Macroscopic equations for the adiabatic piston

A simplified version of a classical problem in thermodynamics -- the adiabatic piston -- is discussed in the framework of kinetic theory. We consider the limit of gases whose relaxation time is extremely fast so that the gases contained on the left and right chambers of the piston are always in equilibrium (that is the molecules are uniformly distributed and their velocities obey the Maxwell-Boltzmann distribution) after any collision with the piston. Then by using kinetic theory we derive the collision statistics from which we obtain a set of ordinary differential equations for the evolution of the macroscopic observables (namely the piston average velocity and position, the velocity variance and the temperatures of the two compartments). The dynamics of these equations is compared with simulations of an ideal gas and a microscopic model of gas settled to verify the assumptions used in the derivation. We show that the equations predict an evolution for the macroscopic variables which catches the basic features of the problem. The results here presented recover those derived, using a different approach, by Gruber, Pache and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).Comment: 13 pages, 7 figures (revTeX4) The paper has been completely rewritten with new derivation and results, supplementary information can be found at http://denali.phys.uniroma1.it/~cencini/Papers/cppv07_supplements.pd

Oscillometric—Volumetric Measurements of Pure Gas Adsorption Equilibria Devoid of the Non-Adsorption of Helium Hypothesis

A new method is presented to measure pure gas-adsorption equilibria on porous solids or powders without using a hypothesis on the void volume of the solid adsorbents, such as the non-adsorption of helium hypothesis. The proposed method involves combined volumetric/manometric and dynamic measurements, namely, observations of the frequency of small adiabatic oscillations of the adsorptive gas in equilibrium with the adsorbed phase or adsorbate. The oscillations of the adsorptive gas are initiated by small oscillations of a sphere or a cylinder positioned in a vertical tube above the vessel containing the gas and adsorbents [reversion of experiment by Rüchardt (1929), Flammersfeld (1972), Keller (2014)]. Experiments show that adsorbates have two different phases consisting, respectively, of molecules which are only weakly bound to adsorbent's atoms so that they can participate in the low-frequency gas oscillations (<10 Hz) and other molecules that are strongly bound to adsorbent's atoms so they are ‘stiff’, that is, cannot participate in the gas oscillations, with eigenfrequencies being in the range of 10 10 –10 12 Hz. The theory of these measurements will be presented and data of adsorption equilibria of He, N 2 , Ar and CO 2 on activated carbon BAX 1100 and zeolite KÖSTROLITH 4ABFK at near ambient conditions will be given and discussed to a certain extent