Temperature dependent averages of statistical mechanics

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Abstract
An equation is derived which relates the change in statistical mechanical averages with temperature to other averages. It is shown that in a special case, the equation reduces to the virial theorem of statistical mechanics. The general equation is used to derive equations relating heat capacities to averages involving the potential energy. As a further application, equations are derived giving the way in which the moments 〈xn〉 change with temperature.