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Related Concept Videos

Entropy02:39

Entropy

26.1K
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...
26.1K
Entropy01:18

Entropy

2.8K
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...
2.8K
Third Law of Thermodynamics02:38

Third Law of Thermodynamics

17.0K
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.
17.0K
Entropy and the Second Law of Thermodynamics01:20

Entropy and the Second Law of Thermodynamics

3.3K
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...
3.3K
Entropy and the Second Law of Thermodynamics01:26

Entropy and the Second Law of Thermodynamics

377
Consider an isolated system in which a hot object is placed in contact with a cold one. This is an irreversible process that eventually leads both objects to reach the same equilibrium temperature. It is crucial to note that the constituents of any substance exhibit increased disorder at higher temperatures. As a cold substance absorbs heat, its constituents become more disordered. The energy transfer from a hotter object to a cooler one increases the system's disorder or randomness. This...
377
Entropy Change in Reversible Processes01:10

Entropy Change in Reversible Processes

2.4K
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.
2.4K

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Analysis and Specification of Starch Granule Size Distributions
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Numerical calculation of granular entropy.

Daniel Asenjo1, Fabien Paillusson1, Daan Frenkel1

  • 1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.

Physical Review Letters
|March 25, 2014
PubMed
Summary
This summary is machine-generated.

We developed a new simulation method to count particle packing configurations, significantly faster than previous techniques. This method confirms that packing entropy is extensive, providing a new definition for granular entropy.

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Area of Science:

  • Physics
  • Computational Physics
  • Statistical Mechanics

Background:

  • Understanding particle packing is crucial in materials science and statistical mechanics.
  • Existing methods for enumerating distinct particle packings are computationally intensive and limited in scale.
  • The concept of entropy in granular systems has been a subject of theoretical debate.

Purpose of the Study:

  • To develop a highly efficient numerical method for computing the number of distinct particle packing configurations.
  • To investigate the system size dependence of packing entropy for polydisperse soft disks.
  • To redefine granular entropy in a way that aligns with theoretical expectations of extensivity.

Main Methods:

  • Modification of the Xu, Frenkel, and Liu method for direct enumeration of particle packings.
  • Numerical simulations to compute the number of ways N particles can pack into a volume V.
  • Analysis of system size dependence for systems up to 128 polydisperse soft disks.

Main Results:

  • The new simulation technique outperforms existing direct enumeration methods by over 200 orders of magnitude.
  • Demonstrated that packing entropy, when properly defined, is an extensive property.
  • Proposed a redefined granular entropy formula: S = − Σ(i)p(i) ln pi − lnN!, which is computationally reliable and extensive.

Conclusions:

  • The developed simulation approach offers a significant advancement in calculating particle packing configurations.
  • The study provides strong evidence for the extensivity of a properly defined packing entropy.
  • The redefined granular entropy satisfies key theoretical properties, offering a new perspective on granular matter thermodynamics.