Estimate section of area under Maxwell-Boltzmann Curve

[TehDarkArchon]

Homework Statement

When it comes to evaluating integrals, there are two ways you can do it. First, you know
that the integration of a function is the area under a curve, as shown in the left hand diagram.
However, if you are looking over a narrow range along the x-axis, you can make an estimation
for the area as shown on the right:

Use the integral estimation represented on the right to calculate the fraction of Krypton atoms
moving between 200 m/s to 210 m/s at 30 °C from the Maxwell-Boltzmann distribution. Hint:
∆x=10 m/s, now how do you get ∆y?

Homework Equations

$/$y(x)dx = $\sum$y(n∆x)∆x
Total area of curve = 1

The Attempt at a Solution

I tried plugging in some numbers but it wasnt working too well...any advice?

 

[SteamKing]

You could show us the numbers you got. That would get you more help.

 

[TehDarkArchon]

Yeah sorry about that. The Maxwell-Boltzmann distribution is 4*pi*(m/2*pi*k*T)^3/2*v²*e^-mv2/2kT and obviously ∆x=10 m/s, so I plugged in 10 for v and 0.0838 kg/mol for m and end up with 0 which doesn't make sense...=\

 

[Dick]

Yeah sorry about that. The Maxwell-Boltzmann distribution is 4*pi*(m/2*pi*k*T)^3/2*v²*e^-mv2/2kT and obviously ∆x=10 m/s, so I plugged in 10 for v and 0.0838 kg/mol for m and end up with 0 which doesn't make sense...=\

Why would you plug in 10m/s for v? v is supposed to be between 200m/s and 210m/s, isn't it?

 

[TehDarkArchon]

Yeah it is, so that doesn't make sense. I also tried subbing in 210 and 200 for the equation and subtracting them and I still get 0, unless I'm just typing it in completely wrong or something

 

[Dick]

Yeah it is, so that doesn't make sense. I also tried subbing in 210 and 200 for the equation and subtracting them and I still get 0, unless I'm just typing it in completely wrong or something

Don't subtract them. The height delta(y) is the value of the Maxwell-Boltzmann distribution AROUND v=200 to 210m/s. This is an estimate. You can use any value between 200 and 210 though I'd probably pick 205, just to compromise.

 

[TehDarkArchon]

I figured out what I was doing wrong (in conjection with using 205 m/s). I should've been using 1.39x10^-25 kg for the mass of krypton. After plugging that in i got y(205m/s) = 0.01133 which brings the area to 10 x .01133 = 0.11 m. A much more sensible answer than 0 haha. Thanks a lot everyone for your help!