Published by Clarendon Press, Oxford in 1999. This book covers several chapters. The first and second laws of thermodynamics, statistical mechanis, Maxwell and Planck's distribution and fermi-bose particles.
Glass plate 0", Rotating drum Fig. 7.5 A schematic view of the apparatus used to study the distribution of speeds of particles emerging from a hole in an oven. The beam of particles passes through collimated slits before passing through a hole in a rotating cylinder. The particles take a finite time to cross the cylinder. The fastest particles hit the glass plate first. the slowest ones arrive later and are deposited on a different part of the glass plate. By studying the spatial distribution of the particles deposited on the plate we can infer the distribution of speeds of the particles.
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7.5. The beam is collimated and then passes through a tiny slit in a rotating drum. Typically the drum rotates at a frequency, j, of 5000 r.p.m. If the drum were ,at.rest, all the molecules in the collimated beam would strike the face opposite the slit. As the drum is rotating, the faster molecules in the beam arrive at a point slightly shifted from the point opposite the slit, the slower ones arrive at a point which is shifted much more. Suppose the drum has a diameter d. The time for a molecule of speed u to cross the drum is t = diu. In this time the drum rotates through an angle B = 27rfd/u. The faster molecules are shifted by a small angle, the slower ones by a large angle. By measuring the distribution of particles as a function of angle, we can infer the distribution of emerging particles as a function of speed. Ex periments that have been done ill this way have confirmed that the particles do follow the predicted distribution. In Fig. 7.
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6 we show some of the data collected by Miller and Kusch (1955) for thallium atoms. The data collected at two tem 'peratures fall on the same curve provided the amplitude of the peak is scaled to be two, and the speed is divided by the speed at the peak. The solid line shown in Fig. 7.6 is the theoretical cutve, eqn (7.5.2), scaled the same way.
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In many situations only the molecules that travel at high speed really matter. For example, evaporation from a liquid involves molecules crossing the surface of the liquid. The faster molecules are more able to leave than the slower. The rate at which a chemical reaction proceeds often varies with temperature. The high speed molecules which are present at high temperatures have enough energy to Molecular beams 157 :: .------~-l f(1I) I 10 [ 0.5
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