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Adiabatic Processes for an Ideal Gas

Adiabatic Processes for an Ideal Gas

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...

Pressure and Volume in an Adiabatic Process

Pressure and Volume in an Adiabatic Process

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,

Work Done in an Adiabatic Process

Work Done in an Adiabatic Process

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...

Boundary Layer Characteristics

Boundary Layer Characteristics

When a fluid encounters a solid surface, a boundary layer forms due to the interaction between the fluid's motion and the stationary surface. This phenomenon is characterized by a thin region adjacent to the surface where viscous forces dominate, influencing the fluid's velocity profile. The development of the boundary layer begins at the leading edge of the surface and evolves as the fluid moves downstream.As the fluid flows over the surface, friction between the fluid and the wall slows down...

Isochoric and Isobaric Processes

Isochoric and Isobaric Processes

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.
Suppose 1000 g of water is heated from 40 degrees...

Variation of Atmospheric Pressure

Variation of Atmospheric Pressure

Change in atmospheric pressure with height is particularly interesting. The decrease in atmospheric pressure with increasing altitude is due to the decreasing gravitational force per unit area as we move away from the surface of the earth.
Assuming the air temperature is constant at a given altitude and that the ideal gas law of thermodynamics describes the atmosphere to a good approximation, one can find the variation of atmospheric pressure with height.
Let p(y) be the atmospheric pressure at...

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Updated: Jun 7, 2026

Exploring the Effects of Atmospheric Forcings on Evaporation: Experimental Integration of the Atmospheric Boundary Layer and Shallow Subsurface

Exploring the Effects of Atmospheric Forcings on Evaporation: Experimental Integration of the Atmospheric Boundary Layer and Shallow Subsurface

Published on: June 8, 2015

Range-dependent adiabatic connections.

A M Teale¹, S Coriani, T Helgaker

¹Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway. a.m.teale@kjemi.uio.no

The Journal of Chemical Physics

|November 2, 2010

Summary

This summary is machine-generated.

This study extends adiabatic connection calculations for electronic systems. The error-function connection shows promise for developing new exchange-correlation functionals, unlike the Gaussian-attenuated version.

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Area of Science:

Quantum Chemistry
Computational Physics
Density Functional Theory

Background:

The adiabatic connection (AC) method links the Kohn-Sham (KS) system to the physical interacting system.
Generalized Lieb functionals vary electronic interaction strength linearly, keeping potential or density fixed.

Purpose of the Study:

Generalize the AC scheme to arbitrary two-electron operators.
Investigate alternative AC paths, specifically error-function and Gaussian-attenuated error-function connections.
Assess the utility of these AC paths for developing new exchange-correlation functionals.

Main Methods:

Implementation of a generalized AC scheme for two-electron operators.
Analysis of error-function and Gaussian-attenuated error-function AC paths.
Exploration of high-density and strong static correlation regimes in two-electron systems.

Main Results:

The error-function AC displays features amenable to modeling the AC integrand for new functional development.
The Gaussian-attenuated error-function AC is found to be less promising.
The study explores implications for range-separated schemes.

Conclusions:

The generalized AC scheme offers a pathway for developing novel exchange-correlation functionals.
The error-function AC is a promising avenue for future research in functional design.
The Gaussian-attenuated error-function AC appears less suitable for current functional development strategies.