Pistonics

the foundation of elementary thermodynamics

John W. Perram, Eigil Præstgaard, Edgar R. Smith

    Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

    Resumé

    By arguing that the expression 3PV/2 for the kinetic energy of an ideal gas is its internal energy function, we avoid the standard appeal to an equipartition theorem and, by analysing the Carnot cycle for a cylinder of gas enclosed by a piston, we show that the Kelvin temperature of an ideal gas is proportional to its internal energy. We report molecular dynamics experiments with ideal gas particles and show that they can exchange energy with their container. We then construct a dynamical system modelling the motion of the piston and heat transfer to the surroundings when the piston is released into a region of different pressure. For isothermal processes, we show that the system decays to equilibrium through damped oscillations in such a way that the work done by the enclosed gas is equal to the negative of the work done by the external pressure. We then show that simple control strategies applied to the dynamical system can make it resemble a quasi-static process. We then generalise the dynamical system to a two-compartment adiabatic cylinder in which the gases in the two chambers are separated by a movable piston. We show that, if the piston is subjected to infinitesimal kinetic friction, in all cases it relaxes to the stable fixed point predicted by equilibrium thermodynamics.
    OriginalsprogEngelsk
    TidsskriftMolecular Simulation
    Vol/bind37
    Udgave nummer4
    Sider (fra-til)334-249
    Antal sider16
    ISSN0892-7022
    DOI
    StatusUdgivet - 28 mar. 2011

    Citer dette

    Perram, John W. ; Præstgaard, Eigil ; Smith, Edgar R. / Pistonics : the foundation of elementary thermodynamics. I: Molecular Simulation. 2011 ; Bind 37, Nr. 4. s. 334-249.
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    Perram, JW, Præstgaard, E & Smith, ER 2011, 'Pistonics: the foundation of elementary thermodynamics', Molecular Simulation, bind 37, nr. 4, s. 334-249. https://doi.org/10.1080/08927022.2011.557831

    Pistonics : the foundation of elementary thermodynamics. / Perram, John W.; Præstgaard, Eigil; Smith, Edgar R.

    I: Molecular Simulation, Bind 37, Nr. 4, 28.03.2011, s. 334-249.

    Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

    TY - JOUR

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    T2 - the foundation of elementary thermodynamics

    AU - Perram, John W.

    AU - Præstgaard, Eigil

    AU - Smith, Edgar R.

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    Y1 - 2011/3/28

    N2 - By arguing that the expression 3PV/2 for the kinetic energy of an ideal gas is its internal energy function, we avoid the standard appeal to an equipartition theorem and, by analysing the Carnot cycle for a cylinder of gas enclosed by a piston, we show that the Kelvin temperature of an ideal gas is proportional to its internal energy. We report molecular dynamics experiments with ideal gas particles and show that they can exchange energy with their container. We then construct a dynamical system modelling the motion of the piston and heat transfer to the surroundings when the piston is released into a region of different pressure. For isothermal processes, we show that the system decays to equilibrium through damped oscillations in such a way that the work done by the enclosed gas is equal to the negative of the work done by the external pressure. We then show that simple control strategies applied to the dynamical system can make it resemble a quasi-static process. We then generalise the dynamical system to a two-compartment adiabatic cylinder in which the gases in the two chambers are separated by a movable piston. We show that, if the piston is subjected to infinitesimal kinetic friction, in all cases it relaxes to the stable fixed point predicted by equilibrium thermodynamics.

    AB - By arguing that the expression 3PV/2 for the kinetic energy of an ideal gas is its internal energy function, we avoid the standard appeal to an equipartition theorem and, by analysing the Carnot cycle for a cylinder of gas enclosed by a piston, we show that the Kelvin temperature of an ideal gas is proportional to its internal energy. We report molecular dynamics experiments with ideal gas particles and show that they can exchange energy with their container. We then construct a dynamical system modelling the motion of the piston and heat transfer to the surroundings when the piston is released into a region of different pressure. For isothermal processes, we show that the system decays to equilibrium through damped oscillations in such a way that the work done by the enclosed gas is equal to the negative of the work done by the external pressure. We then show that simple control strategies applied to the dynamical system can make it resemble a quasi-static process. We then generalise the dynamical system to a two-compartment adiabatic cylinder in which the gases in the two chambers are separated by a movable piston. We show that, if the piston is subjected to infinitesimal kinetic friction, in all cases it relaxes to the stable fixed point predicted by equilibrium thermodynamics.

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    KW - Dynamical Systems

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