Free Volume of the Hard Spheres Gas
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| Title: | Free Volume of the Hard Spheres Gas |
|---|---|
| Language: | English |
| Authors: | Shutler, P. M. E., Martinez, J. C., Springham, S. V. |
| Source: | European Journal of Physics. May 2007 28(3):615-624. |
| Availability: | Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP |
| Peer Reviewed: | Y |
| Physical Description: | |
| Page Count: | 10 |
| Publication Date: | 2007 |
| Document Type: | Journal Articles Reports - Research |
| Descriptors: | Physics, Scientific Concepts, Monte Carlo Methods, Computer Simulation, Equations (Mathematics) |
| DOI: | 10.1088/0143-0807/28/3/023 |
| ISSN: | 0143-0807 |
| Abstract: | The Enskog factor [chi] plays a central role in the theory of dense gases, quantifying how the finite size of molecules causes many physical quantities, such as the equation of state, the mean free path, and the diffusion coefficient, to deviate from those of an ideal gas. We suggest an intuitive but rigorous derivation of this fact by showing how all these instances of [chi] amount to different ways of looking at the derivative of the free volume with respect to the packing density. We show how to compute the free volume explicitly for finitely many molecules in a finite box and demonstrate excellent agreement between its derivative and mean free paths obtained from computer simulations, where the number of molecules N varies from 1000 down to 2, and where the mean free paths vary from many times the molecular diameter at low density down to a small fraction of the molecular diameter at high density. Since the boundary corrections involved are relatively simple and intuitive this strengthens the link between the teaching of large N theory for real physical systems, and the running of small N simulations in undergraduate physics laboratories. (Contains 6 figures.) |
| Abstractor: | As Provided |
| Number of References: | 8 |
| Entry Date: | 2009 |
| Accession Number: | EJ829429 |
| Database: | ERIC |
| FullText | Text: Availability: 0 |
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| Header | DbId: eric DbLabel: ERIC An: EJ829429 AccessLevel: 3 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Free Volume of the Hard Spheres Gas – Name: Language Label: Language Group: Lang Data: English – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Shutler%2C+P%2E+M%2E+E%2E%22">Shutler, P. M. E.</searchLink><br /><searchLink fieldCode="AR" term="%22Martinez%2C+J%2E+C%2E%22">Martinez, J. C.</searchLink><br /><searchLink fieldCode="AR" term="%22Springham%2C+S%2E+V%2E%22">Springham, S. V.</searchLink> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="SO" term="%22European+Journal+of+Physics%22"><i>European Journal of Physics</i></searchLink>. May 2007 28(3):615-624. – Name: Avail Label: Availability Group: Avail Data: Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail: info@ioppubusa.com; Web site: http://www.iop.org/EJ/journal/EJP – Name: PeerReviewed Label: Peer Reviewed Group: SrcInfo Data: Y – Name: PhysDesc Label: Physical Description Group: PhysDesc Data: PDF – Name: Pages Label: Page Count Group: Src Data: 10 – Name: DatePubCY Label: Publication Date Group: Date Data: 2007 – Name: TypeDocument Label: Document Type Group: TypDoc Data: Journal Articles<br />Reports - Research – Name: Subject Label: Descriptors Group: Su Data: <searchLink fieldCode="DE" term="%22Physics%22">Physics</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+Concepts%22">Scientific Concepts</searchLink><br /><searchLink fieldCode="DE" term="%22Monte+Carlo+Methods%22">Monte Carlo Methods</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+Simulation%22">Computer Simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Equations+%28Mathematics%29%22">Equations (Mathematics)</searchLink> – Name: DOI Label: DOI Group: ID Data: 10.1088/0143-0807/28/3/023 – Name: ISSN Label: ISSN Group: ISSN Data: 0143-0807 – Name: Abstract Label: Abstract Group: Ab Data: The Enskog factor [chi] plays a central role in the theory of dense gases, quantifying how the finite size of molecules causes many physical quantities, such as the equation of state, the mean free path, and the diffusion coefficient, to deviate from those of an ideal gas. We suggest an intuitive but rigorous derivation of this fact by showing how all these instances of [chi] amount to different ways of looking at the derivative of the free volume with respect to the packing density. We show how to compute the free volume explicitly for finitely many molecules in a finite box and demonstrate excellent agreement between its derivative and mean free paths obtained from computer simulations, where the number of molecules N varies from 1000 down to 2, and where the mean free paths vary from many times the molecular diameter at low density down to a small fraction of the molecular diameter at high density. Since the boundary corrections involved are relatively simple and intuitive this strengthens the link between the teaching of large N theory for real physical systems, and the running of small N simulations in undergraduate physics laboratories. (Contains 6 figures.) – Name: AbstractInfo Label: Abstractor Group: Ab Data: As Provided – Name: Ref Label: Number of References Group: RefInfo Data: 8 – Name: DateEntry Label: Entry Date Group: Date Data: 2009 – Name: AN Label: Accession Number Group: ID Data: EJ829429 |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=eric&AN=EJ829429 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1088/0143-0807/28/3/023 Languages: – Text: English PhysicalDescription: Pagination: PageCount: 10 StartPage: 615 Subjects: – SubjectFull: Physics Type: general – SubjectFull: Scientific Concepts Type: general – SubjectFull: Monte Carlo Methods Type: general – SubjectFull: Computer Simulation Type: general – SubjectFull: Equations (Mathematics) Type: general Titles: – TitleFull: Free Volume of the Hard Spheres Gas Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Shutler, P. M. E. – PersonEntity: Name: NameFull: Martinez, J. C. – PersonEntity: Name: NameFull: Springham, S. V. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Type: published Y: 2007 Identifiers: – Type: issn-print Value: 0143-0807 Numbering: – Type: volume Value: 28 – Type: issue Value: 3 Titles: – TitleFull: European Journal of Physics Type: main |
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