What Does the Area Under a Maxwell-Boltzmann Distribution Curve Indicate?

[RCB]

Homework Statement

What does the area under a Maxwell Boltzmann Distribution curve represent

Homework Equations

The Attempt at a Solution

So I know that the y-axis is no. molecules
x-axis is energy of molecules

I also know that the area under the graph is proportional to the total no. of molecules in the system.

However, would I be correct in assuming the total area under the curve is equal to the total energy within a system. I concluded this because no. molecules * energy (at a point) should give the total energy within a system

Is this assumption correct?

 

[Simon Bridge]

So I know that the y-axis is no. molecules
x-axis is energy of molecules

That doesn't sound right - surely the vertical axis is probability?
Check your concepts. It's not a bar graph.

 

[Andrew Mason]

Homework Statement

What does the area under a Maxwell Boltzmann Distribution curve represent

Homework Equations

The Attempt at a Solution

So I know that the y-axis is no. molecules
x-axis is energy of molecules

I also know that the area under the graph is proportional to the total no. of molecules in the system.

However, would I be correct in assuming the total area under the curve is equal to the total energy within a system. I concluded this because no. molecules * energy (at a point) should give the total energy within a system

Is this assumption correct?

Yes, if it is a Maxwell-Boltzmann energy distribution.

If the distribution is normalized so that the area under the graph is 1, the area under the curve between two energy values can be thought of as a probability of finding a molecule in that energy range.

AM

 

[cepheid]

Yes, if it is a Maxwell-Boltzmann energy distribution.

If the distribution is normalized so that the area under the graph is 1, the area under the curve between two energy values can be thought of as a probability of finding a molecule in that energy range.

AM

Or alternatively it can be thought of as the fraction of the total number of particles that lie in that energy interval (given a large enough sample), correct?