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The Entropy of van der Waals Fluid
Yanhua Lei1, Xiongliang Wang2, Huapeng Sun1
1Hunan Provincial Key Laboratory of Xiangnan Rare-Precious Metals Compounds and Applications, School of Chemistry and Environmental Science, Xiangnan University, Chenzhou, Hunan Province, 423000, China.
This study derives thermodynamic state functions using the van der Waals equation in 2D and 3D spaces. While heat capacities differ from ideal gases, adsorbate entropy shows linear correlations with gas and liquid phases.
Area of Science:
- Thermodynamics
- Statistical Mechanics
- Physical Chemistry
Background:
- Thermodynamic state functions are crucial in various scientific disciplines.
- The van der Waals (vdW) equation provides a more realistic model than ideal gas laws.
- Understanding state functions in reduced dimensions is essential for surface science and materials.
Purpose of the Study:
- To derive the vdW equation of state and state functions in 2D and 3D using statistical thermodynamics.
- To investigate the behavior of heat capacities and entropy for vdW fluids.
- To explore the relationship between adsorbate entropy and gas/liquid phase entropy.
Main Methods:
- Statistical thermodynamic derivations.
- Application of the van der Waals equation of state.
- Analysis of thermodynamic state functions in 2D and 3D.
Main Results:
- Heat capacity at constant volume (CV,m) or area (CA,m) remains identical to ideal gas.
- Heat capacity at constant pressure (Cp,m) and other state functions deviate from ideal gas behavior.
- Entropy and free energy changes for vdW fluids are explicitly expressed in terms of volume.
- Adsorbate entropy exhibits a linear relationship with gas-phase entropy at constant volume and liquid-phase entropy.
Conclusions:
- The vdW equation offers a framework for understanding thermodynamic properties beyond ideal gas assumptions.
- Linear correlations between adsorbate and phase entropies are established, with implications for adsorption studies.
- A reference state for real gases/fluids at constant molar volume is proposed.
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