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Dimensional transitions in thermodynamic properties of ideal Maxwell-Boltzmann gases
Istanbul Technical University, Energy Institute.
Istanbul Technical University, Energy Institute.ORCID iD: 0000-0002-7431-5115
2015 (English)In: Physica Scripta, ISSN 0031-8949, E-ISSN 1402-4896, Vol. 90, article id 045208Article in journal (Refereed) Published
Abstract [en]

An ideal Maxwell–Boltzmann gas confined in various rectangular nanodomains is considered underquantum size effects. Thermodynamic quantities are calculated from their relations with the partitionfunction, which consists of triple infinite summations over momentum states in each direction. Toobtain analytical expressions, summations are converted to integrals for macrosystems by acontinuum approximation, which fails at the nanoscale. To avoid both the numerical calculation ofsummations and the failure of their integral approximations at the nanoscale, a method which gives ananalytical expression for a single particle partition function (SPPF) is proposed. It is shown that adimensional transition in momentum space occurs at a certain magnitude of confinement. Therefore,to represent the SPPF by lower-dimensional analytical expressions becomes possible, rather thannumerical calculation of summations. Considering rectangular domains with different aspect ratios, acomparison of the results of derived expressions with those of summation forms of the SPPF is made.It is shown that analytical expressions for the SPPF give very precise results with maximum relativeerrors of around 1%, 2% and 3% at exactly the transition point for single, double and triple transitions,respectively. Based on dimensional transitions, expressions for free energy, entropy, internal energy,chemical potential, heat capacity and pressure are given analytically valid for any scale.

Place, publisher, year, edition, pages
2015. Vol. 90, article id 045208
National Category
Condensed Matter Physics
Identifiers
URN: urn:nbn:se:uu:diva-380285OAI: oai:DiVA.org:uu-380285DiVA, id: diva2:1299050
Available from: 2019-03-26 Created: 2019-03-26 Last updated: 2019-03-26

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