Ostwald´s Rule and the Principle of the Shortest Way

AbstractWe consider a substance X with two monotropic modifications 1 and 2 of different thermodynamic stability ΔH1 < ΔH2. Ostwald´s rule states that first of all the instable modification 1 crystallizes on cooling down liquid X, which subsequently turns into the stable modification 2. Numerous examples verify this rule, however what is its reason? Ostwald´s rule can be traced back to the principle of the shortest way. We start with Hamilton´s principle and the Euler-Lagrange equation of classical mechanics and adapt it to thermodynamics. Now the relevant variables are the entropy S, the entropy production P = dS/dt, and the time t. Application of the Lagrangian F(S, P, t) leads us to the geodesic line S(t). The system moves along the geodesic line on the shortest way I from its initial non-equilibrium state i of entropy Si to the final equilibrium state f of entropy Sf. The two modifications 1 and 2 take different ways I1 and I2. According to the principle of the shortest way, I1 < I2 is realized in the first step of crystallization only. Now we consider a supercooled sample of liquid X at a temperature T just below the melting point of 1 and 2. Then the change of entropy ΔS1 = Sf 1 - Si 1 on crystallizing 1 can be related to the corresponding chang of enthalpy by ΔS1 = ΔH1/T. Now it can be shown that the shortest way of crystallization I1 corresponds under special, well-defined conditions to the smallest change of entropy ΔS1 < ΔS2 and thus enthalpy ΔH1 < ΔH2. In other words, the shortest way of crystallization I1 really leads us to the instable modification 1. This is Ostwald´s rule.

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Virtual Work & d’Alembert’s Principle

10.1093/oso/9780198822370.003.0013 ◽

2018 ◽

Author(s):

Peter Mann

Keyword(s):

Euler Equations ◽

Virtual Work ◽

Lagrange Equation ◽

Classical Mechanics ◽

Rigid Bodies ◽

Gibbs Function ◽

Constraint Force ◽

Appell Equations ◽

Jourdain's Principle ◽

D'alembert's Principle

This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a detailed covering of the Gibbs–Appell equations as the most general equations in classical mechanics. Their reduction to Hamilton’s principle is examined and they are used to derive the Euler equations for rigid bodies. The chapter also discusses Hertz’s least curvature, the Gibbs function and Euler equations.

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Optimizing Our Patients’ Entropy Production as Therapy? Hypotheses Originating from the Physics of Physiology

Entropy ◽

10.3390/e22101095 ◽

2020 ◽

Vol 22 (10) ◽

pp. 1095

Author(s):

Andrew J. E. Seely

Keyword(s):

Entropy Production ◽

Treatment Strategies ◽

Fractal Structures ◽

Multi Scale ◽

Emergent Order ◽

Respiratory Rate Variability ◽

Vascular Structures ◽

Response To Exercise ◽

Improve Health ◽

Non Equilibrium

Understanding how nature drives entropy production offers novel insights regarding patient care. Whilst energy is always preserved and energy gradients irreversibly dissipate (thus producing entropy), increasing evidence suggests that they do so in the most optimal means possible. For living complex non-equilibrium systems to create a healthy internal emergent order, they must continuously produce entropy over time. The Maximum Entropy Production Principle (MEPP) highlights nature’s drive for non-equilibrium systems to augment their entropy production if possible. This physical drive is hypothesized to be responsible for the spontaneous formation of fractal structures in space (e.g., multi-scale self-similar tree-like vascular structures that optimize delivery to and clearance from an organ system) and time (e.g., complex heart and respiratory rate variability); both are ubiquitous and essential for physiology and health. Second, human entropy production, measured by heat production divided by temperature, is hypothesized to relate to both metabolism and consciousness, dissipating oxidative energy gradients and reducing information into meaning and memory, respectively. Third, both MEPP and natural selection are hypothesized to drive enhanced functioning and adaptability, selecting states with robust basilar entropy production, as well as the capacity to enhance entropy production in response to exercise, heat stress, and illness. Finally, a targeted focus on optimizing our patients’ entropy production has the potential to improve health and clinical outcomes. With the implications of developing a novel understanding of health, illness, and treatment strategies, further exploration of this uncharted ground will offer value.

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Extended Thermodynamic Approach for Non-Equilibrium Gas Flow

Communications in Computational Physics ◽

10.4208/cicp.301011.180512a ◽

2013 ◽

Vol 13 (5) ◽

pp. 1330-1356 ◽

Cited By ~ 8

Author(s):

G. H. Tang ◽

G. X. Zhai ◽

W. Q. Tao ◽

X. J. Gu ◽

D. R. Emerson

Keyword(s):

Heat Transfer ◽

Equilibrium State ◽

Gas Flow ◽

Rarefied Gas ◽

Flow Characteristics ◽

Bimodal Distribution ◽

Thermodynamic Approach ◽

Navier Stokes ◽

Extended Thermodynamic ◽

Non Equilibrium

AbstractGases in microfluidic structures or devices are often in a non-equilibrium state. The conventional thermodynamic models for fluids and heat transfer break down and the Navier-Stokes-Fourier equations are no longer accurate or valid. In this paper, the extended thermodynamic approach is employed to study the rarefied gas flow in microstructures, including the heat transfer between a parallel channel andpressure-driven Poiseuille flows through a parallel microchannel andcircular microtube. The gas flow characteristics are studied and it is shown that the heat transfer in the non-equilibrium state no longer obeys the Fourier gradient transport law. In addition, the bimodal distribution of streamwise and spanwise velocity and temperature through a long circular microtube is captured for the first time.

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