Pressure for 2-D gas

1. Jan 10, 2014

unscientific

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

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

2. Relevant equations

3. 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 travelling 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?

2. Jan 11, 2014

TSny

That looks right to me.