Editing Siméon Denis Poisson (section)

=== Thermodynamics ===
In his work on heat conduction, Joseph Fourier maintained that the arbitrary function may be represented as an infinite trigonometric series and made explicit the possibility of expanding functions in terms of [[Bessel function]]s and [[Legendre polynomials]], depending on the context of the problem. It took some time for his ideas to be accepted as his use of mathematics was less than rigorous. Although initially skeptical, Poisson adopted Fourier's method. From around 1815 he studied various problems in heat conduction. He published his [http://catalog.hathitrust.org/Record/001988678 ''Théorie mathématique de la chaleur''] in 1835.<ref>{{Cite book|last=Kline|first=Morris|title=Mathematical Thought from Ancient to Modern Times|publisher=Oxford University Press|year=1972|isbn=0-19-506136-5|location=United States of America|pages=678–9|chapter=28.2: The Heat Equation and Fourier Series}}</ref>

During the early 1800s, Pierre-Simon de Laplace developed a sophisticated, if speculative, description of gases based on the old [[caloric theory]] of heat, to which younger scientists such as Poisson were less committed. A success for Laplace was his correction of Newton's formula for the speed of sound in air that gives satisfactory answers when compared with experiments. The [[Speed of sound#Speed of sound in ideal gases and air|Newton–Laplace formula]] makes use of the specific heats of gases at constant volume <math>c_V</math>and at constant pressure <math>c_P</math>. In 1823 Poisson redid his teacher's work and reached the same results without resorting to complex hypotheses previously employed by Laplace. In addition, by using the gas laws of [[Robert Boyle]] and [[Joseph Louis Gay-Lussac]], Poisson obtained the equation for gases undergoing [[Adiabatic process|adiabatic changes]], namely <math>PV^{\gamma} = \text{constant}</math>, where <math>P</math> is the pressure of the gas, <math>V</math> its volume, and <math>\gamma = \frac{c_P}{c_V}</math>.<ref name=":8">{{Cite book|last=Lewis|first=Christopher|title=Heat and Thermodynamics: A Historical Perspective|publisher=Greenwood Press|year=2007|isbn=978-0-313-33332-3|location=United States of America|chapter=Chapter 2: The Rise and Fall of the Caloric Theory}}</ref>