Abstract

Many different averages and means encountered in science and other fields may be regarded as special cases of the generalized mean of order a, which may be defined for all real valves of a. The property of the generalized mean that it is a monotonically increasing (nondecreasing) function of a has such wide applications as to show: (1) that the root mean square speed of the molecules in a gas, whether at equilibrium or not, is larger than the mean speed; (2) that the entropy change accompanying adiabatic temperature equilibration processes is always positive; (3) that the weight average polymer molecular weight is larger than the number average molecular weight.

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