Degrees of Freedom for Oxygen (O2) Gas
The number of degrees of freedom ($f$) indicates the independent ways a molecule can store energy. For a gas molecule, these typically include translational, rotational, and vibrational modes.
Molecular Type Analysis
Oxygen (O2) is a diatomic molecule. At standard temperatures and pressures commonly considered in introductory physics and chemistry, vibrational energy modes are often negligible ('frozen out'). Therefore, we primarily consider translational and rotational degrees of freedom.
Translational Degrees of Freedom
A molecule moving in three-dimensional space has 3 translational degrees of freedom, corresponding to its motion along the x, y, and z axes.
Number of translational degrees of freedom = 3.
Rotational Degrees of Freedom
A linear diatomic molecule can rotate about two independent axes perpendicular to the bond connecting the two atoms. Rotation about the bond axis itself has negligible moment of inertia and is typically ignored.
Number of rotational degrees of freedom = 2.
Total Degrees of Freedom Calculation
The total degrees of freedom ($f$) is the sum of the translational and rotational degrees of freedom for a diatomic molecule at typical temperatures:
$f = \text{Translational} + \text{Rotational}$
$f = 3 + 2$
$f = 5$
Therefore, the number of degrees of freedom for an Oxygen (O2) gas molecule, considering only translational and rotational modes, is 5.
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