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Related Concept Videos

Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
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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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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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Standard Entropy Change for a Reaction03:00

Standard Entropy Change for a Reaction

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Entropy is a state function, so the standard entropy change for a chemical reaction (ΔS°rxn) can be calculated from the difference in standard entropy between the products and the reactants.
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Entropy and the Second Law of Thermodynamics01:20

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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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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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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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Dynamic Maximum Entropy Reduction.

Václav Klika1, Michal Pavelka2, Petr Vágner2,3

  • 1Department of Mathematics-FNSPE, Czech Technical University, Trojanova 13, 12000 Prague, Czech Republic.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

We introduce Dynamic MaxEnt (DynMaxEnt), a novel method for simplifying complex physical system descriptions. This approach effectively reduces detailed equations to less detailed ones, ensuring closure and enabling multi-level analysis.

Keywords:
MaxEntOhm’s lawcomplex fluidsdynamic MaxEntheat conductionmodel reductionnon-equilibrium thermodynamics

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Physical systems exhibit complexity describable at various detail levels.
  • Bridging different descriptive levels requires robust mathematical frameworks.

Purpose of the Study:

  • To develop a method for deriving less detailed equations from more detailed ones.
  • To introduce Dynamic MaxEnt (DynMaxEnt) for systematic model reduction.

Main Methods:

  • The Dynamic MaxEnt (DynMaxEnt) method distinguishes between state and conjugate variables.
  • State variables are reduced via the principle of maximum entropy (MaxEnt).
  • Conjugate variables' relaxation ensures the closure of reduced equations.

Main Results:

  • DynMaxEnt facilitates passage from detailed to simplified state variable equations.
  • An infinite chain of successive DynMaxEnt approximations can be generated.
  • The method's efficacy is demonstrated across diverse systems.

Conclusions:

  • DynMaxEnt offers a principled approach to multi-level physical system description.
  • The method provides a systematic way to derive closed, reduced equations.
  • Applicable to diverse fields including fluid dynamics and heat transfer.