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Pressure and Volume in an Adiabatic Process01:27

Pressure and Volume in an Adiabatic Process

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Free expansion of a gas is an adiabatic process. However, there are few differences between free expansion and adiabatic expansion. During free expansion, no work is done, and there is no change in internal energy. But, for an adiabatic expansion, work is done, and there is a change in internal energy. During an adiabatic process, the relation between the pressure and volume is obtained from the condition for the adiabatic process, that is, 
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Adiabatic Processes for an Ideal Gas01:18

Adiabatic Processes for an Ideal Gas

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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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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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Isochoric and Isobaric Processes01:21

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A thermodynamic process that occurs at constant volume is called an isochoric process. According to the first law of thermodynamics, heat supplied or removed from the system is partially utilized to perform work and change the internal energy of the system. However, in an isochoric process, the volume remains constant. Hence, the work done by the system is zero. Therefore, the exchange of heat changes the internal energy of the system only. 
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Work Done in an Adiabatic Process01:20

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Consider the adiabatic compression of an ideal gas in the cylinder of an automobile diesel engine. The gasoline vapor is injected into the cylinder of an automobile engine when the piston is in its expanded position. The temperature, pressure, and volume of the resulting gas-air mixture are 20 °C, 1.00 x 105 N/m2, and 240 cm3 , respectively. The mixture is then compressed adiabatically to a volume of 40 cm3. Note that, in the actual operation of an automobile engine, the compression is not...
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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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Evolution of Staircase Structures in Diffusive Convection
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Adiabatic processes like isothermal processes.

Pierre Nazé1

  • 1Departamento de Física, Instituto de Geociências e Ciências Exatas, Universidade Estadual Paulista "Júlio de Mesquita Filho", 13506-900, Rio Claro, SP, Brazil.

Physical Review. E
|July 19, 2023
PubMed
Summary

Adiabatic processes closely resemble isothermal ones, sharing thermodynamic compatibility criteria. Thermally isolated systems exhibit a defined relaxation time, akin to isothermal systems, obeying the second law of thermodynamics.

Area of Science:

  • Thermodynamics
  • Statistical Mechanics
  • Condensed Matter Physics

Background:

  • Adiabatic and isothermal processes are fundamental thermodynamic concepts.
  • Linear-response theory and the second law of thermodynamics govern system evolution.
  • Understanding relaxation times is crucial for characterizing system dynamics.

Purpose of the Study:

  • To demonstrate the parallels between adiabatic and isothermal processes.
  • To investigate the thermodynamic implications of time-averaged excess work in isolated systems.
  • To analyze the Landau-Zener model through the lens of linear-response theory.

Main Methods:

  • Comparison of thermodynamic compatibility criteria for isolated and isothermal systems.
  • Analysis of time-averaged excess work and relaxation functions.

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  • Application of linear-response theory to the Landau-Zener model.

    • Main Results:

    • Identical criteria for compatibility of linear-response theory with the second law for adiabatic and isothermal processes.
    • Discovery of a well-defined relaxation time for thermally isolated systems.
    • Observation of negative entropy production rates in nonmonotonic and rapid Landau-Zener protocols.

    Conclusions:

    • Adiabatic processes can exhibit behaviors strikingly similar to isothermal processes.
    • Averaging relaxation functions provides a consistent framework for understanding dynamics in isolated systems.
    • The Landau-Zener model reveals unique thermodynamic behaviors under specific conditions.