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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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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.
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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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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...
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Third Law of Thermodynamics02:38

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A pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K) may be described by a single microstate, as its purity, perfect crystallinity,and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.
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Entropy Change in Reversible Processes01:10

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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.
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Contrasting thermodynamic and hydrodynamic entropy.

Mahendra K Verma1, Rodion Stepanov2,3, Alexandre Delache4,5

  • 1Department of Physics, <a href="https://ror.org/05pjsgx75">Indian Institute of Technology Kanpur</a>, Kanpur 208016, India.

Physical Review. E
|December 18, 2024
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Summary
This summary is machine-generated.

This study quantifies multiscale disorder using hydrodynamic entropy in fluid turbulence. Hydrodynamic entropy is not extensive, preventing its addition to thermodynamic entropy for a complete disorder measure.

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Area of Science:

  • Physics
  • Fluid Dynamics
  • Statistical Mechanics

Background:

  • Quantifying disorder in complex systems is crucial.
  • Existing entropy measures have limitations at different scales.

Purpose of the Study:

  • To quantify multiscale disorder using hydrodynamic entropy.
  • To analyze the properties of hydrodynamic entropy in various systems.

Main Methods:

  • Application of hydrodynamic entropy to Euler and hydrodynamic turbulence.
  • Analysis of hydrodynamic entropy for the time-dependent Ginzburg-Landau equation and Ising spins.

Main Results:

  • Hydrodynamic entropy quantifies multiscale disorder effectively.
  • Hydrodynamic entropy is not an extensive property.
  • Hydrodynamic and thermodynamic entropies cannot be directly added.

Conclusions:

  • Hydrodynamic entropy offers a unique perspective on disorder.
  • The non-extensive nature of hydrodynamic entropy has implications for statistical mechanics.
  • Further research is needed to integrate different entropy measures.