Posted by Steve Simon on January 15, 2013, 7:52 am, in reply to "equipartition"
Heat capacity is about how much energy a system has at a given temperature. Let's think in one dimension. For a monatomic gas the Hamiltonian is
H=p^2/(2m)
So only the momentum contributes to the energy of the system. We count this as a single degree of freedom for the purpose of the equipartition theorem. However for a one dimensional harmonic oscillator the Hamiltonian is
H=p^2/(2m)+(k/2) x^2
So that both momentum and position contribute to the energy. Thus we count two degrees of freedom for the purpose of the equipartition theorem.
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