Ideal gas - percentage of fraction of molecules

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

Honestly speaking , I have absolutely no idea about this problem .This doesn't happen often .In the KTG chapter , only definition and formula of Average , RMS and Most probable speeds is given .

This question is for an entrance exam which requires minimum application of calculus . So I am guessing there is a formula for this problem which I am unaware of .

Please help me solve this problem in a simple way .

 

[gneill]

Does your text not cover the Maxwell-Boltzmann distribution? Likely the Average , RMS and Most probable speed were derived using it.

 

[BvU]

Honestly speaking , I have absolutely no idea about this problem

You should know this does not count as an attempt -- so we're not allowed to help .

Could it be you don't know what distribution you need for this ? i doubt that ...

 

[Jahnavi]

Thanks @gneill for replying .

Does your text not cover the Maxwell-Boltzmann distribution? Likely the Average , RMS and Most probable speed were derived using it.

Please see the attached image from the textbook .As you can see nothing is derived .Only definitions and formula are given .

 

[gneill]

Please see the attached image from the textbook .As you can see nothing is derived .Only definitions and formula are given .

What about equation 24.13 at the bottom of the page?

 

[Jahnavi]

What about equation 24.13 at the bottom of the page?

OK . But I don't understand how to use this equation .

Do I need to find dN/N ? Or do I need to integrate this equation ? What will be the limits of N and v ?

 

[gneill]

OK . But I don't understand how to use this equation .

Do I need to find dN/N ? Or do I need to integrate this equation ? What will be the limits of N and v ?

Yes, dN/N would be the fraction of molecules with speeds between v and v+dv. Since the range of speeds given is pretty narrow, you should be able to get a pretty good approximation using dv ≅ Δv . Integration would give you an exact result, but the integral might be a bit tricky.

 

[Jahnavi]

Should I go ahead with v = 323 and ∆v = 3 or v = 324 and ∆v = 2 ?

 

[gneill]

Should I go ahead with v = 323 and ∆v = 3 or v = 324 and ∆v = 2 ?

The latter.

 

[Jahnavi]

Thank you gneill !