Calculating % of molecules at given temperature with a given velocity

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Homework Help Overview

The problem involves calculating the percentage of water molecules at a temperature of 300K that have a speed greater than 1 km/s. The context is rooted in statistical mechanics and molecular speed distributions.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to integrate the speed distribution from 1000 m/s to infinity. There is uncertainty about how to properly set up the integral and account for the specific range of interest.

Discussion Status

Some participants have attempted numerical evaluation of the integral but report results that raise questions about the correctness of their approach. There is an ongoing exploration of potential errors in the calculations or setup.

Contextual Notes

Participants note the requirement to evaluate the answer numerically, which may impose constraints on their methods. There is also a suggestion that assumptions or settings in their calculations might be incorrect.

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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