POISSON, (SIMÉON-DENIS). - THE MATHEMATICAL ANALYSIS OF HEAT - POISSON'S ISENTROPE.

Sur la Chaleur des Gaz et des vapeurs.

(Paris, Crochard, 1823). 8vo. Without wrappers. In 'Annales de Chimie et de Physique', Series 2 - Volume 23, Cahier 4. With halftitle to vol. 23. Pp. 337-444 (entire issue offered). Poisson's paper: pp. 337-352.

First appearance of Poisson's importent paper on the mathematical treatment of "specific heats".

"In "Sur la chaleur des gaz et des vapeurs," published in August 1823 in Annales de chimie et de physique, Poisson developed ideas published four months before by Laplace in Book XII of Mécanique céleste. Poisson introduced all the precautions needed to render the confused notion of quantity of heat susceptible to mathematical analysis. He called quantity of heat the magnitude that characterizes the transition of a given mass of gas from an arbitrary initial state of temperature and pressure to another state. This definition makes more abstract the quantitative aspect that naturally follows from the concept of heat as a caloric fluid. Poisson could thus deal comfortably with this magnitude, since for him it is simply a function q of p, p, and ø (pressure, density, and temperature). The equation of state p= ap(1+aø) was already classic, and the growing acceptance of the notions of specific heats, at constant pressure and constant volume, allowed him to write the simple partial differential equation of which should be the integral. He also showed that independently of any additional hypothesis, and whatever the arbitray function used in the integration, the adiabatic transformations (the term did not yet exist) correspond to the formulas p · py = constant and (?+266.67)·p1y= constant, y being the ratio of the specific heats, assumed constant."(DSB).

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