A physical point of view on the arithmetic and geometric mean inequality

IF 0.6 4区教育学 Q4 EDUCATION, SCIENTIFIC DISCIPLINES

European Journal of Physics Pub Date : 2023-11-09 DOI:10.1088/1361-6404/ad0b3b

Michele Modestino, Roberto De Luca, Orazio Faella

引用次数: 0

Abstract

Abstract We propose a simple experiment designed to justify the arithmetic and geometric mean inequality by means of the laws of thermodynamics. The experiment consists in measuring the entropy variation ΔS in the thermodynamic irreversible process of cooling a metal in water. By considering the metal and water as a single isolated system, the arithmetic and geometric theorem is seen to hold by noticing that ΔS is positive for this irreversible transformation. These interdisciplinary activities may be used to reinforce basic concepts in thermodynamics in high school or first-year college students.

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从物理角度看算术和几何平均不等式

摘要:我们提出了一个简单的实验，旨在用热力学定律证明算术和几何平均不等式。实验是测量金属在水中冷却的热力学不可逆过程中的熵变ΔS。把金属和水看作一个孤立的系统，注意到ΔS对这个不可逆的变换是正的，就可以看出算术和几何定理是成立的。这些跨学科的活动可以用来加强高中或大学一年级学生的热力学基本概念。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

European Journal of Physics 物理-物理：综合

CiteScore

1.70

自引率

28.60%

发文量

128

审稿时长

3-8 weeks

期刊介绍： European Journal of Physics is a journal of the European Physical Society and its primary mission is to assist in maintaining and improving the standard of taught physics in universities and other institutes of higher education. Authors submitting articles must indicate the usefulness of their material to physics education and make clear the level of readership (undergraduate or graduate) for which the article is intended. Submissions that omit this information or which, in the publisher''s opinion, do not contribute to the above mission will not be considered for publication. To this end, we welcome articles that provide original insights and aim to enhance learning in one or more areas of physics. They should normally include at least one of the following: Explanations of how contemporary research can inform the understanding of physics at university level: for example, a survey of a research field at a level accessible to students, explaining how it illustrates some general principles. Original insights into the derivation of results. These should be of some general interest, consisting of more than corrections to textbooks. Descriptions of novel laboratory exercises illustrating new techniques of general interest. Those based on relatively inexpensive equipment are especially welcome. Articles of a scholarly or reflective nature that are aimed to be of interest to, and at a level appropriate for, physics students or recent graduates. Descriptions of successful and original student projects, experimental, theoretical or computational. Discussions of the history, philosophy and epistemology of physics, at a level accessible to physics students and teachers. Reports of new developments in physics curricula and the techniques for teaching physics. Physics Education Research reports: articles that provide original experimental and/or theoretical research contributions that directly relate to the teaching and learning of university-level physics.