The historical importance of the physics of gases was not only that it provided a direct insight into the nature of heat but also that when heat was applied to gases and vapours its effects were more obvious and more easily quantifiable than when it was applied to solid and liquids.  In other words, gases and vapours provided the means whereby heat could readily produce mechanical effects. – D. S. L. Cardwell [1]

To truly understand the history of energy, we must first understand the history of the study of gases, starting with the ideal gas.

Thank goodness for the ideal gas.  It lends itself so beautifully to study and education.  The exactness of the relationship between its properties can’t get much simpler.

            PV = nRT                                                                                                

But the simplicity is somewhat misleading, as many, many years were required to put this law together.  Ingenuity, patience, accuracy, reliable equipment, new analytical technologies, meticulous experiments and a thinking mind were all required to realize this tremendous accomplishment. Here’s how it went down.

Robert Boyle (P-V)

The great thing about the ideal gases is that their properties, and especially the change in their properties since energy is all about change, readily lend themselves to direct measurement.  The first to demonstrate this was Robert Boyle (1627-91).  As a dedicated and persistent experimentalist and researcher whose demonstrated skills led to his being selected as a founder of the Royal Society, Boyle together with Robert Hooke (1635-1703) studied the relationship between pressure and volume of a gas trapped in an upside-down tube immersed in a bath of mercury at constant ambient temperature.  As the height of mercury was changed, so changed the volume of the gas.  From this, Boyle determined in 1662 that gas pressure (as measured by the height of mercury) is inversely proportional to volume.

            P ∝ 1/V                   Boyle’s Law (fixed temperature and mass)

Although it took awhile, others followed Boyle’s lead and pursued their own studies of the relationship between any two of the variables while keeping the third constant (this inherently assumes that the number of moles, n, is fixed).  Since Boyle developed a relationship for pressure and volume, temperature remained to be addressed, which presented somewhat of a conceptual challenge as one could envision zero volume and zero pressure.  But zero temperature?  What could this mean?  And where would it be found?

Joseph-Louis Gay-Lussac: volume-temperature (V-T)

While Guillaume Amontons (1663-1705) seems to have been the first to recognize the importance of actually measuring how gas volume and pressure vary with temperature, it would take another century until Joseph-Louis Gay-Lussac (1778-1850) obtained the necessary accuracy in measurements to draw conclusions.  By 1802 Gay-Lussac determined that air and other gases, such as oxygen, nitrogen, hydrogen and carbon dioxide, all expand by the same fraction when heated through the same temperature.  He also determined the coefficient of expansion to be 1/267, which thus meant that upon adding the constant of 267 to the temperature reading (degrees Celsius), the following relationship would hold.

            V ∝ T                      Gay-Lussac’s Law (volume-temperature)

The above law is sometimes referred to as Charles Law, especially in the English-speaking world, based on the work of Jacques Charles (1746-1823) some fifteen years earlier.  But such reference was due to an English-favoring historical revision by P. G. Tait.  As Cardwell commented, “the facts do not in any way justify the ascription of this law to J. A. C. Charles… [and so] we deny the claim made on behalf of Charles and shall in future refer to the law as Gay-Lussac’s law.” [2]

Joseph-Louis Gay-Lussac: pressure-temperature (P-T)

In 1807, Gay-Lussac continued his experimental studies by carrying out a series of experiments designed to determine the relationship between the specific heats of gases and their densities.  In the course of these studies, he found that the change of gas temperature was directly proportional to the change of pressure.

            P ∝ T                      Gay-Lussac’s Law (pressure-temperature)

Amedeo Avogadro (n)

As the above studies involved constant mass, mass thus became the final gas property requiring study.  In 1811 Amedeo Avogadro (1776-1856), building on Gay-Lussac’s work, proposed his famed hypothesis [3] writing, “… the number of integral molecules in any gas is always the same for equal volumes.”  Fixed volume (at the same temperature and pressure) meant fixed number of molecules.  Knowing mass of the gas then enabled Avogadro to determine the relative molecular weights of various gases:  the ratio of weights must equal the ratio of molecular weights.  Avogadro’s work told us the following relationship.

            V ∝ n                      Avogadro’s Law

Émile Clapeyron

It was finally Émile Clapeyron in 1834 who tied together the P-V-T properties into the ideal gas law, which, when including Avogadro’s work showing that the law can be scaled by the number of molecules, became:

            PV = nRT                Ideal Gas Law

The Ideal Gas Law – impact

The ideal gas law provided an excellent quantified relationship between readily measurable properties of gas and served to forward discussions from the abstract to the concrete.  Carnot, Clapeyron, Thomson and Clausius all relied on the ideal gas law and its inherent simplicity to guide their specific analysis of the steam engine.  The law itself was the result of extensive and accurate studies by a range of scientists and fortunately was done independent of any guiding philosophy of heat.  Pressure, volume and temperature stood on their own as directly measurable properties of nature, independent of any assumptions about what that nature was. 

The beauty of the ideal gas law lies not only in its simplicity but also in the power of what it shows, specifically the relationship between PV and T, for in this relationship one catches a glimpse of the relationship between work and heat which became the basis for the mechanical theory of heat and the subsequent higher-level theory of energy and its conservation.

Explore more!

The use of the ideal gas law pervades thermodynamics. Find out why in my book Block by Block – The Historical and Theoretical Foundations of Thermodynamics. Thank you for listening!

[1] Cardwell, D. S. L. 1971. From Watt to Clausius; the Rise of Thermodynamics in the Early Industrial Age. Ithaca, N.Y: Cornell University Press, pp. 128-129.

[2] Cardwell, 1971, pp. 130-131.

[3] Crosland, M. P. 2008. “Gay-Lussac, Joseph Louis.” In Complete Dictionary of Scientific Biography, 5:317–27. Charles Scribner’s Sons.