- #1

alfab

- 8

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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.