- #1

igowithit

- 6

- 1

## Homework Statement

Consider a gas of molecules of mass m at equilibrium at temperature T. Obtain an expression for the fraction of molecules having kinetic energy e = 1/2mC

^{2}in the range e to e + de.

This is problem 5.3, page 48 of Vincenti and Kruger's Intro to Physical Gas Dynamics

## Homework Equations

Maxwellian speed distribution

## The Attempt at a Solution

I'm not sure where to start really, so I don't have much of a solution.

If I were finding the fraction of molecules with kinetic energy LESS than 1/2mC

^{2}, I would integrate the speed distribution function from 0 to 1/2mC

^{2}. But I'm not sure about finding the fraction at exactly 1/2mC

^{2}.

My first thoughts were to change the speed distribution to an energy distribution by knowing that c

^{2}= 2e/m, and then integrating the kinetic energy distribution from 0 to inf to find the total kinetic energy. Then divide 1/2mC

^{2}by that total to find a fraction. Don't feel like this is right.

Anyone care to nudge me in the right direction?