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Related Concept Videos

Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

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The second law of thermodynamics can be stated quantitatively using the concept of entropy. Entropy is the measure of disorder of the system.
The relation  between entropy and disorder can be illustrated with the example of the phase change of ice to water. In ice, the molecules are located at specific sites giving a solid state, whereas, in a liquid form, these molecules are much freer to move. The molecular arrangement has therefore become more randomized. Although the change in average...
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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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Second Law of Thermodynamics00:53

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The Second Law of Thermodynamics states that entropy, or the amount of disorder in a system, increases each time energy is transferred or transformed. Each energy transfer results in a certain amount of energy that is lost—usually in the form of heat—that increases the disorder of the surroundings. This can also be demonstrated in a classic food web. Herbivores harvest chemical energy from plants and release heat and carbon dioxide into the environment. Carnivores harvest the...
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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

Entropy

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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 Second Law of Thermodynamics01:14

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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. Scientists refer to the measure of randomness or disorder within a system as entropy. High entropy means high disorder and low energy. To better understand entropy, think of a student’s bedroom. If no energy or work were put into it, the room would quickly become messy. It would exist in a very disordered state, one of high entropy. Energy must be...
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Related Experiment Video

Updated: Nov 27, 2025

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
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A Fourth Order Entropy Stable Scheme for Hyperbolic Conservation Laws.

Xiaohan Cheng1

  • 1School of Science, Chang'an University, Xi'an 710064, China.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary

This study introduces a fourth-order accurate, entropy-stable numerical scheme for hyperbolic conservation laws. The method ensures high resolution for discontinuities and maintains stability, crucial for accurate fluid dynamics simulations.

Keywords:
conservation lawsentropy conservativeentropy stablenon-oscillatory reconstructionsign property

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Preparation of Free-Surface Hyperbolic Water Vortices
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Related Experiment Videos

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Area of Science:

  • Computational fluid dynamics
  • Numerical analysis
  • Applied mathematics

Background:

  • Hyperbolic conservation laws model phenomena like fluid flow.
  • Accurate numerical solutions are essential for simulating these laws.
  • Existing schemes may struggle with discontinuities or stability.

Purpose of the Study:

  • To develop a novel fourth-order accurate, entropy-stable numerical scheme.
  • To approximate solutions for one-dimensional hyperbolic conservation laws.
  • To enhance resolution at sharp discontinuities while maintaining stability.

Main Methods:

  • Employed a fourth-order entropy conservative flux.
  • Incorporated a numerical diffusion operator.
  • Utilized a fourth-order non-oscillatory reconstruction with the sign property.

Main Results:

  • The scheme achieves fourth-order accuracy in smooth regions.
  • It maintains high resolution across sharp discontinuity transitions.
  • The numerical scheme is proven to be entropy stable.

Conclusions:

  • The developed scheme effectively approximates entropy solutions.
  • It offers a robust and accurate method for hyperbolic conservation laws.
  • Numerical experiments validate the scheme's capability and performance.