论文标题
平均温度的热力学定义
Thermodynamic definition of mean temperature
论文作者
论文摘要
平均温度的概念对于包括气候科学，流体动力学和生物物理学在内的许多领域至关重要。但是，到目前为止，其正确的热力学基础缺乏甚至是不可能的。物理上正确的定义不应基于均值的数学概念（例如平均几何或平均算术算术），因为它们忽略了温度概念的特殊性，并且因为它们不是唯一的。我们提供基于以下两个假设的平均温度的热力学定义。首先，由于正确的定义应必须涉及最初非平衡系统中的平衡过程，因此（分别）（分别）（分别）（分别）（分别）（分别）（分别）（分别）（分别）（分别）（分别）（分别）可逆的平衡和完全不可逆的平衡极端。其次，在热力学方法中，我们假设平均温度主要取决于能量和熵。加上维度分析，这两个假设导致平均温度的独特定义。具有温度独立的热容量的理想和（范德华）非理想气体的平均温度是由一般和紧凑的公式给出的，该公式（除初始温度以外）仅取决于热能和气体的浓度。
The notion of mean temperature is crucial for a number of fields including climate science, fluid dynamics and biophysics. However, so far its correct thermodynamic foundation is lacking or even believed to be impossible. A physically correct definition should not be based on mathematical notions of the means (e.g. the mean geometric or mean arithmetic), because they ignore the peculiarities of the notion of temperature, and because they are not unique. We offer a thermodynamic definition of the mean temperature that is based upon the following two assumptions. First, as the correct definition should necessarily involve equilibration processes in the initially non-equilibrium system, the mean temperature is bounded from below and above via looking at (respectively) the reversible versus fully irreversible extremes of equilibration. Second, within the thermodynamic approach we assume that the mean temperature is determined mostly by energy and entropy. Together with the dimensional analysis, the two assumptions lead to a unique definition of the mean temperature. The mean temperature for ideal and (van der Waals) non-ideal gases with temperature-independent heat capacity is given by a general and compact formula that (besides the initial temperatures) only depends on the heat-capacities and concentration of gases.
