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

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Homework Help Overview

The discussion revolves around the interpretation of the area under a Maxwell-Boltzmann distribution curve, particularly in the context of molecular energy distributions. Participants are exploring the relationship between the area under the curve and the total number of molecules in a system, as well as its implications for energy representation.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify whether the area under the curve represents total energy or the total number of molecules. There is also a question about the correct interpretation of the axes of the graph, with some suggesting that the vertical axis represents probability rather than the number of molecules.

Discussion Status

There is an ongoing exploration of the assumptions regarding the area under the curve, with some participants affirming that it can represent probabilities under certain conditions. Multiple interpretations are being discussed, particularly regarding normalization and the implications for understanding molecular distributions.

Contextual Notes

Some participants are questioning the definitions and concepts related to the Maxwell-Boltzmann distribution, indicating potential confusion about the graph's representation and the assumptions being made about the area under the curve.

RCB
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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?
 
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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.
 
RCB said:

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
 
Andrew Mason said:
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?
 

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