# How Long to Achieve Uniform Mixture in Helium Gas Experiment?

• Jameskd
In summary, the conversation discusses an experiment on a dilute isotopic mixture of helium gas using a spherical vessel filled with 4He gas at one atmosphere pressure. A small amount of 3He gas is then introduced through a valve on one side, and an estimate is requested for the time it takes for a uniform mixture to form. The suggestion is made to consider the time dependence of the root mean square travel distance in a random walk in 1D for a better approach. The questioner also asks for tips on how to begin the problem.
Jameskd
Homework Statement
Estimating how long it would take to achieve a uniform mixture.
Relevant Equations
J = DA dC/dx, C=N/V
This is an experiment on a dilute isotopic mixture of helium gas. A spherical vessel of diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small amount of 3He gas is introduced through a valve on one side of the vessel. Make a rough estimate of how long one must wait before a uniform mixture has formed (use the result for the time dependence of the root mean square travel distance in a random walk in 1D.) Suggest a better way to make a uniform mixture.

I am unsure how to begin this question, for starters I thought of a high concentration to a low concentration, so where the valve is to the rest of the sphere. But I'm just struggling to start. Any tips?

Start out by writing down for us the equation for the time dependence of the rms distance in random walk.

## 1. What is Fick's Law?

Fick's Law is a mathematical equation that describes the diffusion of particles from an area of high concentration to an area of low concentration. It is commonly used in chemistry and biology to understand how molecules move through a medium.

## 2. How is Fick's Law calculated?

Fick's Law is calculated using the equation J = -D(dC/dx), where J is the flux or rate of diffusion, D is the diffusion coefficient, and (dC/dx) is the concentration gradient. This equation can be used to determine the rate of diffusion for a particular substance in a given medium.

## 3. What is the significance of time in Fick's Law?

Time is an important factor in Fick's Law because it determines how long it takes for particles to diffuse from one area to another. The longer the time, the greater the distance the particles can travel, resulting in a higher rate of diffusion.

## 4. What is the relationship between Fick's Law and RMS (Root Mean Square) velocity?

Fick's Law and RMS velocity are related because they both describe the movement of particles in a given medium. Fick's Law focuses on the overall rate of diffusion, while RMS velocity specifically measures the average speed of the particles as they move. Both concepts are important in understanding the behavior of particles in a medium.

## 5. How is Fick's Law used in real-world applications?

Fick's Law has many practical applications, such as in the pharmaceutical industry to understand how drugs diffuse through the body, in environmental science to study the movement of pollutants in air or water, and in material science to determine how substances diffuse through materials. It is also used in everyday products like perfumes and air fresheners to understand how their scents spread through a room.

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