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Topic: Maxwell-Boltzmann Velocity Distribution  (Read 9018 times)

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Offline interminable

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Maxwell-Boltzmann Velocity Distribution
« on: March 08, 2009, 04:07:26 PM »
I've got a problem that I'm supposed to solve by spreadsheet:

The Maxwell-Boltzmann velocity distribution allows for estimation of the fraction of molecules that have velocities in excess of the escape velocity (11.2 km/s).
Calculate the fraction of hydrogen atoms at 1500 K that have velocities in excess of 11.2 km/s.

Given:  ( :delta: N)/N = {4pi*(m/(2pi*k*T))^1.5 * exp(-mv^2/(2kT))}  :delta: v
And it says I'm supposed to use a spreadsheet to evaluate the right side of this equation.

I've set up a spreadsheet, and made a column with velocity values and another column for the right side of the equation - but I'm not sure how this leads me to finding the fraction, since evaluating the right hand side gives me a different fraction for each velocity. The  :delta: v throws me off as well, because we're looking for atoms with velocities from 11.2 km/s to infinity?

Help would be greatly appreciated, thanks!

Offline Hunt

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Re: Maxwell-Boltzmann Velocity Distribution
« Reply #1 on: March 20, 2009, 06:38:58 PM »
I think you're just being asked to solve the integral using microsoft excel because the integral limits are from 11.2 till infinity i.e. you need a software or a graphing calculator to solve it. Dont let the delta v confuse you , you need to set it to an infinitesimal change dv and then integrate f(v)dv with the proper integral boundaries.

Offline Hunt

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Re: Maxwell-Boltzmann Velocity Distribution
« Reply #2 on: March 20, 2009, 06:44:54 PM »
P.S. I'm not so sure Excel can solve improper integrals.

Offline interminable

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Re: Maxwell-Boltzmann Velocity Distribution
« Reply #3 on: March 21, 2009, 08:13:10 PM »
It was just the fact that it was going to infinity that was confusing me, because the answers I was getting didn't seem to make any sense - i.e. way too many atoms escaping to be logical.

Worked out when I just did a sort of Riemann sum idea, and summed from 0 to 11.2 and subtracted that answer from 1.

Thanks.

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