Generalised Isentropic Relations in Thermodynamics
Isentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations f...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Energies |
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| Online Access: | https://www.mdpi.com/1996-1073/16/5/2281 |
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| author | Pim Nederstigt Rene Pecnik |
| author_facet | Pim Nederstigt Rene Pecnik |
| author_sort | Pim Nederstigt |
| collection | DOAJ |
| description | Isentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations for isentropic transformations in gas dynamics are limited to ideal gases, the inability to analytically describe isentropic processes for non-ideal gases is a fundamental shortcoming. This work presents generalised isentropic relations in thermodynamics based on the work by Kouremenos et al., where three isentropic exponents <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>P</mi><mi>v</mi></mrow></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>T</mi><mi>v</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>P</mi><mi>T</mi></mrow></msub></semantics></math></inline-formula> are introduced to replace the ideal gas isentropic exponent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> to incorporate the departure from the non-ideal gas behaviour. The general applicability of the generalised isentropic relations is presented by exploring its connections to existing isentropic models for ideal gases and incompressible liquids. Generalised formulations for the speed of sound, the Bernoulli equation, compressible isentropic flow transformations, and isentropic work are presented thereafter, connecting previously disjoint theories for gases and liquids. Lastly, the generalised expressions are demonstrated for practical engineering examples, and their accuracy is discussed. |
| first_indexed | 2024-03-11T07:26:29Z |
| format | Article |
| id | doaj.art-59b4e472c6b9425d9467e4b11f2495a6 |
| institution | Directory Open Access Journal |
| issn | 1996-1073 |
| language | English |
| last_indexed | 2024-03-11T07:26:29Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Energies |
| spelling | doaj.art-59b4e472c6b9425d9467e4b11f2495a62023-11-17T07:36:33ZengMDPI AGEnergies1996-10732023-02-01165228110.3390/en16052281Generalised Isentropic Relations in ThermodynamicsPim Nederstigt0Rene Pecnik1Department of Process & Energy, Delft University of Technology, 2628 CD Delft, The NetherlandsDepartment of Process & Energy, Delft University of Technology, 2628 CD Delft, The NetherlandsIsentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations for isentropic transformations in gas dynamics are limited to ideal gases, the inability to analytically describe isentropic processes for non-ideal gases is a fundamental shortcoming. This work presents generalised isentropic relations in thermodynamics based on the work by Kouremenos et al., where three isentropic exponents <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>P</mi><mi>v</mi></mrow></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>T</mi><mi>v</mi></mrow></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>γ</mi><mrow><mi>P</mi><mi>T</mi></mrow></msub></semantics></math></inline-formula> are introduced to replace the ideal gas isentropic exponent <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>γ</mi></semantics></math></inline-formula> to incorporate the departure from the non-ideal gas behaviour. The general applicability of the generalised isentropic relations is presented by exploring its connections to existing isentropic models for ideal gases and incompressible liquids. Generalised formulations for the speed of sound, the Bernoulli equation, compressible isentropic flow transformations, and isentropic work are presented thereafter, connecting previously disjoint theories for gases and liquids. Lastly, the generalised expressions are demonstrated for practical engineering examples, and their accuracy is discussed.https://www.mdpi.com/1996-1073/16/5/2281isentropic relationsreal gas thermodynamicsspeed of soundcompressible fluid flowscompressibilityisentropic work |
| spellingShingle | Pim Nederstigt Rene Pecnik Generalised Isentropic Relations in Thermodynamics Energies isentropic relations real gas thermodynamics speed of sound compressible fluid flows compressibility isentropic work |
| title | Generalised Isentropic Relations in Thermodynamics |
| title_full | Generalised Isentropic Relations in Thermodynamics |
| title_fullStr | Generalised Isentropic Relations in Thermodynamics |
| title_full_unstemmed | Generalised Isentropic Relations in Thermodynamics |
| title_short | Generalised Isentropic Relations in Thermodynamics |
| title_sort | generalised isentropic relations in thermodynamics |
| topic | isentropic relations real gas thermodynamics speed of sound compressible fluid flows compressibility isentropic work |
| url | https://www.mdpi.com/1996-1073/16/5/2281 |
| work_keys_str_mv | AT pimnederstigt generalisedisentropicrelationsinthermodynamics AT renepecnik generalisedisentropicrelationsinthermodynamics |