发表机构
Osaka Kyoiku University; Ikeda Senior High School Attached to Osaka Kyoiku University; Tennoji Senior High School Attached to Osaka Kyoiku University（大阪教育大学; 大阪教育大学附属池田高等学校; 大阪教育大学附属天王寺高等学校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究重新设计水的比热实验，通过尺度分析与数据坍缩帮助学生从数据构建经验模型，并揭示乘法缩放的局限及模型有效域，整合数据驱动与理论推理。
AI 中文摘要
在物理入门实验室中，一个核心教学目标在于帮助学生从经验数据中构建并评估数学模型，而非直接套用给定公式。我们提出了对经典的水的比热实验进行数据驱动式重新设计，强调将尺度分析和数据坍缩作为模型构建的工具。该活动将结构化的实验与解析指导同教师引导的提问相结合，同时刻意推迟热力学理论的引入。学生在各种实验条件下收集温度-时间数据，产生多组最初看似不相关的数据集。通过连续的重新缩放，学生降低了变量空间的维度，并将数据坍缩到一条单一的主曲线上，由此他们构建了一个将能量输入、质量和温度变化联系起来的经验模型。该分析凸显了乘法性缩放的一个局限：量热计的加性贡献无法被消除，导致子系统贡献的结构性不可辨识性。为了阐明模型的有效域，事后引入热力学描述作为界定经验模型解释范围的框架。从这个意义上讲，本工作的核心贡献在于利用数据驱动建模既构建模型，又揭示其内在局限。该实验提供了一个易于理解的范例，展示了如何在入门实验室中整合缩放、数据坍缩和理论推理。
英文摘要
We present a new version of the classic specific heat of water experiment that emphasizes scaling analysis and data collapse as tools for model construction in contrast to the usual approach of using a previously-established formula. The activity combines structured experimental and analytical guidance with instructor-mediated questioning; the corresponding thermodynamic theory is deliberately postponed. Students collect temperature-time data under various conditions, producing multiple data sets that initially appear unrelated. Through successive rescalings, they reduce the dimensionality of the variable space and achieve data collapse onto a single master curve, from which they formulate an empirical model relating energy input, mass, and temperature change. That the effect of the calorimeter cannot be eliminated in the analysis leads to a non-identifiability of the subsystem contributions. The conventional thermodynamic description is introduced a posteriori as a boundary-setting framework for interpreting the empirical model and clarifying its applicability. The central contribution of this work is to use data-driven modeling both to construct models and to reveal their limitations.
Comments36 pages, 3 figures and 1 table. Earlier version posted on Jxiv (https://doi.org/10.51094/jxiv.4171). Version 1 substantially expanded the instructional framing and implementation materials; Version 2 streamlines overlapping discussion and strengthens the overall argument
