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The RMS speed of an ideal gas is calculated using the following equation: v RMS = 3 R T M {\displaystyle v_{\text{RMS}}={\sqrt {3RT \over M}}} where R represents the gas constant , 8.314 J/(mol·K), T is the temperature of the gas in kelvins , and M is the molar mass of the gas in kilograms per mole.
The most probable (or mode) speed is 81.6% of the root-mean-square speed , and the mean (arithmetic mean, or average) speed ¯ is 92.1% of the rms speed (isotropic distribution of speeds). See: Average, Root-mean-square speed; Arithmetic mean; Mean; Mode (statistics)
The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. ... The root-mean-square speed can be calculated by
The mean speed , most probable speed v p, and root-mean-square speed can be obtained from properties of the Maxwell distribution. This works well for nearly ideal, monatomic gases like helium, but also for molecular gases like diatomic oxygen.
Thermal velocity or thermal speed is a typical velocity of the thermal motion of particles that make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature. Technically speaking, it is a measure of the width of the peak in the Maxwell–Boltzmann particle velocity distribution
General Equation Isobaric Δp = 0 ... Equations Mean speed = Root mean square speed = = Modal speed = Mean free path: σ = effective cross-section; n = volume ...
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Physically, the turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes equations, the turbulence kinetic energy can be calculated based on the closure method, i.e. a turbulence model.