write the number of degrees of freedom of a diatomic gas molecule
Degrees of freedom (physics and chemistry) In three-dimensional space, three degrees of freedom are associated with the movement of a particle. A diatomic gas molecule has 5 degrees of freedom[dubious – discuss]. This set may be decomposed in terms of translations, rotations, and vibrations of the molecule. The center of mass motion of the entire molecule accounts for 3 degrees of freedom. In addition, the molecule has two rotational degrees of motion and one[dubious – discuss] vibrational mode. The rotations occur around the two axes perpendicular to the line between the two atoms. The rotation around the atom–atom bond is not a physical rotation[dubious – discuss]. This yields, for a diatomic molecule, a decomposition of:
Van der Waals equation is the volume of the container occupied by each particle (not the velocity of a particle), and k is the Boltzmann constant. It introduces two new parameters: a', a measure of the average attraction between particles, and b', the volume excluded from v by one particle.
Hermitian matrix The diagonal elements must be real, as they must be their own complex conjugate.
Exponentiation Any nonzero number raised to the 0 power is 1:[11]