Absence of convection in a perfect gas

摘要

We investigate the conditions under which a perfect gas subject to a three-dimensional external conservative field is in mechanical equilibrium without being in thermal equilibrium, that is, with a nonvanishing temperature gradient. We find the class of potentials for which this behavior is possible. In particular, gravitational, Coulomb, and centrifugal fields are shown to belong to this class. We obtain the functional form of the temperature field that assures the absence of convection and obtain the stability condition for mechanical equilibrium. (C) 2004 American Association of Physics Teachers.