# Measuring Water Temperature & Diffusion Coefficient with Pollen

• alfab
In summary, the problem is to find the temperature and diffusion coefficient of water by measuring the velocity of pollen grains. The solution involves using the Stokes-Einstein equation to calculate the temperature based on the diffusion coefficient and grain radius. This allows for directly calculating the temperature from the measured velocities of the pollen grains.
alfab
Problem:
We wish to find the temperature and the diffusion coefficient of water by measuring the velocity of pollen grains in the medium, due to brownian motion and other forces.

Attempt:
We have a video clip and are using the program Tracker to measure the position of the pollen grains over time. We are using Einsteins equation for the diffusion coefficient

D = kT/γ

where k is Boltzmann's constant, T is the absolute temperature, and γ is the friction coefficient.

Using the equipartition theorem:

(1/2)m<v2>=(1/2)kT
We found:

D = m<v2>/6πηr
where η is the viscosity of the water, r is the radius of the pollen grain, m is the mass, and v is the velocity of each grain.

The issue:

After doing initial calculations we realized that using the velocities of the pollen grains give a very low temperature as the equipartition function is for the molecules of the water. Is there a way to rewrite this to get the temperature with respect to the grains.

Solution:Yes, there is a way to rewrite the equation to get the temperature with respect to the pollen grains. We can use the Stokes-Einstein equation to calculate the temperature based on the diffusion coefficient and the grain radius: T = 6πηDr/k This equation can be used to calculate the temperature of the water directly from the measured velocities of the pollen grains.

## 1. What is the purpose of measuring water temperature and diffusion coefficient with pollen?

The purpose of measuring water temperature and diffusion coefficient with pollen is to understand the movement and behavior of pollen particles in water. This information can be useful in various fields such as ecology, environmental science, and agriculture.

## 2. How is water temperature measured in this process?

Water temperature can be measured using a thermometer or a temperature probe. The thermometer is inserted into the water and left for a few minutes to obtain an accurate reading. The temperature probe is a more precise instrument that can be directly inserted into the water and gives real-time temperature readings.

## 3. What is the diffusion coefficient of a substance?

The diffusion coefficient is a measure of how quickly a substance moves from an area of high concentration to an area of low concentration. It is affected by factors such as temperature, pressure, and the properties of the substance itself.

## 4. How is the diffusion coefficient of pollen determined?

The diffusion coefficient of pollen can be determined by observing the movement of pollen particles in water over a period of time. By measuring the distance the particles have traveled and the time it took, the diffusion coefficient can be calculated using mathematical formulas.

## 5. What are some potential applications of measuring water temperature and diffusion coefficient with pollen?

Some potential applications include studying the dispersal of pollen in aquatic environments, understanding the impact of water temperature on pollen movement, and predicting the spread of invasive plant species through waterways. This information can also be used in the development of strategies for pollen control and management in water systems.

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