### Abstract

Original language | English |
---|---|

Journal | Molecular Simulation |

Volume | 37 |

Issue number | 4 |

Pages (from-to) | 334-249 |

Number of pages | 16 |

ISSN | 0892-7022 |

DOIs | |

Publication status | Published - 28 Mar 2011 |

### Keywords

- Foundations
- thermodynamics
- Dynamical Systems
- adiabatic piston

### Cite this

*Molecular Simulation*,

*37*(4), 334-249. https://doi.org/10.1080/08927022.2011.557831

}

*Molecular Simulation*, vol. 37, no. 4, pp. 334-249. https://doi.org/10.1080/08927022.2011.557831

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

Research output: Contribution to journal › Journal article › Research › peer-review

TY - JOUR

T1 - Pistonics

T2 - the foundation of elementary thermodynamics

AU - Perram, John W.

AU - Præstgaard, Eigil

AU - Smith, Edgar R.

PY - 2011/3/28

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.

KW - Foundations

KW - thermodynamics

KW - Dynamical Systems

KW - adiabatic piston

U2 - 10.1080/08927022.2011.557831

DO - 10.1080/08927022.2011.557831

M3 - Journal article

VL - 37

SP - 334

EP - 249

JO - Molecular Simulation

JF - Molecular Simulation

SN - 0892-7022

IS - 4

ER -