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26 Nov 2019
Small dust particles suspended in air seem to dance randomly about,a phenomenon called Brownian motion.
For this problem you will need to know Boltzmann's constant: k_{\rmB}=1.38\times10^{-23}\;{\rm J/K}.
A) What would you expect the mean translational kinetic energy K ofsuch particles to be if they are in air at a temperature of 290K?
Express the mean translational kinetic energy numerically, injoules, to two significant figures.
B) Find an expression for the rms (root-mean-square) speed v_rms ofthese particles, assuming them to be spheres of diameter d anddensity rho.
Small dust particles suspended in air seem to dance randomly about,a phenomenon called Brownian motion.
For this problem you will need to know Boltzmann's constant: k_{\rmB}=1.38\times10^{-23}\;{\rm J/K}.
A) What would you expect the mean translational kinetic energy K ofsuch particles to be if they are in air at a temperature of 290K?
Express the mean translational kinetic energy numerically, injoules, to two significant figures.
B) Find an expression for the rms (root-mean-square) speed v_rms ofthese particles, assuming them to be spheres of diameter d anddensity rho.
Lelia LubowitzLv2
30 May 2019
