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assume assumption atmosphere atoms average Avogadro's Law axis becomes boundary Boyle's Law calculated Chapter clusters coefficient components condition coordinates corresponding cubic centimetre denote dissipation distance double molecule dudvdw dxdydz dynamical dynamical system elastic spheres element of volume equal field of force finite fluid follows fraction function gases generalised space given by equation heat Hence hydrogen infinitely probable infinitesimal integral intermolecular forces isothermal J. J. Thomson kinetic energy Kinetic Theory law of distribution mass Maxwell's mean free path mean value molecular chaos molecular density molecules of class molecules of type momentoids motion normal number of collisions number of molecules obtain obvious plane possible potential energy pressure quantity radius ratio regarded replaced represented result rotation satisfied shews single molecule sphere of molecular steady stream line subsidiary temperatures surface total number unit volume vanishes vessel vibrations viscosity Waals whole
Page 168 - But if we conceive a being whose faculties are so sharpened that he can follow every molecule in its course...
Page 168 - Now let us suppose that such a vessel is divided into two portions A and B, by a division in which there is a small hole, and that a being, who can see the individual molecules, opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will thus, without expenditure of work, raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics.
Page 51 - If we suppose the N particles to start from the origin at the same instant, then this will be the number in the element of volume...
Page 112 - The flow is proportional to the difference of the end pressures and inversely proportional to the square root of the molecular weight of the gas.
Page 54 - Ay, z and z + dz and the velocity components of which lie in the interval between u and u + du, v and v + dv, w and w + dw.
Page 109 - If the system is a gas or mixture of gases not acted on by external forces, the theorem that the average kinetic energy for a single molecule is the same for molecules of different gases is not sufficient to establish the condition of equilibrium of temperature between gases of different kinds, such as oxygen...
Page 5 - ... the results added together. The extension to the case of more than one point of application of the impressed forces is also obvious. To obtain the most general solution satisfying the conditions, the expression for the natural vibrations must also be added ; but these become reduced to insignificance after the motion has been in progress for a sufficient time. The law of friction assumed in the preceding investigation is the only one whose results can be easily followed deductively, and it is...
Page 168 - One of the best established facts in thermodynamics is that it is impossible in a system enclosed in an envelope which permits neither change of volume nor passage of heat, and in which both the temperature and the pressure are everywhere the same, to produce any inequality of temperature or pressure without the expenditure of work.
Page 14 - ... nearly equal ; in general, it would depend on u, v, w, as well as on u, v, w. In the case which is discussed in the present chapter — that in which the molecules are hard elastic spheres — it is usual to assume that the molecules having velocity-components lying within any small specified limit are, at every instant throughout the motion of the gas, distributed at random, independently of the positions or velocities of the other molecules, provided only that two molecules do not occupy the...