{"title":"A physical point of view on the arithmetic and geometric mean inequality","authors":"Michele Modestino, Roberto De Luca, Orazio Faella","doi":"10.1088/1361-6404/ad0b3b","DOIUrl":null,"url":null,"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.","PeriodicalId":50480,"journal":{"name":"European Journal of Physics","volume":" 18","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/1361-6404/ad0b3b","RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"EDUCATION, SCIENTIFIC DISCIPLINES","Score":null,"Total":0}
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.
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.
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