Thermodynamic Properties of the van der Waals Fluid
arXiv:1402.1205 · doi:10.1088/978-1-627-05532-1
Abstract
The van der Waals (vdW) theory of fluids is the first and simplest theory that takes into account interactions between the particles of a system that result in a phase transition versus temperature. Combined with Maxwell's construction, this mean-field theory predicts the conditions for equilibrium coexistence between the gas and liquid phases and the first-order transition between them. However, important properties of the vdW fluid have not been systematically investigated. Here we report a comprehensive study of these properties. Ambiguities about the physical interpretation of the Boyle temperature and the influence of the vdW molecular interactions on the pressure of the vdW gas are resolved. Thermodynamic variables and properties are formulated in reduced units that allow all properties to be expressed as laws of corresponding states that apply to all vdW fluids. Lekner's parametric solution for the vdW gas-liquid coexistence curve in the pressure-temperature plane and related thermodynamic properties [Am. J. Phys. 50, 161 (1982)] is explained and significantly extended. Hysteresis in the first-order transition temperature on heating and cooling is examined and the maximum degrees of superheating and supercooling determined. The latent heat of vaporization and the entropy change on crossing the coexistence curve are investigated. The temperature dependences of the isothermal compressibility, thermal expansion coefficient and heat capacity at constant pressure for a range of pressures above, at and below the critical pressure are systematically studied from numerical calculations including their critical behaviors and their discontinuities on crossing the coexistence curve. Joule-Thomson expansion of the vdW gas is investigated in detail and the pressure and temperature conditions for liquifying a vdW gas on passing through the throttle are determined.
41 pages, 34 figures, 7 tables
Cited by in corpus (38)
- Ruppeiner Geometry, Phase Transitions, and the Microstructure of Charged AdS Black Holes
- On thermal molecular potential among micromolecules in charged AdS black holes
- On the Gibbs-Thomson equation for the crystallization of confined fluids
- Parametric phase transition for Gauss-Bonnet AdS black hole
- Effects of a cloud of strings on the extended phase space of Einstein-Gauss-Bonnet AdS black holes
- Bardeen solution with a cloud of strings
- Interaction potential and thermo-correction to the equation of state for thermally stable Schwarzschild Anti-de Sitter black holes
- Black Hole Chemistry: the first 15 years
- Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity
- Thermodynamics of FRW Universe: Heat Engine
- Joule-Thomson expansion of AdS black holes in quasi-topological electromagnetism
- Universal criticality of thermodynamic curvatures for charged AdS black holes
- Solid H2 in the interstellar medium
- Rate of the phase transition for a charged anti-de Sitter black hole
- van der Waals fluid and charged AdS black hole in the Landau theory
- Phase Transition Dynamics of Black Holes Influenced by Kaniadakis and Barrow Statistics
- Finite-temperature phase diagram and critical point of the Aubry pinned-sliding transition in a 2D monolayer
- Joule-Thomson expansion of higher dimensional nonlinearly charged AdS black hole in Einstein-PMI gravity
- Phase transitions and entropy force of charged de Sitter black holes with cloud of string and quintessence
- Optogenetic switching of migration of contractile cells
- Nucleation on a sphere: the roles of curvature, confinement and ensemble
- A new approach to phase transitions: Einstein gravity and holographic type dark energy
- Sign change in the net force in sphere-plate and sphere-sphere systems immersed in nonpolar critical fluid due to the interplay between the critical Casimir and dispersion van der Waals forces
- Probing phase transitions of regular black holes in anti-de Sitter space with Lyapunov exponent
- Substellar fragmentation in self-gravitating fluids with a major phase transition
- New Comment on Gibbs Density Surface of Fluid Argon: Revised Critical Parameters, L. V. Woodcock, Int. J. Thermophys. (2014) 35, 1770-1784
- Thermodynamics of the Noninteracting Bose Gas in a Two-Dimensional Box
- Quantum thermochemical engines
- Formation of H2-He substellar bodies in cold conditions: Gravitational stability of binary mixtures in a phase transition
- Free energy landscape and kinetics of phase transition in two coupled SYK models
- Joule-Thomson expansion of the torus-like black hole
- Failures of meso-phase hypothesis near vapor-liquid critical point
- Comments on Failures of van der Waals Equation at the Gas Liquid Critical Point, L. V. Woodcock, International Journal of Thermophysics 2018 39 120
- The Effects of Spatial Curvature on Cosmic Evolution
- Proof of phase transition in homogeneous systems of interacting bosons
- Parametric Solution of a Small-Large Black Hole Coexistence Curve
- Van der Waals equation of state and PVT properties of real fluid
- Study of General Relativity and Modified Gravity with Cosmological Constant for Einstein and Jordan Frames