars of any other mass. Here, as so often in astronomy, the stars may be treated as molecules of a gas, and the facts just stated seem to shew that the stars have been mixed long enough for all types of stars to have attained the same "temperature".

One such quantity is of course the energy of the molecule, which we may denote by E; clearly then f(u,vfw,x,y,z) = E (36) is a solution of equation (35). A more general solution is f(u,v,w,x,y,z) = 0(E), (37) where 0(E) is any function whatever of E, as for instance its square or its logarithm. Here E, the total energy of a moving molecule, is given by E = £m(w2 + v2 + w2)-f;\;, (38) s where x * ^he potential energy of a molecule in the field of force, so that the forces acting on the molecule are given by A PRELIMINARY SURVEY 39 It is quite easy to shew* that this expresses the most general solution possible of equation (35), but we need not delay over this proof, as a complete discussion of the whole problem will be given later (Chap.

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