Finding the Initial Rate of Gas Leakage from a Small Hole in a Cubic Container

In summary, the question asks for the initial rate of gas leakage from a cubic container with a small hole, given the container's dimensions, gas density, and external pressure. The formula p=ρc^2/3 is provided as a hint. The attempt at a solution involves considering the movement of particles towards the hole and using the formula to calculate the leakage rate. However, the effect of pressure difference is not explicitly taken into account and further explanation is needed to fully understand the solution.
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Homework Statement


A cubic container with sidelength l has a small hole with cross sectional area a (a<<l). The gas has density ρ and pressure P. Find the initial rate of gas leakage given that the outside pressure is 0.


Homework Equations



The question mentions the formula p=ρc2/3 so I know I have to use this.

The Attempt at a Solution



Assume that 1/3 of the particles are moving in a direction towards the hole. Any molecule in a cylinder of base a and length c will leave the hole in one second so is the leakage rate av/3, and then I can substitute out c with the formula? Is this the correct answer?
 
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  • #2
Any molecule in a cylinder of base a and length c will leave the hole in one second
Not bad - but your result does not appear to take the pressure difference into account.

I'd have wanted to see that explicit - can you explain what your equations mean and how you are using them.
I suspect you have it right, but cannot tell exactly from what you've written down so far.
 
Last edited:

1. What is the rate of leakage from a box?

The rate of leakage from a box refers to the amount of substance or material that is leaking out of a box per unit of time. It is typically measured in units such as liters per hour or grams per second.

2. How is the rate of leakage from a box calculated?

The rate of leakage from a box can be calculated by measuring the volume or weight of the substance that has leaked out of the box over a specific period of time. This value is then divided by the time interval to determine the rate of leakage.

3. What factors can affect the rate of leakage from a box?

The rate of leakage from a box can be influenced by a variety of factors, including the type and condition of the box, the substance being stored in the box, temperature and humidity, and external factors such as pressure or vibrations.

4. How can the rate of leakage from a box be reduced?

The rate of leakage from a box can be reduced by using a box with a tight seal, storing the substance in proper containers within the box, maintaining appropriate temperature and humidity levels, and regularly inspecting and repairing any damage to the box.

5. Why is it important to monitor the rate of leakage from a box?

Monitoring the rate of leakage from a box is crucial for ensuring the safety and integrity of the substance being stored. A high rate of leakage can lead to contamination or loss of the substance, while a low rate of leakage can indicate potential damage or weakness in the box that may need to be addressed.

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