China
Africa
Explore chapters and articles related to this topic
A review of thermodynamic concepts
Published in Ronald L. Fournier, Basic Transport Phenomena in Biomedical Engineering, 2017
The Helmholtz free energy (A) is defined in terms of the internal energy, temperature, and entropy as A = U − TS. The Helmholtz free energy is useful for determining whether or not a given process will occur at constant temperature and volume. The criterion for feasibility of a process at constant temperature and volume is SpontaneousprocessΔA<0EquilibriumΔA=0NospontaneousprocessΔA>0
Wetting Phenomena and Contact Angles
Published in Van P. Carey, Liquid-Vapor Phase-Change Phenomena, 2018
We can gain a different perspective on this relation (3.2) by returning to the notion that the interfaces are actually interfacial regions, as shown in Fig. 3.2, and considering the thermodynamics of the system. We specifically consider a perturbation which results in a differential change in the positions of the interfacial surfaces Slv*, Ssv* and Ssl*, while the temperature and the volume of the individual phases in the system are constant. The resulting change in the total Helmholtz free energy is equal to the sum of the changes in the bulk phases and the interfacial regions () dF = dFυ+dFl+dFs+dFelυ+dFesl+dFesυ
Wetting Phenomena and Contact Angles
Published in Van P. Carey, Liquid-Vapor Phase-Change Phenomena, 2020
We can gain a different perspective on this relation (3.2) by returning to the notion that the interfaces are actually interfacial regions, as shown in Fig. 3.2, and considering the thermodynamics of the system. We specifically consider a perturbation which results in a differential change in the positions of the interfacial surfaces Slv*, Ssv* and Ssl* while the temperature and the volume of the individual phases in the system are constant. The resulting change in the total Helmholtz free energy is equal to the sum of the changes in the bulk phases and the interfacial regions dF=dFv+dFl+dFs+dFelv+dFesl+dFesv
Intramolecular bonding in a statistical associating fluid theory of ring aggregates
Published in Molecular Physics, 2019
S. A. Febra, A. Aasen, C. S. Adjiman, G. Jackson, A. Galindo
Thermodynamic properties and phase behaviour can be obtained from the Helmholtz free energy through standard relations and solving the phase equilibrium conditions of equality of temperature T, pressure P, and chemical potential of each component i across phases. We use reduced variables throughout, with the temperature given as , the volume as , and the pressure as .
Exergetic port-Hamiltonian systems: modelling basics
Published in Mathematical and Computer Modelling of Dynamical Systems, 2021
Markus Lohmayer, Paul Kotyczka, Sigrid Leyendecker
In [23] (p. 25), it is stated that the physical meaning of the Hamiltonian (of a classical dissipative port-Hamiltonian system) is ‘free energy’, rather than energy. In equilibrium thermodynamics, the Helmholtz free energy is a thermodynamic potential obtained from the internal energy via a Legendre transformation with respect to entropy. A potential contains all thermodynamic information about the behaviour of a material at equilibrium, see e.g [36] (p. 10). The thermodynamic potential named after Helmholtz is called a free energy because the maximum entropy principle applied to an isothermal and isochoric nonequilibrium system implies the minimization of its free energy. The difference between its free energy in the initial state and its free energy in the equilibrium state corresponds to the maximum (reversible) work production which can occur as the system passes from the initial to the equilibrium state while interacting with the isothermal reservoir at the same temperature, see e.g [68] (ch. 6). The statement that the Hamiltonian is a ‘free energy’ can thus be explained as follows: An (irrelevant) additive constant in the Hamiltonian can be identified with the combined Helmholtz free energy corresponding to all (neglected) internal energy storage of the overall system. Hence, the term ‘free energy’, as used in [23], additively combines electro-mechanical energy components and constant Helmholtz free energy components corresponding to internal energy storage in the isothermal system and environment. The electro-mechanical energy components have no entropy content since all related degrees of freedom are resolved by the model. Therefore, they are not Legendre-transformed quantities. In this (perhaps not obvious) sense, the Hamiltonian is a (Helmholtz) free energy. The GENERIC literature also mentions that Helmholtz free energy can be used as a single generator for isothermal systems [36] (p. 136).
Modeling the role of phase boundaries on the pullout response of shape memory wire reinforced composites
Published in Mechanics of Advanced Materials and Structures, 2023
Venkatesh Ananchaperumal, Srikanth Vedantam
As described by Vedantam and Abeyaratne [32], the Helmholtz free energy ψ can be expressed as a polynomial expansion of the strain invariants of the parent phase in order to incorporate the symmetries of the phases. The explicit form of the free energy in two dimension is given by where and are the strain invariants.