Gay-Lussac Did Better Than He Knew

In his 1802 paper Joseph Louis Gay-Lussac reported the first definitive experimental evidence that many different gases exhibit the same fractional expansion of volume when heated. This property is known as Charles Law, Amontons Law, Dalton's Law, or the law of volumes. Gay-Lussac concluded from his experiments that many gases expand by 37.5\% when heated from $0 \,^{\circ}{\rm C}$ to $100\,^{\circ}{\rm C}$. Although his result is within 2.5\% of the modern value of $36.6\% = 100/273.15$, the discrepancy is surprising because his direct and simple experimental method allowed him to measure changes in volume with a precision of a few tenths of a percent. An examination of his original paper suggests, however, that he did not take into account that his measurements of the initial and final volumes of gas were made at slightly different pressures. With reasonable assumptions about the diagrams in his paper, one can use Pascal's law and the ideal gas law to correct the measured volumes so that they correspond to the same initial and final pressure. With this correction the results imply $\Delta V/V = .366$. Gay-Lussac did better than he knew.