# 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 thekinetic theory of gases. It is given by the formula:$v\_\{rms\}\; =\; sqrt$3RT}over{M_m

where "v

_{rms}" is theroot mean square speed, "M_{m}" is themolar mass of the gas, "R" is theMolar gas constant , and "T" is thetemperature inKelvin . This works well for bothideal gases likehelium and for molecular gases like diatomicoxygen . This is because despite the larger internal energy in many molecules (compared to that for an atom), 3RT/2 is still the meantranslational kinetic energy.This can also be written in terms of theBoltzmann constant (k) as:$v\_\{rms\}\; =\; sqrt$3kT}over{mwhere m is the mass of the gas.

This can be derived with energy methods:

:$$3}over{2nRT = K.E.where K.E. is the kinetic energy.:$$1}over{2mv^2 = K.E._{molecule}Given that v

^{2}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:$$1}over{2nMv^2 = K.E.Therefore:$v\_\{rms\}\; =\; sqrt$2K.E.}over{mwhich is equivalent.**See also***

Boltzmann constant

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Root mean square**— In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids.It… … Wikipedia**mean**— mean1 /meen/, v., meant, meaning. v.t. 1. to have in mind as one s purpose or intention; intend: I meant to compliment you on your work. 2. to intend for a particular purpose, destination, etc.: They were meant for each other. 3. to intend to… … Universalium**Mean**— This article is about the statistical concept. For other uses, see Mean (disambiguation). In statistics, mean has two related meanings: the arithmetic mean (and is distinguished from the geometric mean or harmonic mean). the expected value of a… … Wikipedia**Maxwell speed distribution**— Classically, an ideal gas molecules bounce around with somewhat arbitrary velocities, never interacting with each other. In reality, however, an ideal gas is subjected to intermolecular forces. It is to be noted that the aforementioned classical… … Wikipedia**Methods of computing square roots**— There are several methods for calculating the principal square root of a nonnegative real number. For the square roots of a negative or complex number, see below. Contents 1 Rough estimation 2 Babylonian method 2.1 Example … Wikipedia**gas**— gasless, adj. /gas/, n., pl. gases, v., gassed, gassing. n. 1. Physics. a substance possessing perfect molecular mobility and the property of indefinite expansion, as opposed to a solid or liquid. 2. any such fluid or mixture of fluids. 3. any… … Universalium**Maxwell–Boltzmann distribution**— Maxwell–Boltzmann Probability density function Cumulative distribution function parameters … Wikipedia**Equipartition theorem**— [ Thermal motion of an α helical peptide. The jittery motion is random and complex, and the energy of any particular atom can fluctuate wildly. Nevertheless, the equipartition theorem allows the average kinetic energy of each atom to be computed … Wikipedia**Boltzmann constant**— For the constant pertaining to energy of black body radiation see Stefan–Boltzmann constant Values of k[1] Units 1.3806488(13)×10−23 J K−1 8.617332 … Wikipedia**Effusion**— In chemistry, effusion is the process where individual molecules flow through a hole without collisions between molecules. This occurs if the diameter of the hole is considerably smaller than the mean free path of the molecules [K.J. Laidler and… … Wikipedia