63 research outputs found
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
Small-Ring Compounds. XXVIII. Isotope-Position Rearrangements of Allylcarbinyl Grignard Reagents
We have observed a remarkable rearrangement while attempting to prepare 4-penten-2-ylarnine (I) through the reaction of the Grignard reagent derived from 4-penten-2-yl chloride (II) with methoxylamine, in that part of the amine formed appeared to be 2-methyl-3-butenylamine (III)
Wird der Abbau organischer Verbindungen tatsächlich durch Chlorsubstitution beschleunigt?
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