Ge Yingbin, Montgomery Samuel L, Borrello Gabriel L
Department of Chemistry, Central Washington University, Ellensburg, Washington 98926, United States.
ACS Omega. 2021 Apr 14;6(16):11083-11085. doi: 10.1021/acsomega.1c01208. eCollection 2021 Apr 27.
Can be less than ? This is a fundamental question in physics, chemistry, chemical engineering, and mechanical engineering. This question hangs in the minds of many students, instructors, and researchers. The first instinct is to answer "Yes, for water between 0 and 4 °C" if one knows that water expands as temperature decreases in this temperature range. The same question is asked in several Physical Chemistry and Physics textbooks. Students are supposed to answer that water contracts when heated at below 4 °C in an isobaric process. Because work is done to the contracting water, less heat is required to increase the water temperature in an isobaric process than in an isochoric process. Therefore, is less than . However, this answer is fundamentally flawed because it assumes, implicitly and incorrectly, that the internal energy change of water depends solely on its temperature change. Neglecting the variation of the internal energy with volume (internal pressure) will invalidate the Clausius inequality and violate the second law of thermodynamics. Once the internal pressure is properly taken into account, it becomes clear that cannot be less than for any substance at any temperature regardless of the sign of the thermal expansion coefficient of the substance.
它能小于 吗？这是物理学、化学、化学工程和机械工程中的一个基本问题。这个问题萦绕在许多学生、教师和研究人员的脑海中。如果一个人知道在这个温度范围内水会随着温度降低而膨胀，那么第一反应就是回答“是的，对于0到4摄氏度之间的水”。几本物理化学和物理教材中都提出了同样的问题。学生们应该回答，在等压过程中，温度低于4摄氏度时水受热会收缩。因为对收缩的水做功，所以在等压过程中升高水温所需的热量比在等容过程中少。因此， 小于 。然而，这个答案从根本上说是有缺陷的，因为它隐含且错误地假设水的内能变化仅取决于其温度变化。忽略内能随体积（内压）的变化会使克劳修斯不等式无效，并违反热力学第二定律。一旦正确考虑内压，就会清楚地看到，对于任何物质在任何温度下， 都不可能小于 ，无论该物质热膨胀系数的符号如何。
