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.

中文翻译：

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算术平均数和几何平均不等式的物理观点


我们提出了一个简单的实验，旨在通过热力学定律证明算术平均数和几何平均数不等式的合理性。该实验旨在测量金属在水中冷却的热力学不可逆过程中的熵变 ΔS。通过将金属和水视为一个孤立的系统，算术和几何定理被认为是成立的，因为注意到 ΔS 对于这种不可逆的转变是正的。这些跨学科活动可用于强化高中生或大学一年级学生的热力学基本概念。