# MandysNotes

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## Thermodynamics and Statistical Mechanics

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Saturday, 08 February 2014 19:51

### Maxwell's Equations

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Gauss's Law:

$\nabla \cdot {\color{WildStrawberry} E} = {\color{RedOrange}4\pi} {\color{ForestGreen} \rho}$

Ampere's Law:

$\nabla \mathbf{\times} {\color{RoyalBlue} B } = \frac{{\color{RedOrange}4\pi}}{{\color{Goldenrod}c}} {\color{Purple} J } + \frac{1}{{\color{Goldenrod}c}} \frac{\partial {\color{WildStrawberry} E }}{ \partial t}$

Tuesday, 13 November 2012 19:33

### A Quick and Dirty Derivation of the Maxwell Distribution

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Suppose we are given a certain quantity of an ideal gas at some fixed temperature, and we want to know what sort of distribution of velocities to associate with this gas.
That is, given a range of velocities, $\Delta v = v_\beta - v_\alpha,$
what is the number of molecules, $\Delta n,$with velocities in the region of phase space $\Delta v= \Delta v_x \Delta v_y \Delta v_z?$