# Maxwell-Boltzmann curve

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does the area under a Maxwell-Boltzmann curve show the total energy of a system?

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#4

(Original post by

does the area under a Maxwell-Boltzmann curve show the total energy of a system?

**jsmith6131**)does the area under a Maxwell-Boltzmann curve show the total energy of a system?

_{a}line, it's the total number of particles that don't have enough energy to react, and to the right of it is the total number of particles that do have enough energy to react.

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no guys just imagine a standrd curve JUST 1 with no Ea line.

The TOTAL AREA under the ENTIRE curve - does that equal the area of the system?

The TOTAL AREA under the ENTIRE curve - does that equal the area of the system?

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thats is abundantly obvious from the y-axis (no of molecules) but area is base*height

so no. molecules * energy so I would presume that total area = total energy

do you agree

so no. molecules * energy so I would presume that total area = total energy

do you agree

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#9

I haven't done chemistry since A level , but if a point on the Maxwell-Boltzmann curve represents the number of particles at a particular energy level, then the integral over the entire curve, that is to say the area you are describing, should represent the number of particles over all energy levels, i.e the total number of particles in the system. (I hope :P )

Further evidence for this would be that the area to the left of the Ea line represents the number of particles that don't have energy to react, and area to the right is number of particles that do have sufficient energy to react (from the definition of activation energy). Thus considering the area on both sides must be the total number of particles, since you would be adding the number of particles that cannot react, to the number of particles that can (and because this forms a partition in the system, it must be including all particles)

Further evidence for this would be that the area to the left of the Ea line represents the number of particles that don't have energy to react, and area to the right is number of particles that do have sufficient energy to react (from the definition of activation energy). Thus considering the area on both sides must be the total number of particles, since you would be adding the number of particles that cannot react, to the number of particles that can (and because this forms a partition in the system, it must be including all particles)

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#11

trust me the area under the graph represents the total number of molecules present! Dont listen to these idiots.

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#12

(Original post by

a little confused...are you agreeing with me or not?

**jsmith6131**)a little confused...are you agreeing with me or not?

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#13

The Maxwell-Boltzmann distribution can be used to describe the distribution of velocities (or speeds) of the molecules as well as momentum, though it is frequently used to express the distribution of energies, as kinetic energy depends on speed.

So when you ask about what the area under the curve represents, you need to say what you are plotting on the curve.

Are you talking about a curve of the number of molecules against

Are you referring to a probability density curve (probably) or a cumulative curve?

If you are asking about the probability density curve then the area under any portion of it is the total number (or fraction*) of molecules having that range of speeds, velocities, momenta, or energies.

http://www.chemguide.co.uk/physical/...mperature.html (scroll down)

(Or any search for "area under the Maxwell-Boltzmann curve")

* In a probability density curve the total area under the curve usually represents the total number of molecules or 100%. So a portion of the curve represents that fraction or % of the total.

So when you ask about what the area under the curve represents, you need to say what you are plotting on the curve.

Are you talking about a curve of the number of molecules against

**velocity**(range) or about number of molecules in a particular**energy**range?Are you referring to a probability density curve (probably) or a cumulative curve?

If you are asking about the probability density curve then the area under any portion of it is the total number (or fraction*) of molecules having that range of speeds, velocities, momenta, or energies.

http://www.chemguide.co.uk/physical/...mperature.html (scroll down)

(Or any search for "area under the Maxwell-Boltzmann curve")

* In a probability density curve the total area under the curve usually represents the total number of molecules or 100%. So a portion of the curve represents that fraction or % of the total.

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no I am referring to the curve

y-axis: no. molecules

x-axis: energy

y-axis: no. molecules

x-axis: energy

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#15

**jsmith6131**)

does the area under a Maxwell-Boltzmann curve show the total energy of a system?

If you are talking about the Maxwell-Boltzmann curve for molecular energies then

it is a so called probability density curve.

So the area under it (or any portion of it) represents the number of molecules (or rather the fraction of the total number) that have energies between the values of E on the x axis.

Mathematically, a probability density curve is not the same as a standard curve you plot like a velocity time graph. Statistical functions behave differently.

The answer to

**your**question is "no".

Did you look at the link I gave?

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yes that was one of the sources I came across when looking for the answer

but my book had a question in it asking what does the area under the maxwell-bolztmann energy curve represent, i said "no of molecules in the system" and this was wrong

so i figured it must be something else!

but my book had a question in it asking what does the area under the maxwell-bolztmann energy curve represent, i said "no of molecules in the system" and this was wrong

so i figured it must be something else!

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#18

I agree completely! But everyone at physics class (including the teacher!) made fun of me for doing so. They think it is the total number of molecules.

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#19

(Original post by

no guys just imagine a standrd curve JUST 1 with no Ea line.

The TOTAL AREA under the ENTIRE curve - does that equal the area of the system?

**jsmith6131**)no guys just imagine a standrd curve JUST 1 with no Ea line.

The TOTAL AREA under the ENTIRE curve - does that equal the area of the system?

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#20

x-axis: energy, 'E'

so the area becomes (if we consider a straight line of zero gradient):

area= energy multiplied by no of molecules/energy

= # of molecules

Q.E.D.

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