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The H\(_2\) molecule has 3 translational degrees of freedom, 2 rotational degrees of freedom, and 1 vibrational degree of freedom in the collective motion picture. In practice, such a treatment is inconvenient and it is better to group the spatial degrees of freedom according to the type of motion. If the Hamiltonian includes the potentials that characterize interaction between the particles, our equations of motion would be correct. In principle, we could try to ignore all this and treat each atom as one particle. As a linear molecule it has two rotational degrees of freedom, which also contribute to internal energy and to the partition function. In fact, an H\(_2\) molecule is not only an oscillator, it is also a rotor. Neglect of the vibrational degrees of freedom will lead to wrong results for internal energy, heat capacity, the partition function, and entropy, at least at high temperatures. We see this already when considering H\(_2\) gas, where each molecule can be approximated by a harmonic oscillator (Section ). For gases consisting of molecules, it does not suffice to consider only translational motion as in Maxwell’s kinetic theory of gases. Such effects are absent in an ideal gas that consists of point particles, a model that is reasonable for noble gases far from condensation.
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In Section we have seen that the treatment of condensed phases can be complicated by collective motion of particles.