论文标题
在液体震荡临界点上缩放的热力学推导
Thermodynamic derivation of scaling at the liquid-vapor critical point
论文作者
论文摘要
仅使用热力学和一般平衡条件，我们研究了液体蒸气相变临界点附近流体的熵。通过假设在临界点附近的共存曲线的一般形式，我们表明，熵作为能量和粒子密度的函数的功能依赖性必要遵守宽度假设的缩放形式。我们的分析允许讨论相应缩放函数的性质，并以有趣的预测是，临界等温线在能量和颗粒密度之间与共存曲线具有相同的功能依赖性。除了推导临界指数的预期相等性的推导外，导致缩放的条件还表明，尽管恒定体积的特定热量可以在临界点处发散，但等温可压缩性必须这样做。
With the use of thermodynamics and general equilibrium conditions only, we study the entropy of a fluid in the vicinity of the critical point of the liquid-vapor phase transition. By assuming a general form for the coexistence curve in the vicinity of the critical point, we show that the functional dependence of the entropy as a function of energy and particle densities necessarily obeys the scaling form hypothesized by Widom. Our analysis allows for a discussion on the properties of the corresponding scaling function, with the interesting prediction that the critical isotherm has the same functional dependence, between the energy and particles densities, as the coexistence curve. In addition to the derivation of the expected equalities of the critical exponents, the conditions that lead to scaling also imply that while the specific heat at constant volume can diverge at the critical point, the isothermal compressibility must do so.
