Calculating % of molecules at given temperature with a given velocity

AI Thread Summary
To calculate the percentage of water molecules at 300K with speeds greater than 1 km/s, the integral of the velocity distribution must be evaluated from 1000 m/s to infinity. The user attempted to simplify the integral but received a result of zero, indicating a possible error in the calculation or setup. Clarification is needed on how to properly account for the limits of integration and the constants involved. The discussion emphasizes the importance of correctly applying the principles learned in class to achieve an accurate numerical evaluation. Proper guidance on the integration process is essential for resolving the issue.
r34p3rex
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Homework Statement



What percentage of molecules in water at 300K will have a speed greater than 1 km/s (evaluate numerically)?


Homework Equations


2}e^{-\frac{mv^{2}}{2KT}}dv.gif



The Attempt at a Solution


Based on what we did in class, I take it I'm supposed to integrate the distribution from 1000 to infinity.

After moving the constants out of the integral, I'm left with this:
gif.gif


I know that

gif.gif


But how do I account for the fact that I'm only interested in the integral between 1000 and infinity?
 
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The instructions say to evaluate the answer numerically.
 
SammyS said:
The instructions say to evaluate the answer numerically.

I punched it into my calculator and after a few minutes of calculating, it tells me the integral is 0.

Am I doing something wrong?
 
r34p3rex said:
I punched it into my calculator and after a few minutes of calculating, it tells me the integral is 0.

Am I doing something wrong?
Probably something is being done wrong, or something is set wrong.
 

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