Register to reply

Maxwell-boltzmann distribution

by CatWoman
Tags: distribution, maxwellboltzmann
Share this thread:
CatWoman
#1
Aug1-09, 12:51 PM
P: 30
1. The problem statement, all variables and given/known data

The area under the Maxwell-Boltzmann distribution of speeds of molecules of mass m in a gas at temperature T above a speed v can be estimated as

1/2 (m/2πkT)^(1/2) v exp(-(mv^2)/kT)

Show that the maximum likely speed of a gas molecule in the air in a typical room (i.e. the speed above which the Maxwell-Boltzmann distribution gives a probability of 1/N, where N is the number of molecules in the room) is of order 4<v^2>^1/2 (where <v^2>^1/2 = (3kT/m)^1/2).



2. Relevant equations



3. The attempt at a solution

I think the question means that the Maxwell-Boltzmann distribution curve is approx a 1/N curve at and above a certain value of N. I was going to equate the max-bolt curve equation to 1/N, except the question gives the equation for the area. Then I thought I should integrate the 1/N curve to get the area then 1/N dN gives ln N. Then I can equate the areas. Then use PV=NkT so that

ln(PV/kT) = 1/2 (m/2 pi kT) exp -(mv/kT)

I was then going to plug in values for T (293Kelvin) and m (mass of nitrogen molecule) but this is really hard to solve for v so I think it must be wrong.

Any help would be really great! Thanks
Phys.Org News Partner Science news on Phys.org
World's largest solar boat on Greek prehistoric mission
Google searches hold key to future market crashes
Mineral magic? Common mineral capable of making and breaking bonds
Geezer
#2
Aug7-09, 02:07 AM
P: 292
If you recall from calc, when you want to find a max or min, you need to take a derivative...
CatWoman
#3
Aug7-09, 04:22 AM
P: 30
Oh yeah! So if iI have the formula for the area then I need to differentiate twice then set equal to zero to get the maxima? I did this and got V^2=(18 pi k T/m)^1/2. This doesn't match the answer so I don't know if my working is wrong or something else.


Register to reply

Related Discussions
Maxwell Boltzmann distribution Introductory Physics Homework 2
Maxwell-Boltzmann Distribution Advanced Physics Homework 1
Maxwell-Boltzmann Distribution Introductory Physics Homework 3
Maxwell/Maxwell-Boltzmann Distribution Classical Physics 1
Maxwell-Boltzmann Distribution Introductory Physics Homework 1