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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 .
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 ]
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 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)
where D is the diffusivity of A through B, proportional to the average molecular velocity and, therefore dependent on the temperature and pressure of gases. The rate of diffusion N A is usually expressed as the number of moles diffusing across unit area in unit time. As with the basic equation of heat transfer, this indicates that the rate of ...
These methods are termed mixed or hybrid quantum-mechanical and molecular mechanics methods (hybrid QM/MM). [51] The most important advantage of hybrid QM/MM method is the speed. The cost of doing classical molecular dynamics (MM) in the most straightforward case scales O(n 2), where n is the number of atoms in the system. This is mainly due to ...
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
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.