please show working for false statements will be much appreciated!

1. Which of the following statements are true, in the context of the equipartition theorem? (If you believe a statement is false, give reasons) (a) Specific heat is a degree of freedom (b) The z component of the momentum of an ideal-gas molecule is a quadratic degree of freedom (c) For equipartition to hold, the internal energy must be a quadratic function of the degree of freedom. (d) For equipartition to hold, the Hamiltonian must be a quadratic function of the degree of freedom. (e) If equipartition holds, the internal energy contribution is a quadratic function of temperature. (f) If equipartition holds, the specific heat is independent of temperature (g) Equipartition holds at sufficiently low temperatures (h) All systems obey equipartition at sufficiently high temperatures