Derivation of Boltzmann Equation

In summary, the conversation is about the Boltzmann equation and its relation to statistical mechanics and kinetic theory. The conversation also mentions the availability of the equation on Wikipedia and a link to the original paper written by Boltzmann himself. The conversation ends with a thank you to Physics Forum and MIT for providing resources to learn more about the topic.
  • #1
quantum123
306
1
Hi:

How do you derive the Boltzmann equation?
Thanks.
 
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  • #2
I made up some seminar notes on this... Let's see...

This should be found in any standard statistical physics text.
 

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  • #3
Hi:
What you have given is Boltzmann distribution.
I want Bolztmann equation.
The former is statistical mechanics, the latter is kinetic theory.
Kinetic theory has gone out of fashion somewhat, but I am still quite interested in it.
 
  • #5
Does anyone have the original paper written by Boltzmann himself (translated in English)?
 
  • #7
No I do not have access.
You mean you still have to pay $$$ for a piece of paper written 200 years ago?
That is discouraging.
 
  • #8
http://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2007/lecture-notes/
 
Last edited by a moderator:
  • #9
Wow, thanks Physics Forum and MIT.
I will go read it.
 

1. What is the Boltzmann equation?

The Boltzmann equation is a mathematical formula that describes the evolution of the probability distribution of particles in a gas. It is used to understand how the individual particles in a gas behave and interact with each other.

2. Who developed the Boltzmann equation?

The Boltzmann equation was developed by Austrian physicist Ludwig Boltzmann in the late 19th century. He was a pioneer in the field of statistical mechanics and is best known for his work on the thermodynamic properties of gases.

3. What is the significance of the Boltzmann equation?

The Boltzmann equation is significant because it allows us to make predictions about the behavior of a gas at the microscopic level. It provides a link between the macroscopic properties of a gas, such as temperature and pressure, and the individual particles that make up the gas.

4. How is the Boltzmann equation derived?

The Boltzmann equation is derived from the Boltzmann transport equation, which describes the evolution of a distribution function in phase space. This equation takes into account the interactions between particles and considers the effects of collisions and external forces on the distribution function.

5. What are some applications of the Boltzmann equation?

The Boltzmann equation has many applications in physics and engineering. It is used to study the properties of gases, liquids, and solids, and has been applied to fields such as fluid dynamics, plasma physics, and astrophysics. It is also used in the development of new materials and technologies, such as semiconductors and nanotechnology.

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