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

In summary, the question is asking for the size of a cubical element in a container that will result in a 0.1% variation in the number of particles at standard conditions. This is related to the deviation formula N^(1/2), where N is the number of particles. To solve for N, one must set 0.001N = N^1/2 and solve for N, which is approximately 1 million. From there, one can use Avogadro's number and the volume of a mole at standard conditions to calculate the necessary size of the cubical element.
  • #1
Lagraaaange
82
0

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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  • #2
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.
 
  • #3
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?
 
  • #4
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?
 

What is the kinetic theory of matter?

The kinetic theory of matter states that all particles in matter are constantly in motion and that the temperature of a substance is directly related to the average kinetic energy of its particles.

What are the assumptions of the kinetic theory?

The assumptions of the kinetic theory include that all particles in a substance are in constant motion, the particles are constantly colliding with each other and the walls of their container, and there is empty space between the particles.

Why is the size of a cubical element important in the kinetic theory?

The size of a cubical element is important in the kinetic theory because it affects the accuracy of the calculations used to determine the behavior of particles in a substance. A smaller cubical element allows for more precise calculations, but can also be computationally expensive.

How do scientists determine the size of a cubical element in the kinetic theory?

The size of a cubical element is typically determined by the specific substance being studied and the level of accuracy needed for the calculations. Generally, a smaller cubical element is used for more complex substances and larger elements for simpler substances.

Are there any limitations to the assumptions of the kinetic theory?

Yes, there are limitations to the assumptions of the kinetic theory. For example, the theory does not account for intermolecular forces, which can affect the behavior of particles in a substance. Additionally, at very high pressures or low temperatures, the assumptions may no longer hold true.

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