关键词: 热力学, 微分几何, 涨落理论, 汤姆孙-贝特洛原理, 临界点, 物态方程

Abstract: The interesting connections between thermodynamics and geometry have all but

vanished from the literature.Three thermodynamic issues are treated with geometry.The first is

how to geometrically interpret the Thom- sen-Berthelot principle，leading to the third law of

thermodynamics.The second is why the van der Waals parame- ters a and b depend on the temperature

once the equation of state is viewed as a two-dimensional surface.The third is that the

thermodynamic fluctuations permit metric representations associated with the Riemann geometry，and

the van der Waals equation of state is used to demonstrate the scalar curvature measures the

interactions.Attempts to un- derstand the thermodynamics within geometry do not only offer an

effective teaching and learning，but also may be helpful to find new research areas.

Key words: thermodynamics, differential geometry, fluctuation theory, Thomsen-Berthelot principle, critical point, equation of state