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Related Concept Videos

Entropy02:39

Entropy

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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Entropy01:18

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The first law of thermodynamics is quantitatively formulated via an equation relating the internal energy of a system, the heat exchanged by it, and the work done on it. A quantitative formulation of the second law of thermodynamics leads to defining a state function, the entropy.
When an ideal gas expands isothermally, the disorder in the gas increases. From the molecular perspective, the gas molecules have more volume to move around in.
Consider an infinitesimal step in the expansion, which...
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The Thermodynamics of Mixing01:28

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Mixing is a fascinating phenomenon in thermodynamics, particularly when considering the Gibbs energy of a mixture at constant temperature and pressure. This energy, denoted as G, tends to decrease during spontaneous mixing processes, offering insights into the composition changes that occur.Imagine two ideal gases, initially separated in different containers, with amounts nA and nB, respectively, both at a temperature T and pressure p. The chemical potentials of these gases have their 'pure'...
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Entropy Changes Accompanying Specific Processes01:21

Entropy Changes Accompanying Specific Processes

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Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression...
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Entropy and Solvation02:05

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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ...
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Second Law of Thermodynamics02:49

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In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, a significant conclusion regarding the relation between this property and spontaneity may be reached. In thermodynamic models, the...
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Evolution of Staircase Structures in Diffusive Convection
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Diffusive mixing and Tsallis entropy.

Daniel O'Malley1, Velimir V Vesselinov1, John H Cushman2

  • 1Computational Earth Science, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|May 15, 2015
PubMed
Summary
This summary is machine-generated.

This study introduces a generalized Brownian motion that maximizes Tsallis q entropy, offering a new model for nonergodic systems. This approach accounts for random diffusion coefficients, with applications in porous media transport.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Thermodynamics
  • Complex Systems

Background:

  • Classical Brownian motion is a fundamental diffusive process maximizing Boltzmann-Gibbs entropy.
  • Tsallis q entropy is a nonadditive generalization for nonergodic systems.
  • Existing models may not fully capture complex transport phenomena.

Purpose of the Study:

  • To generalize Brownian motion by maximizing Tsallis q entropy instead of Boltzmann-Gibbs entropy.
  • To introduce a novel framework for modeling diffusive processes in nonergodic systems.
  • To explore applications in understanding transport in porous media.

Main Methods:

  • Development of a generalized Brownian motion model.
  • Incorporation of a random diffusion coefficient into the Brownian measure.
  • Derivation of the diffusion coefficient's distribution as a function of the Tsallis parameter q (1

Main Results:

  • A new class of Brownian motion maximizing Tsallis q entropy is established.
  • The probability distribution of the random diffusion coefficient is determined for 1
  • The model provides a theoretical basis for anomalous diffusion phenomena.

Conclusions:

  • The generalized Brownian motion offers a more comprehensive description for systems exhibiting nonergodicity.
  • The derived diffusion coefficient distribution is crucial for modeling complex transport.
  • This framework has potential applications in fields like geophysics and materials science.