A Treatise On the Kinetic Theory of Gases

Cover A Treatise On the Kinetic Theory of Gases
A Treatise On the Kinetic Theory of Gases
Samuel Hawksley Burbury
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And K being small the solution agrees with that of Art. 29. It does not however agree with that of Art. 29 when K", &c. Cannot be neglected. Which result then are we to accept in this case ? Evidently the result e~^ x, because Art. 29 is based on the tacit assumption of condition A, and therefore holds only for small values of K. To sum up the discussions of this problem.
o If K be neglected, the law of density is e~ 2hx, with T = -^ . If K 3, &c. , but not K, be neglected, the law is e~ 2ftx e
...~' c, with If /c 2, &c. , are not to be neglected, the law is - h ^6~ K, with T ^ ~ VIII. ] GENERAL THEORY OF THE STATIONARY MOTION. 107 Boltzmanris Minimum function.
104. The following theorem is not to be compared in egance with the theorem founded on condition A, Art. 38, but has the advantage that condition A is not assumed.
Let f(u l . . . U n x l . . . Z n ), or /, be any positive function of the coordinates x^... Z ny and velocities u^... U n, of a system of molecules, and of certain parameters a, 6, &c.


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