  The problem of defining the average kinetic energy of statistical systems is
addressed. The conditions of applicability for the formula, relating the
average kinetic energy with the mass derivative of the internal energy, are
analysed. It is shown that incorrectly using this formula, outside its region
of validity, leads to paradoxes. An equation is found for a parametric
derivative of the average for an arbitrary operator. A special attention is
paid to the mass derivative of the internal energy, for which a general formula
is derived, without invoking the adiabatic approximation and taking into
account the mass dependence of the potential-energy operator. The results are
illustrated by the case of a low-temperature dilute Bose gas.
