98-763 Ch. Gruber and J. Piasecki
Stationary Motion of the Adiabatic Piston (29K, LaTeX file) Dec 22, 98
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Abstract. We consider a one-dimensional system consisting of two infinite ideal fluids, with equal pressures but different temperatures T_1 and T_2, separated by an adiabatic movable piston whose mass $M$ is much larger than the mass $m$ of the fluid particules. This is the infinite version of the controversial adiabatic piston problem. The stationary non-equilibrium solution of the Boltzmann equation for the velocity distribution of the piston is expressed in powers of the small parameter \epsilon=\sqrt{m/M}, and explicitly given up to order \epsilon^2. In particular it implies that although the pressures are equal on both sides of the piston, the temperature difference induces a non-zero average velocity of the piston in the direction of the higher temperature region. It thus shows that the asymmetry of the fluctuations induces a macroscopic motion despite the absence of any macroscopic force. This same conclusion was previously obtained for the non-physical situation where M=m.

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