What Temperature Gives Nitrogen Molecules an RMS Speed of 1.5 m/s?

Using the equation and conversion factors, you can easily calculate the temperature. In summary, to find the temperature at which nitrogen molecules have an rms speed of 1.5, you can use the equation V=(3*K_b*T/m)^.5 and the mass of nitrogen (4.677E-26 kg) to calculate the temperature to be 0.0025 kelvin.
  • #1
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Homework Statement



1.5 is a typical walking speed.
At what temperature would nitrogen molecules have an rms speed of 1.5 ?


Homework Equations



V=(3*K_b*T/m)^.5
V is the rms speed
K_b is Boltzmann's constant
T is temp in kelvin
m is mass


The Attempt at a Solution



I am going to make the foolish assumption that when they mean mass, they mean the mass of one nitrogen molecule. So the mass of a proton and a neutron is 1.67E-27kg and the mass of an electron is 9.11E-31kg. One nitrogen atom has 7 protons, 7 neutrons and 7 electrons and multiply that by two because of the second nitrogen atom. So ((1.67E-27)(14)+(7)(9.11E-32))(2)=4.677E-26 kg.

Now I rearrange my equation to solve for T and plug in.

mV^2/(3*K_b)=T

(4.677E-26)(1.5)^2/(3*K_b) = .0025 kelvin

Am I close?

Thanks!
 
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  • #2
Never mind. My answer is correct.
 
  • #3
Good job. For future reference, it may be easier and quicker to look up the mass of nitrogen or other elements in a periodic table.
 

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