Ideal gas law — LLMpedia

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Ideal gas law The ideal gas law relates pressure, volume, temperature, and amount for a hypothetical ideal gas using PV = nRT. It summarizes empirical findings from experiments by Robert Boyle, Jacques Charles, and Joseph Louis Gay-Lussac and is foundational in Thermodynamics and Statistical mechanics. The law is central to calculations in engineering at institutions such as Massachusetts Institute of Technology, Imperial College London, and ETH Zurich and is taught in courses at University of Cambridge, Harvard University, and Stanford University.

Overview

The ideal gas law expresses a relationship among pressure (P), volume (V), temperature (T), and amount of substance (n) through the universal gas constant (R), used in practice at facilities like Sandia National Laboratories, Los Alamos National Laboratory, and CERN. It unifies earlier empirical laws attributed to Robert Boyle, Edme Mariotte, Jacques Charles, and Joseph Louis Gay-Lussac and provides a starting point for models in Chemical engineering programs at California Institute of Technology and University of Tokyo. In many applications in industries such as Boeing, Siemens, and Royal Dutch Shell, the law approximates behavior when intermolecular forces are negligible, a condition investigated at centers including Max Planck Institute for Dynamics and Self-Organization, Lawrence Berkeley National Laboratory, and National Institute of Standards and Technology.

Derivations connect macroscopic and microscopic perspectives via kinetic theory developed by scientists like James Clerk Maxwell and Ludwig Boltzmann, and use assumptions explored in texts from Isaac Newton-era mechanics to modern treatments at Princeton University and University of Oxford. From kinetic theory, pressure arises from particle momentum transfer against container walls, a concept elaborated in works at Royal Society meetings and lectures by Michael Faraday and Lord Kelvin. Statistical mechanics formulations employ ensembles introduced by Josiah Willard Gibbs and mathematical techniques used in studies at Institute for Advanced Study and University of Göttingen to derive PV = nRT under assumptions of point-like, non-interacting particles.

Engineers at General Electric, Rolls-Royce, and Siemens apply the law in preliminary design of gas turbines, while chemists at Dow Chemical Company and BASF use it for stoichiometric calculations. Meteorologists at National Weather Service and Met Office use ideal-gas approximations in atmospheric models for dry air, and astrophysicists at NASA and European Space Agency employ it for low-density stellar atmospheres. Laboratory examples include isothermal compression experiments in setups at Massachusetts Institute of Technology and École Polytechnique and calculations of molar volume at standard temperature and pressure used in curricula at Columbia University and University of Chicago.

Deviations occur near condensation lines and critical points studied by researchers at Royal Institution and Max Planck Institute for Chemical Physics of Solids, where interactions modeled by Johannes van der Waals and others become significant. Real gases follow equations of state such as the van der Waals equation, Redlich–Kwong equation, and Peng–Robinson equation developed and applied by corporations like ExxonMobil and research groups at Shell and BP. High-pressure, low-temperature regimes are examined in cryogenic research at CERN and Los Alamos National Laboratory, and supercritical fluids are exploited in processes pioneered by firms such as Siemens and studied at Oak Ridge National Laboratory.

Experimental verification historically used apparatus described in publications of the Royal Society and instruments manufactured by firms like Carl Zeiss AG and Thermo Fisher Scientific to measure P, V, and T. Standard units utilize the International System of Units defined by bodies such as the International Bureau of Weights and Measures and adopted by national agencies like National Institute of Standards and Technology and Physikalisch-Technische Bundesanstalt. The universal gas constant R is determined via calorimetry and acoustic methods developed in laboratories at NIST, Imperial College London, and University of Paris (Sorbonne), and practical pressure units such as pascal and atmosphere are traceable to standards maintained by organizations including BIPM and NIST.

The law synthesizes 17th–19th century empirical findings by experimenters including Robert Boyle, Edme Mariotte, Jacques Charles, and Joseph Louis Gay-Lussac and theoretical unification by Amedeo Avogadro and Johann Josef Loschmidt. Later formalization arose from kinetic theory by James Clerk Maxwell and Ludwig Boltzmann and from statistical mechanics advanced by Josiah Willard Gibbs. Institutional developments occurred at academies such as the Académie des Sciences, Royal Society, and universities including University of Göttingen and University of Vienna, with industrial adoption by firms like BASF and Dow Chemical Company.

Category:Physical laws