Nonmonotonic pressure as a function of the density in a fluid without attractive forces
A simple result for the pressure of a hard sphere fluid that was developed many years ago by Rennert is extended in a straightforward manner by adding additional terms that are of the same form as Rennert's formula. The resulting expression is moderately accurate but its accuracy does not neces...
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| Дата: | 2013 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут фізики конденсованих систем НАН України
2013
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/120845 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Nonmonotonic pressure as a function of the density in a fluid without attractive forces / D. Henderson // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43001:1-4. — Бібліогр.: 7 назв. — англ. |
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irk-123456789-1208452017-06-14T03:03:19Z Nonmonotonic pressure as a function of the density in a fluid without attractive forces Henderson, D. A simple result for the pressure of a hard sphere fluid that was developed many years ago by Rennert is extended in a straightforward manner by adding additional terms that are of the same form as Rennert's formula. The resulting expression is moderately accurate but its accuracy does not necessarily improve as additional terms are included. This expression has the interesting consequence that the pressure can have a maximum, as the density increases, which is consistent with the freezing of the hard spheres. This occurs solely as a consequence of repulsive interactions. Only the Born-Green-Yvon and Kirkwood theories show such behavior for hard spheres and they require the numerical solution of an integral equation. The procedure outlined here is ad hoc but is, perhaps, useful just as the popular Carnahan-Starling equation for the hard sphere pressure is also ad hoc but useful. Простий результат для тиску плину твердих сфер, який був отриманий багато рокiв тому Реннертом, розширено в простий спосiб шляхом додавання членiв, якi мають такий же вигляд як формула Реннерта. Результуючий вираз є посередньо точним, але його точнiсть не обов’язково покращиться, якщо включити додатковi члени. Цiкавим наслiдком отриманого виразу є те, що тиск може мати максимум, коли густина зростає, що узгоджується iз твердненням твердих сфер. Це вiдбувається виключно як наслiдок короткодiйних взаємодiй. Лише теорiї Борна-Грiна-Iвона i Кiрквуда показують таку поведiнку для твердих сфер i вони потребують числового розв’язку iнтегрального рiвняння. Процедура, окреслена тут є ad hoc, але можливо є корисною такою ж мiрою, як i популярне рiвняння Карнагана-Старлiнга для тиску твердих сфер, яке є також ad hoc, але корисним. 2013 Article Nonmonotonic pressure as a function of the density in a fluid without attractive forces / D. Henderson // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43001:1-4. — Бібліогр.: 7 назв. — англ. 1607-324X PACS: 05.20.-y, 05.20.Jj, 64.10.+h, 64.30.+t, 64.70.Hz DOI:10.5488/CMP.16.43001 arXiv:1312.3547 http://dspace.nbuv.gov.ua/handle/123456789/120845 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
A simple result for the pressure of a hard sphere fluid that was developed many years ago by Rennert is extended in a straightforward manner by adding additional terms that are of the same form as Rennert's formula. The resulting expression is moderately accurate but its accuracy does not necessarily improve as additional terms are included. This expression has the interesting consequence that the pressure can have a maximum, as the density increases, which is consistent with the freezing of the hard spheres. This occurs solely as a consequence of repulsive interactions. Only the Born-Green-Yvon and Kirkwood theories show such behavior for hard spheres and they require the numerical solution of an integral equation. The procedure outlined here is ad hoc but is, perhaps, useful just as the popular Carnahan-Starling equation for the hard sphere pressure is also ad hoc but useful. |
| format |
Article |
| author |
Henderson, D. |
| spellingShingle |
Henderson, D. Nonmonotonic pressure as a function of the density in a fluid without attractive forces Condensed Matter Physics |
| author_facet |
Henderson, D. |
| author_sort |
Henderson, D. |
| title |
Nonmonotonic pressure as a function of the density in a fluid without attractive forces |
| title_short |
Nonmonotonic pressure as a function of the density in a fluid without attractive forces |
| title_full |
Nonmonotonic pressure as a function of the density in a fluid without attractive forces |
| title_fullStr |
Nonmonotonic pressure as a function of the density in a fluid without attractive forces |
| title_full_unstemmed |
Nonmonotonic pressure as a function of the density in a fluid without attractive forces |
| title_sort |
nonmonotonic pressure as a function of the density in a fluid without attractive forces |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120845 |
| citation_txt |
Nonmonotonic pressure as a function of the density in a fluid without attractive forces / D. Henderson // Condensed Matter Physics. — 2013. — Т. 16, № 4. — С. 43001:1-4. — Бібліогр.: 7 назв. — англ. |
| series |
Condensed Matter Physics |
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AT hendersond nonmonotonicpressureasafunctionofthedensityinafluidwithoutattractiveforces |
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2023-10-18T20:38:17Z |
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2023-10-18T20:38:17Z |
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