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Classical Physics
Mechanics
Measuring Water Temperature & Diffusion Coefficient with Pollen
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[QUOTE="alfab, post: 6235118, member: 619816"] 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 [B]D = kT/γ[/B] where k is Boltzmann's constant, T is the absolute temperature, and γ is the friction coefficient. Using the equipartition theorem: [B](1/2)m<v[SUP]2[/SUP]>=(1/2)kT[/B] We found: [B]D = m<v[SUP]2[/SUP]>/6πηr[/B] 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. [/QUOTE]
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Classical Physics
Mechanics
Measuring Water Temperature & Diffusion Coefficient with Pollen
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