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arXiv · 2209.03323

The R\"uchardt experiment revisited: using simple theory, accurate measurement and python based data analysis

Chris Shearwood·Peter A. Sloan
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Abstract

This project uses the R\"uchardt 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 mid year undergraduate student. We present simple derivations of the main relationships that govern the experiment, a detailed data analysis of the physics of the apparatus and of the experimental data. We find $f(\textrm{He}) = 3.48 \pm 0.14$, $f(\textrm{N}_2) = 4.92 \pm 0.24$, $f(\textrm{Air}) = 4.96 \pm 0.25$, $f(\textrm{CO}_2) = 6.46 \pm 0.39$ 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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Chris Shearwood, Peter A. Sloan. 2022-09-07. The R\"uchardt experiment revisited: using simple theory, accurate measurement and python based data analysis. https://doi.org/10.1088/1361-6404/acc5c2

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