摘要
分析热力学乃是用分析力学的方法来研究平衡态热力学。本文用较简单的方法证明了“熵最大”变分原理与“Gibbs自由能最小”变分原理或“Helmholtz自由能最小”变分原理是等价的;以这三个Gibbs变分原理为出发点,导出了平衡态热力学的正则方程。由平衡态热力学中的正则方程,可以证明热力学基本Poisson括号成立。本文的另一主要任务是借助于Gibbs变分原理,讨论平衡态热力学中热力学量的正则变换。可以得到热力学正则变换的四种形式。在分析(平衡态)热力学中也可提出“化准Hamiltonian为压强或容积的正则变换技术”。作为应用正则变换的实例,讨论了理想气体并得到了简明的结果。
Analytical Thermodynamics is a study for thermodynamics by Analytical Mechanics method. The Gibbs variational principle for 'minimum Gibbs free-energy'or 'minimum Helmholtz free-energy 'proved to be the Gibbs variational principle for 'maximum entropy'by very simple method, and the canonical e-quations in equilibrium thermodynamics can be guided by Gibbs variational principles. From canonical c-quations in equilibrium thermodynamics, the basic Poisson's brackets can be proved. The second major objective is discussion for the canonical transformation of thermodynamical quantities in equilibrium thermodynamics by the Gibbs variational principle. And, the canonical transformations have four forms. The quasi-Hamilton-Jacobi equation can be written. 'The canonical transformation technique for changing qua-si-Hamiltonian into a pressure or a volume' in equilibrium thermodynamics can also be produced. As an example of using the canonical transformation, the ideal gas was discussed.
出处
《力学季刊》
CSCD
北大核心
2003年第4期462-472,共11页
Chinese Quarterly of Mechanics
