# Why does corrected Maxwell Boltzmann have decimals?

• cooev769
In summary, the corrected Maxwell Boltzmann distribution accounts for the variation in particle energies in a gas or liquid, resulting in energy values that can be decimals. This is different from the original distribution, which assumes all particles have the same energy and only has whole number energy values. The presence of decimals in the corrected distribution indicates the variation in particle energies. The corrected distribution is useful for accurately representing energy distribution in gases and liquids, particularly in thermodynamics and statistical mechanics. While it can be applied to all gases and liquids, it is most accurate for systems at equilibrium with a large number of particles. In systems with fewer particles or non-equilibrium conditions, the distribution may not be as accurate.
cooev769
So I have just been reading up on statistical thermodynamics and have no idea why the bose-einstein, fermi dirac and maxwell boltzman are all integers, that makes sense, but then when you make the degenerate correction to the maxwell Boltzmann by dividing by N! we get decimal answers. Why is this?

Thanks!

What do you mean with "all integers"? There are several expressions that are not integers.
Unrelated: does the difference between 46444364765232142364752464 and 46444364765232142364752464.3 matter? Arbitrary numbers of course.

Because it is only an approximation.

## 1. Why does corrected Maxwell Boltzmann have decimals?

The corrected Maxwell Boltzmann distribution accounts for the fact that not all particles in a gas or liquid have the same energy. This means that the energy values in the distribution can be any decimal number, resulting in the distribution having decimals.

## 2. How is the corrected Maxwell Boltzmann distribution different from the original distribution?

The original Maxwell Boltzmann distribution assumes that all particles in a gas or liquid have the same energy, resulting in energy values that are only whole numbers. The corrected distribution takes into account the variation in particle energies, resulting in energy values that can be decimals.

## 3. What does the presence of decimals in the corrected Maxwell Boltzmann distribution indicate?

The presence of decimals in the corrected distribution indicates that not all particles in a gas or liquid have the same energy. This can be due to factors such as temperature variations or intermolecular collisions.

## 4. How is the corrected Maxwell Boltzmann distribution useful?

The corrected distribution allows for a more accurate representation of the energy distribution in a gas or liquid. This is particularly useful in fields such as thermodynamics and statistical mechanics, where understanding the distribution of particle energies is important.

## 5. Can the corrected Maxwell Boltzmann distribution be applied to all gases and liquids?

Yes, the corrected distribution can be applied to all gases and liquids. However, it is most accurate for gases and liquids that are at equilibrium and have a large number of particles. In systems with fewer particles or non-equilibrium conditions, the distribution may not accurately represent the energy distribution.

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