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?

 

[asteriatic]

Yes, your assumption is correct. The area under a Maxwell-Boltzmann Distribution curve represents the total energy of the system. This is because the y-axis represents the number of molecules at a given energy level, and the x-axis represents the energy of those molecules. Multiplying the number of molecules by their energy at a given point gives the total energy of those molecules in the system. Therefore, the total area under the curve represents the total energy of all the molecules in the system. This is a useful tool for understanding the distribution of energies within a system and can be used to calculate important thermodynamic properties such as the average energy and temperature of the system.