Calculating Gas Particle Effusion Rate Through Two Holes

In summary, the conversation discusses the rate at which particles emerge from a small circular hole after passing through a larger hole and being collimated. It is shown that the rate can be represented by the equation \frac{1}{4}nA\left\langle v \right\rangle \frac{a^2}{d^2}, where n is the particle density and a and d are the radius and distance of the small hole, respectively. The conversation also mentions that no collisions occur after the gas effuses through the first hole.
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Homework Statement


A gas effuses into a vacuum through a small hole of area A. The particles are then collimated by passing through a very small circular hole of radius a, in a screen a distance d from the first hole. Show that the rate at which particles emerge from the second hole is
[tex]\frac{1}{4}nA\left\langle v \right\rangle \frac{a^2}{d^2}[/tex],
where n is the particle density. We also assume that no collisions occur after the gas effuses through the first hole.


Homework Equations


We know that the effusion rate from the first hole is
[tex]\frac{1}{4}n\left\langle v \right\rangle[/tex]
but I have no idea how to proceed.


The Attempt at a Solution

 
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  • #2
I'm not sure how to begin. I understand that particles will be collimated by the small hole, but I don't know how to proceed from here.
 

Related to Calculating Gas Particle Effusion Rate Through Two Holes

1. How is the effusion rate of gas particles through two holes calculated?

The effusion rate of gas particles through two holes is calculated using Graham's law of effusion, which states that the rate of effusion is inversely proportional to the square root of the molar mass of the gas particles. This means that the lighter the gas particles, the faster they will effuse through the holes.

2. What is the formula for calculating the effusion rate through two holes?

The formula for calculating the effusion rate through two holes is: effusion rate = (rate of hole 1) / (rate of hole 2) = (1/√molar mass of gas 1) / (1/√molar mass of gas 2) = √(molar mass of gas 2 / molar mass of gas 1).

3. How does the size of the holes affect the effusion rate of gas particles?

The size of the holes does not directly affect the effusion rate of gas particles. However, the size of the holes can indirectly affect the effusion rate if it allows for a difference in pressure between the two sides of the holes. A larger hole would allow for a greater pressure difference, resulting in a higher effusion rate.

4. Can the temperature and pressure of the gas affect the effusion rate?

Yes, the temperature and pressure of the gas can affect the effusion rate. According to the kinetic molecular theory, as temperature increases, the average kinetic energy of the gas particles also increases, leading to a higher effusion rate. Similarly, as pressure increases, there is a greater likelihood for gas particles to escape through the holes, resulting in a higher effusion rate.

5. Why is calculating the effusion rate through two holes important in scientific research?

Calculating the effusion rate through two holes is important in scientific research because it allows for the determination of molar masses of unknown gases. By measuring the effusion rate of a gas through a hole and comparing it to the effusion rate of a known gas, the molar mass of the unknown gas can be calculated using the formula mentioned in question 2. This information is crucial for understanding the properties and behavior of various gases in different environments.

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