# Temperature of nitrogen

1. May 3, 2010

### hover

1. The problem statement, all variables and given/known data

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

2. Relevant 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

3. 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!

2. May 3, 2010

### hover

Never mind. My answer is correct.

3. May 3, 2010

### Redbelly98

Staff Emeritus
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.