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

In summary, the conversation discusses finding the expression for pressure of a 2-D gas in terms of velocity. It involves integrating velocity and angle to get the speed distribution and then using this to calculate the number of molecules and change in momentum for one molecule to find pressure.
  • #1
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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:

[tex] f_{(v^2)} = (\frac{a}{\pi}) e^{-av^2} , a = \frac{m}{2kT} [/tex]

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

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

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

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

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

Is that right?
 
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  • #2
That looks right to me.
 

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

1. What is the formula for calculating pressure in a 2D gas?

The formula for calculating pressure in a 2D gas is P = Nm^2/2A, where P is the pressure, N is the number of particles, m is the mass of each particle, is the average speed of the particles, and A is the area of the container.

2. How do I find the expression for in a 2D gas?

The expression for in a 2D gas can be found using the equation v = √(2kT/m), where k is the Boltzmann constant, T is the temperature, and m is the mass of each particle.

3. What units are used for pressure in a 2D gas?

The units for pressure in a 2D gas are typically expressed in pascals (Pa) or atmospheres (atm). However, any unit of force per unit area can be used as long as it is consistent throughout the calculation.

4. Can I use this formula for any 2D gas, regardless of the type of particles?

Yes, this formula can be used for any 2D gas as long as the particles are ideal gases. This means that the particles do not interact with each other and the volume of the particles is negligible compared to the container they are in.

5. How does temperature affect the pressure in a 2D gas?

According to the ideal gas law, pressure is directly proportional to temperature. This means that as temperature increases, the pressure in a 2D gas will also increase. This relationship is reflected in the formula for pressure in a 2D gas, where temperature is a factor in both the speed and mass of the particles.

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