Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Deviation from Ideal Behaviour01:23

Deviation from Ideal Behaviour

Real gases do not perfectly obey the ideal gas laws, especially at high pressures and low temperatures or when they are about to condense to a liquid. These deviations occur due to intermolecular forces between gas molecules. Repulsive forces aid expansion and are significant when molecules are very close together, typically at high pressure. Attractive forces assist compression and have a longer range, being effective over several molecular diameters. They become significant when molecules are...
Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law03:19

Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law

Through experiments, scientists established the mathematical relationships between pairs of variables, such as pressure and temperature, pressure and volume, volume and temperature, and volume and moles, that hold for an ideal gas.
Ideal Gas Equation01:17

Ideal Gas Equation

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.
Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation04:01

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and molecular formula problems to determining the density and molar mass of a gas. However, the behavior of a gas is often non-ideal, meaning that the observed relationships between its pressure, volume, and temperature are not accurately described by the gas laws.
Van der Waals Equation01:10

Van der Waals Equation

The ideal gas law is an approximation that works well at high temperatures and low pressures. The van der Waals equation of state (named after the Dutch physicist Johannes van der Waals, 1837−1923) improves it by considering two factors.
First, the attractive forces between molecules, which are stronger at higher densities and reduce the pressure, are considered by adding to the pressure a term equal to the square of the molar density multiplied by a positive coefficient a. Second, the volume...
Gas Solubility01:31

Gas Solubility

Gas solubility in liquids forms liquid-gas solutions, such as soft drinks, where carbon dioxide is dissolved in water, and the ocean, where the solubility of oxygen and carbon dioxide supports marine life. The ability of oceans to dissolve gases impacts weather conditions in the troposphere.However, gas-liquid interactions vary. For instance, hydrogen chloride gas is highly soluble in water, while oxygen's solubility is much lower. Because these solutions are non-ideal, Raoult’s law, which...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Probing the Degree of Coherence through the Full 1D to 3D Crossover.

Physical review letters·2023
Same author

Thermalization processes induced by quantum monitoring in multilevel systems.

Physical review. E·2021
Same author

E_{8} Spectra of Quasi-One-Dimensional Antiferromagnet BaCo_{2}V_{2}O_{8} under Transverse Field.

Physical review letters·2021
Same author

Critical Transport and Vortex Dynamics in a Thin Atomic Josephson Junction.

Physical review letters·2020
Same author

Integrable Floquet Hamiltonian for a Periodically Tilted 1D Gas.

Physical review letters·2019
Same author

One-dimensional long-range percolation: A numerical study.

Physical review. E·2018

Related Experiment Video

Updated: Jun 14, 2026

Adsorption Device Based on a Langatate Crystal Microbalance for High Temperature High Pressure Gas Adsorption in Zeolite H-ZSM-5
09:46

Adsorption Device Based on a Langatate Crystal Microbalance for High Temperature High Pressure Gas Adsorption in Zeolite H-ZSM-5

Published on: August 25, 2016

Expectation values in the Lieb-Liniger Bose gas.

M Kormos1, G Mussardo, A Trombettoni

  • 1SISSA and INFN, Sezione di Trieste, via Beirut 2/4, I-34151 Trieste, Italy.

Physical Review Letters
|April 7, 2010
PubMed
Summary

We developed a new method to calculate expectation values in the Lieb-Liniger model for ultracold Bose gases at any temperature. This approach accurately computes the three-body recombination rate, crucial for understanding Bose gas behavior.

More Related Videos

Troubleshooting and Quality Assurance in Hyperpolarized Xenon Magnetic Resonance Imaging: Tools for High-Quality Image Acquisition
09:55

Troubleshooting and Quality Assurance in Hyperpolarized Xenon Magnetic Resonance Imaging: Tools for High-Quality Image Acquisition

Published on: January 5, 2024

Related Experiment Videos

Last Updated: Jun 14, 2026

Adsorption Device Based on a Langatate Crystal Microbalance for High Temperature High Pressure Gas Adsorption in Zeolite H-ZSM-5
09:46

Adsorption Device Based on a Langatate Crystal Microbalance for High Temperature High Pressure Gas Adsorption in Zeolite H-ZSM-5

Published on: August 25, 2016

Troubleshooting and Quality Assurance in Hyperpolarized Xenon Magnetic Resonance Imaging: Tools for High-Quality Image Acquisition
09:55

Troubleshooting and Quality Assurance in Hyperpolarized Xenon Magnetic Resonance Imaging: Tools for High-Quality Image Acquisition

Published on: January 5, 2024

Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Atomic, molecular, and optical physics

Background:

  • The Lieb-Liniger model describes one-dimensional ultracold Bose gases.
  • Calculating expectation values is essential for understanding Bose gas properties.
  • The three-body recombination rate is a key factor in Bose gas dynamics.

Purpose of the Study:

  • To introduce a novel computational method for expectation values in the Lieb-Liniger model.
  • To enable calculations at both zero and finite temperatures.
  • To determine the three-body expectation value at finite temperature.

Main Methods:

  • Development of a novel series expansion for computing expectation values.
  • Application of the method to the Lieb-Liniger model.
  • Calculation of quantities at zero and finite temperatures.

Main Results:

  • A new method for computing expectation values in the Lieb-Liniger model is presented.
  • The method exhibits remarkable convergence properties.
  • The three-body expectation value at finite temperature was successfully computed.

Conclusions:

  • The novel method provides an accurate way to calculate crucial quantities for one-dimensional ultracold Bose gases.
  • The computation of the three-body expectation value offers insights into Bose gas recombination rates.
  • This work advances the theoretical understanding and computational capabilities for Bose-Einstein condensates.