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Measuring a speed in Kelvin $K$

Physics Asked by N. auf Kappa on February 13, 2021

Since the Kelvins are a temperature unit and temperature is basically molecule/atoms excitation (so they have a "speed of excitation"), could it be possible to measure a speed (let’s say 10 meters per second) in Kelvins?

One Answer

Sort of, you also need to take the mass of the particles into account (temperature can classically be thought of as vibrational energy, which scales with mass). The equation you're looking for (for a gas) is: $$ v_{RMS} = sqrt{frac{3RT}{M_m}} $$ Where $R$ is the gas constant, $M_m$ is the molar mass and $v_{RMS}$ is the root-mean square speed of the molecules in your gas, e.g. the square root of the average of the square of the velocity: $$v_{RMS} = sqrt{overline{v^2}}$$

Answered by G.Lang on February 13, 2021

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