{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}