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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.
The water molecule has three fundamental molecular vibrations. The O-H stretching vibrations give rise to absorption bands with band origins at 3657 cm −1 (ν 1, 2.734 μm) and 3756 cm −1 (ν 3, 2.662 μm) in the gas phase. The asymmetric stretching vibration, of B 2 symmetry in the point group C 2v is a normal vibration.
Thermal fluctuations generally affect all the degrees of freedom of a system: There can be random vibrations , random rotations , random electronic excitations, and so forth. Thermodynamic variables, such as pressure, temperature, or entropy, likewise undergo thermal fluctuations. For example, for a system that has an equilibrium pressure, the ...
Translational motions—the randomized thermal vibrations of fundamental particles such as atoms and molecules—gives a substance its “kinetic temperature.”Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure.
For solids, the thermal energy is associated primarily with the vibrations of its atoms or molecules about their equilibrium position. In an ideal monatomic gas , the kinetic energy is found exclusively in the purely translational motions of the particles.
By exactly the same reasoning as in the translational case, equipartition implies that in thermal equilibrium the average rotational energy of each particle is 3 / 2 k B T. Similarly, the equipartition theorem allows the average (more precisely, the root mean square) angular speed of the molecules to be calculated. [6]
The transfer of momentum between molecules is explicitly accounted for in Revised Enskog theory, which relaxes the requirement of a gas being dilute. The viscosity equation further presupposes that there is only one type of gas molecules, and that the gas molecules are perfect elastic and hard core particles of spherical shape.
The term "thermal energy" is often used ambiguously in physics and engineering. [1] It can denote several different physical concepts, including: Internal energy : The energy contained within a body of matter or radiation, excluding the potential energy of the whole system, and excluding the kinetic energy of the system moving as a whole.