Escape Velocity of Heated Nitrogen: A Scientific Inquiry

[willstaruss22]

What is the escape velocity of nitrogen heated to 325 K?

 

[Simon Bridge]

Same as the escape velocity for anything.
http://en.wikipedia.org/wiki/Escape_velocity

What you are usually interested in is if the mean velocity of the gas at some temperature is greater than the escape velocity ... in which case you need the relationship between mean velocity and temperature.

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aside:
"the escape velocity of the Earth" would be the minimum speed you need to escape the Earth's gravitational field from it's surface.
"the escape velocity of Nitrogen" would be the minimum speed you need to escape a Nitrogen (atom? molecule?)'s gravitational field from it's surface.
But I'm guessing that is not what you mean :)

 

[willstaruss22]

Yes i meant the escape velocity from the surface if molecular nitrogen was heated to 325 K. I would imagine it would be faster because the colder the temperature the lower the escape velocity.

 

[Simon Bridge]

Again - the escape velocity does not depend on temperature.
You want to look into the kinetic theory of gasses:
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/kintem.html
... since Nitrogen is diatomic, there's an extra two degrees of freedom so:$$KE_{avg}=\frac{5}{2}kT$$ [edit: incorrect - that's all energy ... must be half asleep!]

... a gas at a particular temperature will have a range of speeds - given by the Maxwel-Boltzmann distribution.

 

[mfb]

... since Nitrogen is diatomic, there's an extra two degrees of freedom so:$$KE_{avg}=\frac{5}{2}kT$$

The energy corresponding to rotation does not influence the escape, however. It is kinetic, but it does not change the speed of the molecule.

@willstaruss22: I think it would be more useful if you ask all questions about the atmosphere in a single topic.

 

[Simon Bridge]

I'd have though that energy going into the rotation would be energy not available for translation?
[edit] Oh wait - I see where I stuffed up <sheepish>