{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:40:50Z","timestamp":1760244050263,"version":"build-2065373602"},"reference-count":36,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2008,9,20]],"date-time":"2008-09-20T00:00:00Z","timestamp":1221868800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>A novel thermodynamic treatment of residual entropy in crystals, involving the configurational partition function, is suggested, which is consistent with both classical and statistical thermodynamics. It relates residual entropy to the inherent latent heat which would be released upon cooling if the reversible path were available. The nature of this heat is that if the crystal possessing residual entropy freezes above its Boltzmann\u2019s characteristic temperature of molecular alignment, the difference in energy between different molecular arrangements is overcome by the kT heat bath to form a nearly-ideal solution. However, upon cooling below this characteristic temperature, they would separate with a concomitant release of the corresponding energy, provided the reversible path were available.<\/jats:p>","DOI":"10.3390\/e10030274","type":"journal-article","created":{"date-parts":[[2008,9,29]],"date-time":"2008-09-29T05:43:40Z","timestamp":1222667020000},"page":"274-284","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Residual Entropy, the Third Law and Latent Heat"],"prefix":"10.3390","volume":"10","author":[{"given":"Evguenii","family":"Kozliak","sequence":"first","affiliation":[{"name":"Department of Chemistry, University of North Dakota, Grand Forks, ND 58202, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank L.","family":"Lambert","sequence":"additional","affiliation":[{"name":"Department of Chemistry, Occidental College, Los Angeles, CA 90041, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2008,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2610","DOI":"10.1021\/ja01346a004","article-title":"The Heat Capacity and Entropy of Carbon Monoxide","volume":"54","author":"Clayton","year":"1932","journal-title":"J. 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Lambert [15,16,17,18] since 1999, have successfully advocated this modern interpretation. Nineteen chemistry texts have replaced the traditional \u201centropy is disorder\u201d with an emphasis on entropy as a measure of the quantity of energy dispersed in a process (a list was available on www.entropysite.com at April 2007 and links therefrom.)"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1261","DOI":"10.1119\/1.18389","article-title":"Thermodynamic Entropy: the Spreading and Sharing of Energy","volume":"64","author":"Leff","year":"1996","journal-title":"Am. J. Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1744","DOI":"10.1007\/s10701-007-9163-3","article-title":"Entropy: Its Language, and Interpretation","volume":"37","author":"Leff","year":"2007","journal-title":"Found. 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Soc."},{"key":"ref_26","unstructured":"Petrenko, V.F., and Whitworth, R.W. (1999). Physics of Ice, Oxford University Press."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Goldstein\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t              M.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          On the Reality of Residual Entropies of Glasses and Disordered Crystals\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          J. Chem. Phys.\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          2008\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          128\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          154510\/1\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          154510\/7\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t         but see also [28] and [29].","DOI":"10.1063\/1.2899642"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"067101\/1","DOI":"10.1063\/1.2965901","article-title":"Comment on: \"On the Reality of Residual Entropies of Glasses and Disordered Crystals. \"","volume":"129","author":"Gupta","year":"2008","journal-title":"J. Chem. 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Physics and Chemistry of Ice, Hokkaido University Press."},{"key":"ref_33","unstructured":"\u2018Characteristic\u2019 temperature, in our opinion, is more thermodynamically correct than \u2018glass temperature\u2019 used before [27] because it relates this value to well-defined (exact) \u0394\u03b5\/k linked to the fundamental Boltzmann distribution whereas real-world glasses are often irregular and poorly defined."},{"key":"ref_34","unstructured":"This observation illustrates the fact that no \u201cperpetual motion machine of the second kind\u201d may be constructed based on the hysteresis loop shown in Figure 1 because without the reversible path the loop cannot be completed [27] whereas, once the reversible path is enabled, the loop collapses."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"014415\/1","DOI":"10.1103\/PhysRevB.68.014415","article-title":"Anisotropic Release of the Residual Zero-point Entropy in the Spin Ice Compound Dy2Ti2O7: Kagome Ice Behavior","volume":"68","author":"Higashinaka","year":"2003","journal-title":"Phys. Rev. B."},{"key":"ref_36","first-page":"587","article-title":"Hot (Subcritical) Water Extraction","volume":"37","author":"Hawthorne","year":"2002","journal-title":"Compr. Anal. Chem."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/3\/274\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:20:59Z","timestamp":1760221259000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/10\/3\/274"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,9,20]]},"references-count":36,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2008,9]]}},"alternative-id":["e10030274"],"URL":"https:\/\/doi.org\/10.3390\/e10030274","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2008,9,20]]}}}