Data-driven modeling in the introductory physics laboratory: Scaling analysis and data collapse in the specific heat of water experiment
Abstract
We present a data-driven redesign of the classic specific-heat-of-water experiment that uses scaling analysis and data collapse for model construction rather than beginning with a previously established thermodynamic formula. The activity combines structured experimental and analytical guidance with instructor-mediated questioning, while the thermodynamic description is deliberately postponed. Students collect temperature-time data under different conditions and obtain a collapsed relation between the mass-normalized energy input and temperature rise through successive rescaling. They formulate an empirical model from this relation and test it using additional data not included in its construction. In the post-experimental discussion, the thermodynamic description shows that the fitted empirical constant characterizes the combined response of the water and calorimeter and approximates a quantity that depends weakly on water mass. Reanalysis of the mass-dependent data separates the two contributions, with limited precision over the available water-mass range. The copper cup is an intentional feature of the instructional design: its contribution is large enough to require physical interpretation but varies little enough over the explored mass range for the data to collapse approximately onto a single relation. The same apparatus thereby supports empirical model construction, thermodynamic interpretation, and separation of the component contributions.
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BibTeX
@misc{kushida2026datadriven,
title = {{Data-driven modeling in the introductory physics laboratory: Scaling analysis and data collapse in the specific heat of water experiment}},
author = {Kazumasa Kushida and Tomohiro Oda and Koji Yamaguchi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.15124},
eprint = {2609.15124},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15124},
}
RIS
TY - UNPB
TI - Data-driven modeling in the introductory physics laboratory: Scaling analysis and data collapse in the specific heat of water experiment
AU - Kazumasa Kushida
AU - Tomohiro Oda
AU - Koji Yamaguchi
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.15124
UR - https://arxiv.org/abs/2609.15124
AB - We present a data-driven redesign of the classic specific-heat-of-water experiment that uses scaling analysis and data collapse for model construction rather than beginning with a previously established thermodynamic formula. The activity combines structured experimental and analytical guidance with instructor-mediated questioning, while the thermodynamic description is deliberately postponed. Students collect temperature-time data under different conditions and obtain a collapsed relation between the mass-normalized energy input and temperature rise through successive rescaling. They formulate an empirical model from this relation and test it using additional data not included in its construction. In the post-experimental discussion, the thermodynamic description shows that the fitted empirical constant characterizes the combined response of the water and calorimeter and approximates a quantity that depends weakly on water mass. Reanalysis of the mass-dependent data separates the two contributions, with limited precision over the available water-mass range. The copper cup is an intentional feature of the instructional design: its contribution is large enough to require physical interpretation but varies little enough over the explored mass range for the data to collapse approximately onto a single relation. The same apparatus thereby supports empirical model construction, thermodynamic interpretation, and separation of the component contributions.
ER -