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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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The Carnot Cycle01:30

The Carnot Cycle

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Converting work to heat is an irreversible process, and the purpose of a heat engine is to reverse the effect partially. Heat engines aim to increase the efficiency of the reversal, that is, maximize the work retrieved from heat. If the efficiency of a heat engine were 100%, it would imply reversing the process completely without introducing any other effect. Thus, it would violate the second law of thermodynamics.
What could be the theoretical limit to the efficiency of a heat engine? The...
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The Carnot Cycle and the Second Law of Thermodynamics01:20

The Carnot Cycle and the Second Law of Thermodynamics

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The Carnot engine works between two heat reservoirs of fixed temperatures. The Carnot cycle begs the following question: Is it possible to devise a heat engine that is more efficient than a Carnot engine between two fixed temperatures? The answer lies in designing a Carnot refrigerator.
Since the individual steps in a Carnot cycle can be reversed, the entire cycle is, thus, reversible. If a Carnot cycle is reversed, it becomes a Carnot refrigerator. It extracts heat Qc from a cold reservoir at...
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Efficiency of The Carnot Cycle01:16

Efficiency of The Carnot Cycle

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The hypothetical Carnot cycle consists of an ideal gas subjected to two isothermal and two adiabatic processes. Since the internal energy of an ideal gas depends only on its temperature, which is the same before and after the completion of the Carnot cycle, there is no change in its internal energy. Hence, using the first law of thermodynamics, the total heat exchanged by the ideal gas equals the total work done. Thus, we can quantify the efficiency of the Carnot cycle via the heat exchanged...
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Quantification of Information Encoded by Gene Expression Levels During Lifespan Modulation Under Broad-range Dietary Restriction in C. elegans
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Entropy, Carnot Cycle, and Information Theory.

Mario Martinelli1

  • 1Dipartimento di Elettronica Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy.

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

Entropy, a key thermodynamic concept, is explored through information theory. Analyzing the Carnot cycle reveals that information costs affect energy conversion and free energy availability, offering insights into thermodynamic asymmetries.

Keywords:
Carnot cycleKullback–Leibler divergenceentropyinformation theory

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Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Information Theory

Background:

  • Carnot's analysis of steam engines identified a constant during reversible cycles, later termed entropy.
  • Jaynes proposed a unified view of thermodynamics and information theory using statistical thermodynamics.

Purpose of the Study:

  • To analyze the Carnot cycle using a unitary vision of thermodynamics and information theory.
  • To investigate the implications of entropy changes during isothermal expansion and adiabatic processes.

Main Methods:

  • Application of statistical thermodynamics and information theory to the Carnot cycle.
  • Analysis of entropy changes and Kullback-Leibler distance during isothermal expansion.
  • Examination of energy-to-work conversion during adiabatic processes, considering code conversion costs.

Main Results:

  • A non-zero Kullback-Leibler distance indicates minor free-energy availability from the cycle.
  • The adiabatic process's energy-to-work conversion is affected by code conversion costs.
  • Information-theoretical tools provide a deeper understanding of cycle details and asymmetries.

Conclusions:

  • Information theory offers a novel perspective on thermodynamic cycles.
  • Entropy and information costs play crucial roles in energy conversion efficiency.
  • This approach can elucidate subtle aspects and potential asymmetries within thermodynamic processes.