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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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Nonstandard Reaction Conditions
The interconnection between standard cell potentials and various thermodynamic parameters such as the standard free energy change ΔG° and equilibrium constant K has been previously explored. For example, a redox reaction involving zinc(II) and tin(II) ions at 1 M concentration with Eºcell = +0.291 V and ΔG° = −56.2 kJ is spontaneous.
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Entropy01:18

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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.
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The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
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Hess's Law03:40

Hess's Law

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There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally determined enthalpy changes. Some reactions are difficult, if not impossible, to investigate and make accurate measurements for experimentally. And even when a reaction is not hard to perform or measure, it is convenient to be able to determine the heat involved in a reaction without having to perform an experiment.
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Third Law of Thermodynamics02:38

Third Law of Thermodynamics

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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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A Nernst heat theorem for nonequilibrium jump processes.

Faezeh Khodabandehlou1, Christian Maes1, Karel Netočný2

  • 1Instituut voor Theoretische Fysica, KU Leuven, Belgium.

The Journal of Chemical Physics
|May 23, 2023
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Summary

The steady nonequilibrium heat capacity vanishes at low temperatures due to specific dynamic conditions in Markov jump processes. This research explores the conditions under which thermodynamic laws extend to nonequilibrium systems.

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Physical Chemistry

Background:

  • The Third Law of Thermodynamics traditionally states that entropy approaches a constant minimum at absolute zero.
  • Extending thermodynamic laws to nonequilibrium systems presents significant theoretical challenges.
  • Understanding heat capacity behavior at low temperatures is crucial for fundamental physics.

Purpose of the Study:

  • To investigate the conditions under which steady nonequilibrium heat capacity vanishes with temperature.
  • To explore the extension of the Third Law of Thermodynamics to nonequilibrium steady states.
  • To analyze the role of dynamical activity and relaxation times in low-temperature thermodynamics.

Main Methods:

  • Utilizing Markov jump processes on finite connected graphs.
  • Applying the principle of local detailed balance to identify heat fluxes.
  • Analyzing the nondegeneracy of the stationary distribution at absolute zero.
  • Examining dynamical conditions related to relaxation and dissipation times.

Main Results:

  • Demonstrated that steady nonequilibrium heat capacity vanishes at absolute zero under specific conditions.
  • Identified a dynamic condition for the extension of the Third Law of Thermodynamics to nonequilibrium systems.
  • Showed that sufficient dynamical activity and accessibility of the dominant state are necessary.
  • Established that relaxation times must not exceed the dissipation time.

Conclusions:

  • The vanishing of steady nonequilibrium heat capacity is linked to the discreteness of the system and the stationary distribution at absolute zero.
  • A dynamic condition, ensuring comparable relaxation times from different initial states, is crucial for extending the Third Law of Thermodynamics.
  • The framework of Markov jump processes provides a valuable tool for studying nonequilibrium thermodynamics.