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Related Concept Videos

Isothermal Processes01:21

Isothermal Processes

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A thermodynamic process that occurs at constant temperature is called an isothermal process. Heat slowly flows into the system or out of the system to maintain thermal equilibrium. Processes involving phase changes like water evaporation into steam or freezing water into ice at a constant temperature are examples of Isothermal Processes.
An ideal gas can also undergo isothermal expansion or compression.
For example, consider 1 mole of an ideal gas inside an isolated cylinder at initial volume V...
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Adiabatic Processes for an Ideal Gas01:18

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When an ideal gas is compressed adiabatically, that is, without adding heat, work is done on it, and its temperature increases. In an adiabatic expansion, the gas does work, and its temperature drops. Adiabatic compressions actually occur in the cylinders of a car, where the compressions of the gas-air mixture take place so quickly that there is no time for the mixture to exchange heat with its environment. Nevertheless, because work is done on the mixture during the compression, its...
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The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
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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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Ideal Gas Equation01:17

Ideal Gas Equation

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The ideal gas equation is an equation of state that relates the state variables pressure, volume, temperature, and the number of moles of a hypothetical gas. This equation is a combination of four empirical laws, namely Boyle’s Law, Charles’s Law, Avogadro’s Law, and Gay-Lussac’s Law. When the proportionalities of the above four empirical laws are combined, it results in a single proportionality constant known as the universal gas constant.
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Optimal Thermodynamic Processes For Gases.

Alexei Kushner1,2, Valentin Lychagin3, Mikhail Roop1,3

  • 1Faculty of Physics, Lomonosov Moscow State University, Leninskie Gory, 119991 Moscow, Russia.

Entropy (Basel, Switzerland)
|December 8, 2020
PubMed
Summary
This summary is machine-generated.

This study optimizes thermodynamic processes for gases using optimal control theory. We found a method for ideal gases and an asymptotic solution for real gases to maximize work output.

Keywords:
Hamiltonian systemsPontryagin’s maximum principleaction-angle variablesasymptotical methodsinformation gainmeasurementoptimal controlreal gases

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Area of Science:

  • Thermodynamics
  • Optimal Control Theory
  • Mathematical Physics

Background:

  • Thermodynamic states are represented as Legendrian submanifolds in contact spaces.
  • Optimal control problems are crucial for maximizing work in thermodynamic systems.

Purpose of the Study:

  • To solve an optimal control problem for equilibrium thermodynamics of gases.
  • To find a thermodynamic process that maximizes the work functional.

Main Methods:

  • Utilizing Pontryagin's maximum principle.
  • Applying Liouville integrability and action-angle variables for ideal gases.
  • Employing asymptotic methods for real gases.

Main Results:

  • A method to maximize work functional for gases was identified.
  • The problem for ideal gases was shown to be integrable.
  • Asymptotic solutions were derived for real gases as perturbations of ideal ones.

Conclusions:

  • The study provides a mathematical framework for optimizing thermodynamic processes.
  • The findings offer insights into the behavior of ideal and real gases under optimal control.