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

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Homework Help Overview

The discussion revolves around determining the appropriate size of a cubical element of volume in a gas container, under the assumptions of kinetic theory and uniform particle distribution. The problem specifically addresses how the number of particles within this volume element can vary by 0.1% at standard conditions.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the concept of N, the number of particles, and its relation to standard conditions. There is a focus on understanding how fluctuations in particle number relate to the specified percentage variation. Some participants question the existence of a defined N for standard conditions and discuss the implications of this on the problem.

Discussion Status

The discussion is active, with participants attempting to clarify the relationship between N and the desired percentage fluctuation. There is a recognition that determining N is a preliminary step before addressing the volume aspect. Some guidance has been offered regarding the next steps, but there remains a lack of consensus on how to proceed without additional information.

Contextual Notes

Participants note that the problem may require multiple steps to resolve, emphasizing the need for both the number of particles and the corresponding volume. The absence of specific values or definitions for N at standard conditions is highlighted as a constraint in the discussion.

Lagraaaange
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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
 
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Lagraaaange said:
I don't know what N is for standard conditions.
There is no "N for standard conditions".

The particle number fluctuates by N1/2. At which value of N does this correspond to 0.1% of N?

Relating this to a volume is a step that comes afterwards.
 
mfb said:
There is no "N for standard conditions".

The particle number fluctuates by N1/2. 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
mfb said:
There is no "N for standard conditions".

The particle number fluctuates by N1/2. 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?
 
Lagraaaange said:
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?
 

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