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In the physics of gas molecules, the root-mean-square speed is defined as the square root of the average squared-speed. 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}}}
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
The thermal energy can be used to calculate the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. The root mean square speeds found at room temperature accurately reflect this, ranging from 1370 m/s for helium, down to 240 m/s for xenon.
Similarly, the equipartition theorem allows the average (more precisely, the root mean square) angular speed of the molecules to be calculated. [ 6 ] The tumbling of rigid molecules—that is, the random rotations of molecules in solution—plays a key role in the relaxations observed by nuclear magnetic resonance , particularly protein NMR and ...
Root-mean-square deviation of atomic positions: the average is taken over a group of particles at a single time, where the MSD is taken for a single particle over an interval of time; Mean squared error
In fluid dynamics, turbulence kinetic energy (TKE) is the mean kinetic energy per unit mass associated with eddies in turbulent flow.Physically, the turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity fluctuations.
An analysis of the integral theorem of generalized virial makes it possible to find, on the basis of field theory, a formula for the root-mean-square speed of typical particles of a system without using the notion of temperature: [24]