Rms speed for particles emerging from an oven

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  • #1
ppy
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The rms speed for a particle in a gas can be calculated using the formulae:

u[itex]_{rms}[/itex]=[itex]\sqrt{\int(u^{2}n(u)du)/N}[/itex]

a) Use the formulae and the expression for n(u):

n(u)=([itex]\frac{2^{1/2}N}{\pi^{1/2}}[/itex])([itex]\frac{m}{k_{B}T}[/itex])[itex]^{3/2}[/itex]u[itex]^{2}[/itex]exp(-[itex]\frac{mu^{2}}{2k_{B}T})[/itex]

To estimate the rms speed of Ne atoms in a gas at 300k given that the mass of an Ne atom is 3.32x10[itex]^{-26}[/itex]kg.

b)What is the rms speed of particles emerging from an oven with walls at 500k?

I have done a) and got the answer ([itex]\frac{3k_{B}T}{m}[/itex])[itex]^{1/2}[/itex] and then I got a numerical value.

I am stuck on b) Is the equation to find the rms speed for a particle emerging from an oven different to the rms equation above. I know in my notes the total flux that emerges from the oven is proportional to [itex]\int(un(u)du)[/itex]

Any help would be great thanks
 

Answers and Replies

  • #2
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Hi.
The oven's walls are supposed to be at thermal equilibrium with their content if not otherwise specified; the particles emerging are assumed to be in a gaseous form if not otherwise specified. Thus your formula in (a) should be enough to help you...
 
  • #3
ppy
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Hi.
The oven's walls are supposed to be at thermal equilibrium with their content if not otherwise specified; the particles emerging are assumed to be in a gaseous form if not otherwise specified. Thus your formula in (a) should be enough to help you...
So you are saying to use the result from (a) but we do not know the mass of the particles?
 
  • #4
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Well obviously the answer is going to depend on the mass of the particles, so if it's not specified just give the answer in terms of m...
 
  • #5
ppy
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Well obviously the answer is going to depend on the mass of the particles, so if it's not specified just give the answer in terms of m...
are you saying I just use 3NkT/m and sub in 500k? There is no extra calculation that what was done in part (a)?
 
  • #6
205
16
Your formula in (a) doesn't involve N: m is the only variable left once you have the temperature.
 

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