We discuss the adiabatic two-piston problem for an ideal gas confined between two pistons of equal mass and extend recent work based on the reversible approximation. More realistic equations that account for the roles of the gas temperature and particle mass are applied to extend the analysis of the expansion of the gas from reversible to irreversible behavior to the limit of free expansion. The evolution of quantities, such as temperature, piston speed, adiabatic reversibility coefficients, and entropy, is obtained, and differences between the irreversible and the reversible solutions are investigated.
REFERENCES
1.
E. N.
Miranda
, “Adiabatic reversible compression: A molecular view
,” Eur. J. Phys.
23
(4
), 389
–393
(2002
).2.
J.
Zimba
, “Cooling of an ideal gas by rapid expansion
,” Am. J. Phys.
74
(1
), 54
–59
(2006
).3.
J.
Anacleto
, J. M.
Ferreira
, and A. A.
Soares
, “When an adiabatic irreversible expansion or compression becomes reversible
,” Eur. J. Phys.
30
(3
), 487
–495
(2009
).4.
J.
Anacleto
and J. A. C.
Anacleto
, “Thermodynamical interactions: Subtleties of heat and work concepts
,” Eur. J. Phys.
29
(3
), 555
–566
(2008
).5.
E. A.
Gislason
, “A close examination of the motion of an adiabatic piston
,” Am. J. Phys.
78
(10
), 995
–1001
(2010
).6.
R. C.
Amor
and J. P. H.
Esguerra
, “Evolution of ideal gas mixtures confined in an insulated container by two identical pistons
,” Am. J. Phys.
78
(9
), 916
–919
(2010
).7.
M. W.
Zemansky
and R. H.
Dittman
, Heat and Thermodynamics
, 7th ed. (McGraw-Hill
, New York
, 1997
).8.
E. N.
Miranda
, “What lies between a free adiabatic expansion and a quasi-static one?
,” Eur. J. Phys.
29
(5
), 937
–943
(2008
).9.
J.
Anacleto
and M. G.
Pereira
, “From free expansion to abrupt compression of an ideal gas
,” Eur. J. Phys.
30
(1
), 177
–183
(2009
).10.
J.
Anacleto
and M. G.
Pereira
, “Adiabatic process reversibility: Microscopic and macroscopic views
,” Eur. J. Phys.
30
(3
), L35
–L40
(2009
).11.
See supplementary material at http://dx.doi.org/10.1119/1.3574392 for the software. This document can be reached via a direct link in the online article’s HTML reference section or via the EPAPS homepage (http://www.aip.org/pubservs/epaps.html).
12.
R. P.
Bauman
and H. L.
Cockerham
, “Pressure of an ideal gas on a moving piston
,” Am. J. Phys.
37
(7
), 675
–679
(1969
).13.
H.
Gould
, J.
Tobochnik
, and W.
Christian
, An Introduction to Computer Simulation Methods: Application to Physical Systems
, 3rd ed. (Addison Wesley
, San Francisco, MA
, 2006
).14.
J.
Anacleto
, “Identical thermodynamical processes and entropy
,” Can. J. Phys.
83
(6
), 629
–636
(2005
).15.
Handbook of Chemistry and Physics
, 85th ed., edited by D. R.
Lide
(CRC
, New York
, 2005
).16.
C.
Cercignani
, The Boltzmann Equation and Its Applications
(Springer-Verlag
, Heidelberg
, 1988
).17.
© 2011 American Association of Physics Teachers.
2011
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.