Root mean square speed
Root mean square speed is the measure of the speed of particles in a gas that is most convenient for problem solving within the
kinetic theoryof gases. It is given by the formula
where "vrms" is the
root mean squarespeed, "Mm" is the molar massof the gas, "R" is the Molar gas constant, and "T" is the temperaturein Kelvin. This works well for both ideal gaseslike heliumand for molecular gases like diatomic oxygen. This is because despite the larger internal energy in many molecules (compared to that for an atom), 3RT/2 is still the mean translational kineticenergy.This can also be written in terms of the Boltzmann constant(k) as
:where m is the mass of the gas.
This can be derived with energy methods:
:where K.E. is the kinetic energy.:Given that v2 ignores direction, it is logical to assume that the formula can be extended to the entire sample, replacing "m" with the entire sample's mass, equal to the molar mass times the number of moles, "nM", yielding:Therefore:which is equivalent.
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