Maxwell's Distribution: Integrating Over Velocity Spectrum

In summary, the conversation discussed the possibility of cutting off the Maxwell's distribution when taking into account the speed of light. It was mentioned that particles smaller than light could potentially lead to a cut-off.
  • #1
ChrisVer
Gold Member
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I have one question, I am sorry if it's stupid or something.

So, when we write down the Maxwell's distribution, we integrate over the spectrum of velocities... But that is from 0 to infinity.. (or minus infinitiy to infinity nevermind)
Is there any way someone can cut-off the above? Since we know that nothing can overcome EVER the speed of light?
 
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  • #2
ChrisVer said:
I have one question, I am sorry if it's stupid or something.

So, when we write down the Maxwell's distribution, we integrate over the spectrum of velocities... But that is from 0 to infinity.. (or minus infinitiy to infinity nevermind)
Is there any way someone can cut-off the above? Since we know that nothing can overcome EVER the speed of light?

Good question. See Maxwell–Jüttner distribution.
 
  • #3
If any thing is smaller than light particles then it is possible
 

FAQ: Maxwell's Distribution: Integrating Over Velocity Spectrum

What is Maxwell's distribution?

Maxwell's distribution, also known as the Maxwell-Boltzmann distribution, is a probability distribution that describes the distribution of velocities for particles in a gas at a given temperature.

How is Maxwell's distribution derived?

Maxwell's distribution is derived from the kinetic theory of gases, which assumes that gas particles are constantly moving and colliding with each other. By considering the energy and velocity of these particles, the distribution can be mathematically derived.

What is the significance of Maxwell's distribution?

Maxwell's distribution is important because it provides a fundamental understanding of the behavior of gas particles and helps explain various phenomena, such as the diffusion of gases and the pressure exerted by gases.

How does integrating over the velocity spectrum affect Maxwell's distribution?

Integrating over the velocity spectrum means summing up all the possible velocities of gas particles. This allows us to calculate the average velocity and other important properties of the gas, such as the root-mean-square velocity and the most probable velocity.

What are some real-world applications of Maxwell's distribution?

Maxwell's distribution has many practical applications, such as in the design of gas turbines and rocket engines, as well as in the study of atmospheric gases and molecular motion in chemical reactions.

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