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3. Show that every position or momentum coordinate (eg, px, rz2, etc) which appears only to the second power in the Hamiltonian contributes t/2 to the total energy, and thus 1/2 to the heat capacity. (In practical units, these are kBT/2 and kB/2.) This is the equi partition theorem, which allows one to partially solve many problems by inspection.

Fig: 1