### Abstract

We calculate the asymptotic value of the pair probability density ρ_{2}(r_{2}, r_{1}) for finding a fluid particle at a point r_{2} far in the interior of a fluid, when it is known that there is a particle at r_{1} in contact with the walls (rigid) of the container. This value is different from the well-known expression for the asymptotic value of ρ_{2}(r_{2}, r_{1}) when both r_{2} and r_{1} are in the interior of the fluid. Our derivation is based on the virial theorem for total momentum fluctuations in an equilibrium system and makes use of the assumption that there are no long range correlations in a fluid. Application is made of our result to re-derive simply the expression for the second virial coefficient and the exact equation of state of a hard-sphere gas in one dimension. Quantum systems are also treated.

Original language | English (US) |
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Pages (from-to) | 64-68 |

Number of pages | 5 |

Journal | Physics of Fluids |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1960 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics