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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 .
Maxwell–Boltzmann statistics can be used to derive the Maxwell–Boltzmann distribution of particle speeds in an ideal gas.Shown: distribution of speeds for 10 6 oxygen molecules at -100, 20, and 600 °C.
The average molecular speed can be calculated from the Maxwell speed distribution as = / (or, equivalently, = / ). The rate Φ N {\displaystyle \Phi _{N}} at which a gas of molar mass M {\displaystyle M} effuses (typically expressed as the number of molecules passing through the hole per second) is then [ 4 ]
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)
¯ is the average molecular speed from the Maxwell–Boltzmann distribution [L 1 T −1], T is the thermodynamic temperature [θ 1], μ is the dynamic viscosity [M 1 L −1 T −1], m is the molecular mass [M 1], k B is the Boltzmann constant [M 1 L 2 T −2 θ −1], is the density [M 1 L −3].
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 ...
Note that different definitions of the molecular diameter, as well as different assumptions about the value of atmospheric pressure (100 vs 101.3 kPa) and room temperature (293.17 K vs 296.15 K or even 300 K) can lead to slightly different values of the mean free path.
A molecular vibration is a periodic motion of the atoms of a molecule relative to each other, such that the center of mass of the molecule remains unchanged. The typical vibrational frequencies range from less than 10 13 Hz to approximately 10 14 Hz, corresponding to wavenumbers of approximately 300 to 3000 cm −1 and wavelengths of approximately 30 to 3 μm.