Maxwell speed distribution

In summary, the conversation involves a person being stuck in a definite integral related to the Maxwell speed distribution and wanting to calculate the fraction of Ar in Mars. They mention using the escape velocity and asking about integrating and evaluating between certain values. Eventually, they mention finding tabulated values for the error function or using numerical integration.
  • #1
b.hessen
2
0
halo, I´m stuck in an definite integral...

P(v)=4π (M2πRT)3/2⋅v2⋅e−Mv2nRT (maxwell speed distribution)

How can I calculate the fraction of Ar in mars?

pd. I got already the scape velocity

But... How can I intregrate and evaluate between (0, 5XE3 m/s) or (5XE3 m/s, infinite) ??

Is there any tables for evaluate this??

thanks
 
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  • #2
You can at least find tabulated values for the error function, erf(x) = 0∫x dx' exp(-x'^2). It might be easier just to plug in the numbers and integrate numerically, for example by using wolfram alpha.
 
  • #3
thanks...
I calculated in Origin 8.5 (five minutes) trapezoids area... 50 000 intervals... It work as well and "rough" solution, good for giving a fast solution.
 

1. What is the Maxwell speed distribution?

The Maxwell speed distribution is a probability distribution that describes the distribution of speeds for a gas at a certain temperature. It is named after physicist James Clerk Maxwell and is commonly used in statistical mechanics to describe the behavior of gases.

2. What is the significance of the Maxwell speed distribution?

The Maxwell speed distribution is significant because it helps us understand the behavior of gases at different temperatures. It also allows us to calculate important properties such as the average speed, most probable speed, and root-mean-square speed of gas molecules.

3. How is the Maxwell speed distribution calculated?

The Maxwell speed distribution is calculated using the Maxwell-Boltzmann distribution equation, which takes into account the temperature and mass of gas molecules. It is a continuous function that gives the probability of a gas molecule having a certain speed at a given temperature.

4. What is the relationship between temperature and the Maxwell speed distribution?

The temperature of a gas directly affects the shape of the Maxwell speed distribution. As the temperature increases, the distribution curve becomes broader and flatter, indicating a wider range of speeds for gas molecules. At higher temperatures, there is also a higher probability of finding gas molecules with higher speeds.

5. How does the Maxwell speed distribution relate to the kinetic theory of gases?

The Maxwell speed distribution is a direct result of the kinetic theory of gases, which describes the behavior of gas molecules in terms of their motion and collisions. The distribution shows that gas molecules have a range of speeds, with some moving faster and others moving slower, supporting the principles of the kinetic theory.

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