Calculating Pressure in a 2D Gas: Find Expression for <v>

[unscientific]

Homework Statement

Find an expression for the pressure of a 2-D gas in terms of <v>.

Homework Equations

The Attempt at a Solution

In 2D, velocity distribution is:

$$f_{(v^2)} = (\frac{a}{\pi}) e^{-av^2} , a = \frac{m}{2kT}$$

Integrate all possible angles to get speed distribution and normalize to get speed distribution:

$$w_{(v)} = 2a v e^{-av^2}$$
Number of molecules traveling between speed v and v+dv, at angles between θ and θ + dθ per unit area = $$n \frac {dθ}{2\pi}w_{(v)} dv$$
= $$n \frac{a}{\pi}ve^{-av^2} dv dθ$$

To find pressure, take the above expression * change in momentum of one molecule / (L dt)

$$dP = \frac{n \frac{a}{\pi}ve^{-av^2} dv dθ * (L v cosθ dt) * (2mv cosθ) }{L dt}$$

Then we integrate v from 0 to ∞, θ from 0 to ∏/2.

Is that right?

 

[TSny]

That looks right to me.