This statement can be derived from first principles by noting that under certain conditions, the function Z depends only on the thermodynamic beta to the minus-one-half, and evaluating the derivative of the log of that function with respect to beta.
This statement can be derived from first principles by noting that under certain conditions, the function Z depends only on the thermodynamic beta to the minus-one-half, and evaluating the derivative of the log of that function with respect to beta. 
This statement can be derived from first principles by noting that under certain conditions, the function Z depends only on the thermodynamic beta to the minus-one-half, and evaluating the derivative of the log of that function with respect to beta.
equipartition theorem