Physics

In the context of the equipartition theorem, which of the following statements are false and why?

i) For equipartition to hold, the internal energy must be a quadratic function of the degree of freedom

ii) For equipartition to hold, the Hamiltonian must be a quadratic function of the degree of freedom

iii) Specific heat is a degree of freedom

iv) The z component of the momentum of an ideal-gas molecule is a quadratic degree of freedom

v) If equipartition holds, the internal energy contribution is a quadratic function of temperature.

vi) If equipartition holds, the specific heat is independent of temperature