Download PDF by Joseph Kestin: A Course in Statistical Thermodynamics
By Joseph Kestin
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Extra resources for A Course in Statistical Thermodynamics
This is due to the fact that there are now no rigid constraints assumed 50 2. STATISTICAL THERMODYNAMICS AND MECHANICAL MODELS in the model and the position of every atom in the molecule is specified by three coordinates. Given a polyatomic molecule consisting of n atoms, we must discern two cases. When the molecule is nonlinear, we have 7=3«; / t r + / r = 3 + 3 = 6, and / v = 3/i - 6 = 3(/i - 2) (nonlinear). 10) For linear molecules, / = 3/i; ftt+fr 3 + 2 = 5, and fy = 3n-5 (linear). 11) When the system contains N noninteracting molecules, the total number of degrees of freedom is simply equal to the above numbers multiplied by N.
1) In this way the study of the distribution of momentum components over the molecules has been made equivalent to the study of the distribution of points in the phase space. For a given network of cells, it now suffices to indicate the number of molecules, n, contained in each cell, the occupation numbers, in order to complete the description. Z l / y / Ax / \ Δζ t-—■ \y T z X- */ / / V X X (a) P. 1. Cells in the physical and momentum spaces: a, physical space; b, momentum space. Even this scheme is not entirely acceptable, since molecules cannot be counted and their momenta cannot be measured.
In the case of solids, crystalline materials are imagined to consist of regular arrays of atoms arranged in characteristic lattices in the physical space. Every crystal lattice is assumed to consist of a large number of identical unit cells, and the resulting symmetries are said to determine the characteristic shapes and properties of macroscopic crystals. The atoms in the lattice are supposed to be linked to all others with elastic bonds. The only motions in which the atoms can participate are characteristic vibrations under the restoring forces which the links exert upon them.
A Course in Statistical Thermodynamics by Joseph Kestin