### Abstract

At low temperatures, ice has a residual entropy, presumably caused by an indeterminacy in the positions of the hydrogen atoms. While the oxygen atoms are in a regular lattice, each O-H-O bond permits two possible positions for the hydrogen atom, subject to certain constraints called the "ice condition." The statement of the problem in two dimensions is to find the number of ways of drawing arrows on the bonds of a square planar net so that precisely two arrows point into each vertex. If N is the number of molecules and (for large N) WN is the number of arrangements, then S=NklnW. Our exact result is W=(43)32.

Original language | English (US) |
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Pages (from-to) | 162-172 |

Number of pages | 11 |

Journal | Physical Review |

Volume | 162 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1967 |

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### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*Physical Review*,

*162*(1), 162-172. https://doi.org/10.1103/PhysRev.162.162

}

*Physical Review*, vol. 162, no. 1, pp. 162-172. https://doi.org/10.1103/PhysRev.162.162

**Residual Entropy of Square Ice.** / Lieb, Elliott.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Residual Entropy of Square Ice

AU - Lieb, Elliott

PY - 1967/12/1

Y1 - 1967/12/1

N2 - At low temperatures, ice has a residual entropy, presumably caused by an indeterminacy in the positions of the hydrogen atoms. While the oxygen atoms are in a regular lattice, each O-H-O bond permits two possible positions for the hydrogen atom, subject to certain constraints called the "ice condition." The statement of the problem in two dimensions is to find the number of ways of drawing arrows on the bonds of a square planar net so that precisely two arrows point into each vertex. If N is the number of molecules and (for large N) WN is the number of arrangements, then S=NklnW. Our exact result is W=(43)32.

AB - At low temperatures, ice has a residual entropy, presumably caused by an indeterminacy in the positions of the hydrogen atoms. While the oxygen atoms are in a regular lattice, each O-H-O bond permits two possible positions for the hydrogen atom, subject to certain constraints called the "ice condition." The statement of the problem in two dimensions is to find the number of ways of drawing arrows on the bonds of a square planar net so that precisely two arrows point into each vertex. If N is the number of molecules and (for large N) WN is the number of arrangements, then S=NklnW. Our exact result is W=(43)32.

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U2 - https://doi.org/10.1103/PhysRev.162.162

DO - https://doi.org/10.1103/PhysRev.162.162

M3 - Article

VL - 162

SP - 162

EP - 172

JO - Physical Review

JF - Physical Review

SN - 0031-899X

IS - 1

ER -