The Maxwell Speed Distribution in 2D

In summary, the conversation was about a homework problem involving finding the number of states with a certain speed and normalizing an integral. The person had tried various approaches but was struggling with the integration and asked for help. They then realized they could use a substitution to make the integral easier.
  • #1
fatherdaly
8
0

Homework Statement


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It seemed much easier to screencap than to write out.

Homework Equations



It helps to know that the number of states with speed between u and u+du is 2pi*u du

The Attempt at a Solution



I've tried quite a few things but every time I get to trying to normalise I either get stuck integrating by parts over and over, or using http://en.wikipedia.org/wiki/Gaussian_integral" [Broken]<that, which doesn't arrive at the answer wanted.

If someone could give me a push in the right direction it would be much appreciated.
 
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  • #2
You need some substitution to make the integral doable.
 
  • #3
Ok so I have the integral of v*exp(-[tex]\alpha[/tex]v2) dv between 0 and infinity to normalise. I don't know how a substitution would help because you would still have two functions multiplied by one another.

Edit: I think I'm being stupid. I've substituted for alpha*v^2. Hopefully it will work.
 
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1. What is the Maxwell Speed Distribution in 2D?

The Maxwell Speed Distribution in 2D is a mathematical model that describes the distribution of speeds of particles in a two-dimensional gas at a given temperature. It is based on the Maxwell-Boltzmann distribution, which is a similar model for three-dimensional gases.

2. How does the Maxwell Speed Distribution in 2D differ from the 3D version?

The main difference between the two distributions is the number of dimensions involved. The 2D version only takes into account the speed of particles in two dimensions, while the 3D version considers all three dimensions. This means that the 2D distribution will have a narrower range of speeds compared to the 3D distribution.

3. What factors affect the shape of the Maxwell Speed Distribution in 2D?

The shape of the Maxwell Speed Distribution in 2D is affected by two main factors: temperature and particle mass. As temperature increases, the distribution becomes wider and flatter. And as particle mass increases, the peak of the distribution shifts towards lower speeds.

4. Why is the Maxwell Speed Distribution in 2D important in physics?

The Maxwell Speed Distribution in 2D is important because it helps us understand the behavior of gases and the motion of particles at the molecular level. It also has practical applications in fields such as thermodynamics, statistical mechanics, and fluid dynamics.

5. Can the Maxwell Speed Distribution in 2D be applied to real-world systems?

Yes, the Maxwell Speed Distribution in 2D can be applied to real-world systems such as gases in a two-dimensional container. It provides a useful approximation for the behavior of particles in these systems, and its predictions have been confirmed by experiments.

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