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- Summary
- We are attempting to determine the diffusion coefficient of a water medium by using velocities of pollen grains in the water.

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

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

Using the equipartition theorem:

We found:

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.

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<v**^{2}>=(1/2)kTWe found:

**D = m<v**^{2}>/6πηrwhere 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.