Entropy and the Thermodynamics of a Single Particle

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Entropy and the Thermodynamics of a Single
Particle
W. J. Wilson Department of Engineering and
Physics University of Central Oklahoma Edmond, OK
73034
2012 Oklahoma Academy of Sciences Annual
Technical Meeting University of Central
Oklahoma Edmond, OK November 9, 2012
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First Law Sign Convention

• Chemistry and Physics sign convention

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• For a single particle, U KEPE U(x,v) and
  F F(x,v) are functions of position and velocity
  only so if we use the work on system positive
  sign convention
• which becomes for a free(non-relativistic)
  particle,

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• Now if the change dx and dv occur in time dt
• So for a single particle system,

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• So for a single particle system,
• And for a closed system (no energy allowed to
  enter or escape)
• (i.e., an Adiabatic
  Process)
• We find

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• So for a single particle system, using the work
  done on the system is positive sign convention,
• Yields Newtons 2nd Law in the standard form
• Particle motions governed by Newtons 2nd Law
  correspond to adiabatic processes

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Generalized Newtons 2nd Law

• For a single particle,
• or

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• Now if the change dx and dv occur in time dt
• So for a single particle, isothermal system

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• So,
• Or
• 
  Generalized
• 
  2nd Law !

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• The extra Force-Like term in
• is an entropic force
• or

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Entropic Force Example Long Chain Molecules
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Expansion of Universe is Accelerating

• 2011 Physics Nobel Prize
• Saul Perlmutter (Lawrence Berkeley Lab)
• Brian Schmidt (Australian National Lab)
• Adam Reiss
• (Johns Hopkins)

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Dark Energy as Entropic Force?
Accelerating expansion
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Summary

• 1st Law of Thermodynamics (TdS dU Fdx )
  applied to a single particle leads to a
  generalized 2nd Law
• The entropic force term could give an explanation
  of the observed accelerating expansion of the
  universe.

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References
W. J. Wilson, The Thermodynamics of a Single
Particle System, 2012 Oklahoma Academy of
Sciences Annual Technical Meeting, Durant, OK,
November 11, 2011.Slides available at
http//cyberphysics.org/wwilson. E.C.G.
Stueckelberg and P. B. Scheurer, Thermocinéque
Phénoménologique Galiléenne, (Birkhauser,
Stuttgart, 1974) P.E. Williams, On a Possible
Formulation of Particle Dynamics in Terms of
Thermodynamics Conceptualizations and the Role of
Entropy in It (M.S. Thesis, Naval Postgraduate
School, Monterey, CA, 1976).