- #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 = 1/2mC2 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 1/2mC2, I would integrate the speed distribution function from 0 to 1/2mC2. But I'm not sure about finding the fraction at exactly 1/2mC2.
My first thoughts were to change the speed distribution to an energy distribution by knowing that c2 = 2e/m, and then integrating the kinetic energy distribution from 0 to inf to find the total kinetic energy. Then divide 1/2mC2 by that total to find a fraction. Don't feel like this is right.
Anyone care to nudge me in the right direction?