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Entropy

Entropy

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...

Entropy and the Second Law of Thermodynamics

Entropy and the Second Law of Thermodynamics

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...

The Quantum-Mechanical Model of an Atom

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.

Standard Entropy Change for a Reaction

Standard Entropy Change for a Reaction

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.

Entropy Change in Reversible Processes

Entropy Change in Reversible Processes

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.

Third Law of Thermodynamics

Third Law of Thermodynamics

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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Related Experiment Video

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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Configurational entropy from a replica approach: A density-functional model.

Prakash Vardhan¹, Shankar P Das¹

¹School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India.

Physical Review. E

|March 16, 2022

Summary

This study models metastable liquids using field theory and nonlocal free energy. Results for static correlations and configurational entropy align with existing research, validating the approach.

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Area of Science:

Theoretical physics
Statistical mechanics
Condensed matter physics

Background:

Metastable liquids exhibit complex behavior due to their inherent instability.
Understanding the free-energy landscape is crucial for characterizing liquid states.
Previous models often simplify correlation effects or free-energy landscapes.

Purpose of the Study:

To develop and apply a field-theoretic model for metastable liquids.
To incorporate nonlocal free-energy functionals and three-point correlation effects.
To investigate the relationship between free-energy landscape fragmentation and liquid properties.

Main Methods:

Utilizing a nonlocal free-energy functional with density as the order parameter.
Including three-point correlation effects in the theoretical formulation.
Mapping the many-particle system to a composite system of m identical replicas to evaluate the partition function.
Calculating static correlations and configurational entropy (Sc) in the m=1 limit.

Main Results:

The model successfully incorporates nonlocal effects and correlation functions.
Fragmentation of the free-energy landscape into distinct basins was assumed.
Static correlations and configurational entropy were computed.
The derived Kauzman packing fraction (ηK) shows agreement with established literature values.

Conclusions:

The field-theoretic model provides a robust framework for studying metastable liquids.
The inclusion of nonlocal functionals and correlation effects is significant.
The model's predictions for key liquid properties are consistent with experimental and theoretical benchmarks.