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445lec15

# 445lec15 - PHYS 445 Lecture 15 Equipartition theorem...

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PHYS 445 Lecture 15 - Equipartition theorem 15 - 1 © 2001 by David Boal, Simon Fraser University. All rights reserved; further resale or copying is strictly prohibited. Lecture 15 - Equipartition theorem What's Important: equipartition theorem applications: ideal gas, harmonic oscilator, 3D lattice Text : Reif Skip Secs. 7.1 to 7.4 Cheap tricks: equipartition theorem A simple expression for the mean energy per degree of freedom arises when the total energy of a system is quadratic in its variables; e.g. K = p 2 /2 m or V = kx 2 /2 separates into single-variable expressions, such as K = p 1 2 /2 m 1 + p 2 2 /2 m 2 . For a given degree of freedom (labeled by an index i ), let us write the energy as i = b p i 2 where p i could be a coordinate or its time derivative. Then i = i exp( - ß [ E rem + i ]) dq 1 .. dq f dp 1 .. dp f exp( - ß [ E rem + i ]) dq 1 .. dq f dp 1 .. dp f where E rem is the remaining energy in the system, other than i : E rem = E - i . Because the energy separates into a piece that depends on p i , and the residue which

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