# Planck and Maxwell-boltzman distribution

• Entanglement
In summary, the conversation discusses the relation between two distributions - the Plank distribution and the Boltzmann-Maxwell distribution. The Plank distribution is applicable when particles are indistinguishable, while the Boltzmann-Maxwell distribution is used when particles are distinguishable. The topic was first encountered in a Statistical Modelling course and can be found on page 148-149 of Ross' Probability Models. The conversation ends with Bill expressing interest in refreshing his memory on the subject."
Entanglement
Is there a relation between these two distributions ?

ElmorshedyDr said:
Is there a relation between these two distributions ?

I can't say its something that these days the detail is familiar to me, being stuff from the dim past, but the Plank distribution is what you get if the particles are in principle indistinguishable. The Boltzmann-Maxwell distribution is when they are in principle distinguishable.

Interesting thing is I first came on this not in Physics but as an exercise in a Statistical Modelling course.

Added Later:
Couldn't resit refreshing my memory about it - it's on page 148-149 of Ross - Probability Models

Thanks
Bill

Last edited:

## 1. What is the Planck distribution?

The Planck distribution, also known as the Planck's law or Planck's function, is a mathematical formula that describes the distribution of energies of particles in a blackbody at a given temperature. It was first developed by German physicist Max Planck in 1900.

## 2. What is the significance of the Planck distribution?

The Planck distribution is significant because it provided a solution to the ultraviolet catastrophe, which was a problem in classical physics that stated that an ideal blackbody would emit infinite energy at high frequencies. The Planck distribution accurately describes the distribution of energies at all frequencies and is considered a cornerstone of modern physics.

## 3. What is the Maxwell-Boltzmann distribution?

The Maxwell-Boltzmann distribution is a statistical distribution that describes the speeds of particles in a gas at a given temperature. It was developed by Scottish physicist James Clerk Maxwell and Austrian physicist Ludwig Boltzmann in the late 19th century.

## 4. How does the Maxwell-Boltzmann distribution relate to the Planck distribution?

The Maxwell-Boltzmann distribution is a special case of the Planck distribution for a gas in thermal equilibrium. This means that at a given temperature, the distribution of energies of particles in a gas follows the Maxwell-Boltzmann distribution.

## 5. What are the practical applications of the Planck and Maxwell-Boltzmann distributions?

The Planck and Maxwell-Boltzmann distributions have many practical applications, including in thermodynamics, statistical mechanics, and astrophysics. They are used to calculate the properties of gases, such as pressure and energy, and are also applied in the study of black holes and the early universe.

### Similar threads

• Quantum Physics
Replies
13
Views
594
• Quantum Physics
Replies
4
Views
1K
• Quantum Physics
Replies
26
Views
2K
• Quantum Physics
Replies
4
Views
1K
• Quantum Physics
Replies
14
Views
760
• Quantum Physics
Replies
4
Views
1K
• Quantum Physics
Replies
23
Views
1K
• Quantum Physics
Replies
2
Views
1K
• Quantum Physics
Replies
35
Views
2K
• Quantum Physics
Replies
25
Views
1K