Nitrogen Gas Molecule Speeds and Temperature Relationship

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To determine the temperature of nitrogen gas (N2) where 94.7% of molecules have speeds less than 1500 m/s, the relationship between molecular speed and temperature must be applied. The root mean square speed (Vrms) can be calculated using the equation Vrms = sqrt(3kt/m), where k is the Boltzmann constant and m is the molar mass of N2. The given percentage indicates that the speed of 1500 m/s corresponds to 1.6 times the Vrms, allowing for the calculation of Vrms. By substituting Vrms back into the equation, the temperature can be derived. Understanding these relationships is crucial for solving the problem effectively.
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Homework Statement



Fractions of Molecules in an Ideal Gas with Speeds Less than Various Multiples of v/v_{\rm rms} in the textbook. The molar mass of {\rm{N}}_2 is 28.0 {\rm{ g/mol}}.


For a gas of nitrogen molecules {{\rm{N}}_2 } , what must the temperature be if 94.7\% of all the molecules have speeds less than 1500 \rm m/s?

Homework Equations



Vrms = sqrt(3kt/m)

The Attempt at a Solution



Really don't know where to start with the percentages and the relevance of the fracitons of molecules in an ideal gas with speeds less than various multiples etc??

Any help?
 
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hmmmmmmmmm...:confused:
 
I suppose there is a table in your book which tells you that 94.7% will have a speed smaller than 2x the rms velocity. You now know that 94.7% has a speed smaller than 1500m/s.
It should be easy to get the rms speed from that and then the temperature from your equation
 
I have tried it.

It says 94.7% have a speed less than (v/v_rms = 1.6). this is confsuing me. What does this mean? Clearly from that I can find v_rms, and plug it into the given equation above.
 
How would you use the figure that I am given to find the Vrms ??
 
can you state exactly what is given in your book?
 
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