By David H Trevena, David H. Trevena
Thirty years educating adventure were condensed into this concise introductory e-book on Statistical Mechanics. perfect for moment and 3rd yr undergraduates in physics, utilized arithmetic, actual chemistry, chemical engineering, metallurgy, fabrics technology and polymer technology.
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Extra info for Statistical Mechanics: An Introduction
Sample text
We next use the above example of helium to show t h a t there are many more levels t h a n a t o m s . In doing so we are following the procedure given by Wilks (1961). T h e velocities of t h e helium a t o m s can b e measured by a rotating d r u m method such as t h a t described in T a b o r ' s (1979) book Gases, liquids and solids, 2nd edition. Chapter 4. 5 x 10^ m s " * corresponding to an energy of 2 χ 10~^°}. So the energy levels e range from the lowest values to at least this value of ε = 2 χ 1 0 ~ ' ° J .
Since both β and Τ are the same for our two assemblies, this suggests t h a t β is some sort of measure of the t e m p e r a t u r e , T. 4. However, we now take an assembly which is no longer isolated since we shall gradually add a quantity of heat 6Q to it. This means t h a t in our previous {N, U, V) description of an assembly Ν and V will both be constant but U will not. Since the es depend on V they will not change as the heat 6Q is added but the ns will adjust in value to keep Ω at a m a x i m u m .
10) we get In fNk-\-gk\ . + Psk = 0. 12) This is the Bose-Einstein distribution function. 4 T H E D I L U T E G A S : T H E C L A S S I C A L L I M I T We now consider the case of a 'dilute' gas, by which we mean one for which Nk « gk for all values of k; in other words the energy states are very thinly populated. 9) 42 A m o r e d e t a i l e d t r e a t m e n t of g a s e s [Ch. 6. 8). s. s. is approximately equal to