The Rüchardt experiment revisited: using simple theory, accurate measurement and python based data analysis

Christopher Shearwood; Peter Sloan

doi:10.1088/1361-6404/acc5c2

The Rüchardt experiment revisited: using simple theory, accurate measurement and python based data analysis

Christopher Shearwood, Peter Sloan

Research output: Contribution to journal › Article › peer-review

2 Citations (SciVal)

Abstract

This project uses the Rüchardt experiment to determine the ratio of specific heats and hence the number of degrees of freedom f of different gases by measuring the frequency of damped simple harmonic motion where the gas provides the Hooke's law like spring of a cylinder-piston system. This project links mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics making it an excellent synoptic experiment for a year 2 undergraduate student and we detail our implementation of this team-based learning project. We present, for the Rüchardt experiment, simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and the experimental data. We find f(He) = 3.48 ± 0.14, f(N ₂) = 4.92 ± 0.24, f(Air) = 4.96 ± 0.25, f(CO ₂) = 6.46 ± 0.39 at room temperature and atmospheric pressure. The results for CO ₂ requires a statistical analysis of its vibrational modes. These results show that the expected results can be measured using fairly simple apparatus, coupled with careful analysis of large data sets.

Original language	English
Article number	035102
Journal	European Journal of Physics
Volume	44
Issue number	3
Early online date	27 Apr 2023
DOIs	https://doi.org/10.1088/1361-6404/acc5c2
Publication status	Published - 27 Apr 2023

Bibliographical note

Funding Information:
We thank Dr Simon Crampin and Dr Vicky Scowcroft for critical reading of the manuscript.

Data availability statement
The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.15125/BATH-01199 [26].

Keywords

Ruchardt's experiment
adiabatic coefficient
damped motion
dissipation
piston

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.1088/1361-6404/acc5c2Licence: CC BY

Cite this

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title = "The R{\"u}chardt experiment revisited: using simple theory, accurate measurement and python based data analysis",

abstract = "This project uses the R{\"u}chardt experiment to determine the ratio of specific heats and hence the number of degrees of freedom f of different gases by measuring the frequency of damped simple harmonic motion where the gas provides the Hooke's law like spring of a cylinder-piston system. This project links mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics making it an excellent synoptic experiment for a year 2 undergraduate student and we detail our implementation of this team-based learning project. We present, for the R{\"u}chardt experiment, simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and the experimental data. We find f(He) = 3.48 ± 0.14, f(N 2) = 4.92 ± 0.24, f(Air) = 4.96 ± 0.25, f(CO 2) = 6.46 ± 0.39 at room temperature and atmospheric pressure. The results for CO 2 requires a statistical analysis of its vibrational modes. These results show that the expected results can be measured using fairly simple apparatus, coupled with careful analysis of large data sets.",

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author = "Christopher Shearwood and Peter Sloan",

note = "Funding Information: We thank Dr Simon Crampin and Dr Vicky Scowcroft for critical reading of the manuscript. Data availability statement The data that support the findings of this study are openly available at the following URL/DOI: https://doi.org/10.15125/BATH-01199 [26].",

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N2 - This project uses the Rüchardt experiment to determine the ratio of specific heats and hence the number of degrees of freedom f of different gases by measuring the frequency of damped simple harmonic motion where the gas provides the Hooke's law like spring of a cylinder-piston system. This project links mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics making it an excellent synoptic experiment for a year 2 undergraduate student and we detail our implementation of this team-based learning project. We present, for the Rüchardt experiment, simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and the experimental data. We find f(He) = 3.48 ± 0.14, f(N 2) = 4.92 ± 0.24, f(Air) = 4.96 ± 0.25, f(CO 2) = 6.46 ± 0.39 at room temperature and atmospheric pressure. The results for CO 2 requires a statistical analysis of its vibrational modes. These results show that the expected results can be measured using fairly simple apparatus, coupled with careful analysis of large data sets.

AB - This project uses the Rüchardt experiment to determine the ratio of specific heats and hence the number of degrees of freedom f of different gases by measuring the frequency of damped simple harmonic motion where the gas provides the Hooke's law like spring of a cylinder-piston system. This project links mechanics, electromagnetism, thermodynamics, statistical mechanics and quantum mechanics making it an excellent synoptic experiment for a year 2 undergraduate student and we detail our implementation of this team-based learning project. We present, for the Rüchardt experiment, simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and the experimental data. We find f(He) = 3.48 ± 0.14, f(N 2) = 4.92 ± 0.24, f(Air) = 4.96 ± 0.25, f(CO 2) = 6.46 ± 0.39 at room temperature and atmospheric pressure. The results for CO 2 requires a statistical analysis of its vibrational modes. These results show that the expected results can be measured using fairly simple apparatus, coupled with careful analysis of large data sets.

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The Rüchardt experiment revisited: using simple theory, accurate measurement and python based data analysis

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this

The Rüchardt experiment revisited: using simple theory, accurate measurement and python based data analysis

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Datasets

Dataset for "The Ruchardt experiment revisited: using simple theory, accurate measurement and python based data analysis"

Cite this