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Stationary motion of the adiabatic piston

Author

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  • Gruber, Ch.
  • Piasecki, J.

Abstract

We consider a one-dimensional system consisting of two infinite ideal fluids, with equal pressures but different temperatures T1 and T2, separated by an adiabatic movable piston whose mass M is much larger than the mass m of the fluid particles. 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 ε=m/M, and explicitly given up to order ε2. 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.

Suggested Citation

  • Gruber, Ch. & Piasecki, J., 1999. "Stationary motion of the adiabatic piston," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(3), pages 412-423.
    • Handle: RePEc:eee:phsmap:v:268:y:1999:i:3:p:412-423
    DOI: 10.1016/S0378-4371(99)00095-3
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    References listed on IDEAS

    as
    1. Piasecki, J. & Gruber, Ch., 1999. "From the adiabatic piston to macroscopic motion induced by fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 463-472.
    2. Lieb, Elliott H., 1999. "Some problems in statistical mechanics that I would like to see solved," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 263(1), pages 491-499.
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    Cited by:

    1. Gruber, Ch. & Frachebourg, L., 1999. "On the adiabatic properties of a stochastic adiabatic wall: Evolution, stationary non-equilibrium, and equilibrium states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 272(3), pages 392-428.

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