Kinetic theory equations

That first one you quoted is the average kinetic energy.

What do you mean?

Average kinetic energy is $\bar{\left(\frac{1}{2}mv^2\right)} = \frac{1}{2}m\bar{v}^2$ which is your first expression.

but how can I work out the average kinetic energy for nitrogen from that equation when I only have mass and temperature?

What is the average kinetic energy at 288K of molecules of the following gases: Nitrogen

(equations I'm pretty sure I need to use)
1/2m<c^2> = 3/2kT
pV = 1/3Nm <c^2>
pV = NkT

I know I can use the relative atomic masses from the periodic table for m but just mass and temperature isn't enough information to work out the kinetic energy (I think), can anyone help me out? Are there any assumptions i'm missing?

Average kinetic energy is $\bar{\left(\frac{1}{2}mv^2\right)} = \frac{1}{2}m\bar{v}^2$ which is your first expression.

Your first equation is the average kinetic energy and it depends solely on your value for $T$; there is no mass dependence.


$\bar{T} = \frac{1}{2}m\bar{v}^2 = \frac{3}{2}k_b{T}$