[thomaskurian89]

Suppose I have a graph with velocity of a gas v on the x-axis and number of molecules N on the y-axis, how would I find the number of molecules with v>v_0, where v_0 is a given velocity?

[Repressor]

The area under the line corresponding to the velocities which you want.

[thomaskurian89]

(Original post by Repressor)
The area under the line corresponding to the velocities which you want.

But the area will have units vxN.

[notnek]

(Original post by thomaskurian89)
Suppose I have a graph with velocity of a gas v on the x-axis and number of molecules N on the y-axis, how would I find the number of molecules with v>v_0, where v_0 is a given velocity?

What kind of graph is this? Is it discrete, continuous?

[Podcaster]

(Original post by thomaskurian89)
But the area will have units vxN.

N is a dimensionless quantity. The graph, if a discrete histogram is saying you have 4 molecules with speed 20, 8 molecules with speed 25, 3 molecules with speed 21 and so on as an example. therefore the total number of molecules is 4x20 + 8x25 + 3x21. If the graph is continuous i.e 4.173 molecules with speed 2.182, 4.174 molecules with speed 9.02 or in other words a smooth curve you simply replace the sum with an integral. So the first reply was correct.

EDIT: that was averages related *******s. Read off the graph OP? Like find the corresponding Y value (number of molecules) to the minimum x value (velocity) and the sum of the numbers of molecules above that should equal the answer? i.e given velocity is 2 which corresponds to a y value of 20. If the y values go up to a max of 30 then 10 molecules have velocity greater than 2.

[thomaskurian89]

(Original post by notnek)
What kind of graph is this? Is it discrete, continuous?

Continuous

[notnek]

(Original post by Podcaster)
N is a dimensionless quantity. The graph, if a discrete histogram is saying you have 4 molecules with speed 20, 8 molecules with speed 25, 3 molecules with speed 21 and so on as an example. therefore the total number of molecules is 4x20 + 8x25 + 3x21.

4 molecules + 8 molecules + 3 molecules = 15 molecules

[thomaskurian89]

(Original post by Podcaster)
The graph, if a discrete histogram is saying you have 4 molecules with speed 20, 8 molecules with speed 25, 3 molecules with speed 21 and so on as an example. therefore the total number of molecules is 4x20 + 8x25 + 3x21.

Surely the total number of molecules is 4+8+3.

[Podcaster]

(Original post by notnek)


4 molecules + 8 molecules + 3 molecules = 15 molecules

(Original post by thomaskurian89)
Surely the total number of molecules is 4+8+3.

Late night technical error. Standby for corrections.

Ah right I was thinking of average velocity.

[thomaskurian89]

(Original post by Podcaster)
Read off the graph OP? Like find the corresponding Y value (number of molecules) to the minimum x value (velocity) and the sum of the numbers of molecules above that should equal the answer? i.e given velocity is 2 which corresponds to a y value of 20. If the y values go up to a max of 30 then 10 molecules have velocity greater than 2.

I have a continuous distribution, so that won't work.

[Podcaster]

(Original post by thomaskurian89)
I have a continuous distribution, so that won't work.

Well i don't know. Still pretty sure it has something to do with integrating though.

[dantheman1261]

Do you mean something like http://www.chem.ufl.edu/~itl/2045/lectures/d10_016.GIF (with 'number of' rather than 'fraction of' on the y-axis)?

[thomaskurian89]

(Original post by dantheman1261)
Do you mean something like http://www.chem.ufl.edu/~itl/2045/lectures/d10_016.GIF (with 'number of' rather than 'fraction of' on the y-axis)?

Yes.

[dantheman1261]

(Original post by thomaskurian89)
Yes.

It doesn't entirely make sense, but from what I gather, you just need the area under the graph from v_0 to v_max. Is this a chemistry question? The chemists might be able to give you a definitive answer.

Mathematically though, there are clearly an infinite number of points in each small interval, so taken literally, the graph says there are an infinite number of molecules. In fact, it seems like this is akin to a continuous probability distribution, and so the integral between any two velocities is the number of molecules travelling at a velocity in between those two limits.

[thomaskurian89]

(Original post by dantheman1261)
It doesn't entirely make sense, but from what I gather, you just need the area under the graph from v_0 to v_max. Is this a chemistry question? The chemists might be able to give you a definitive answer.

Mathematically though, there are clearly an infinite number of points in each small interval, so taken literally, the graph says there are an infinite number of molecules. In fact, it seems like this is akin to a continuous probability distribution, and so the integral between any two velocities is the number of molecules travelling at a velocity in between those two limits.

As stated, the answer to the problem is infinity since we have to consider infinitely many velocities. (Note that I have a continuous distribution.) So I guess we cannot have such a graph.