Reversible adiabatic oscillations
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An adiabatic and horizontal cylinder separated into two compartments by an adiabatic piston of mass
, moving without friction, contains, at the initial state, one mole of ideal gas
on each side.
At time
, the operator removes the piston from its equilibrium position of
small compared with the length
(
).
Question
Study the small oscillations of the system.
It is assumed that the transformations are isentropic. So for the gas at the left :
Similarly, for the gas at the right :
The second law of Newton for the piston gives :
Question
Justify the assumptions of adiabatic and reversibility.
For assuming adiabatic, one can evaluate the long time associated with heat exchange by thermal diffusion.
For the reversibility hypothesis, we must neglect the friction due to the viscosity of the air and the piston.
This assumption is questionable because the friction inevitably lead to the arrest of the piston.
