Assumptions of Kinetic Theory: How big should a cubical element be?

[Lagraaaange]

Homework Statement

Assuming uniform distribution. What must be the size of a cubical element of volume in the container so that the number of particles in each volume element may vary by 0.1% when the gas is as standard conditions. Probable deviation is given by N^(1/2) where N is the number of particles.

Homework Equations

Deviation: N^(1/2)

The Attempt at a Solution

I don't know what N is for standard conditions.

Ans. 3300Angstroms

 

[mfb]

I don't know what N is for standard conditions.

There is no "N for standard conditions".

The particle number fluctuates by N^1/2. At which value of N does this correspond to 0.1% of N?

Relating this to a volume is a step that comes afterwards.

 

[Lagraaaange]

There is no "N for standard conditions".

The particle number fluctuates by N^1/2. At which value of N does this correspond to 0.1% of N?

Relating this to a volume is a step that comes afterwards.

But one needs a volume

There is no "N for standard conditions".

The particle number fluctuates by N^1/2. At which value of N does this correspond to 0.1% of N?

Relating this to a volume is a step that comes afterwards.

So we need 0.001N = N^1/2. Solving N = 1,000,000. But I don't see where to go from here without any more info?

 

[mfb]

But one needs a volume

Some problems need more than one step. Finding N is the first step, finding the volume is the second.

So we need 0.001N = N^1/2. Solving N = 1,000,000. But I don't see where to go from here without any more info?

Good. Now you can find the volume that has (on average) 1 million particles in it. How many particles are in a mole? What is the volume of a mole at standard conditions?