In science, Daniel Bernoulli (1700-1782) was a Dutch-born Swiss mathematician, physicist, and physician noted for his 1738 Hydrodynamica in which he outlined the basics of the ideal gas law, the precursors for the kinetic theory of gases, and gave the first basic definition of pressure. Bernoulli defined pressure as: [1]

“The weight P holding down the piston in [a given] position is the same as the weight of the overlying atmosphere, which we shall designate P in what follows.”

Ideal gas law
The origin of the modern formulation of the ideal gas law is difficult to pin down. Bernoulli, however, may have been the first to give a verbal derivation this law. The following diagram shows his famous depiction of fluid particles sealed by the piston and weighted down by the pressure of the atmosphere and weights, which he used to describe the various gas laws. In what seems to be a reference to Boyle’s law (1662), Bernoulli states:

“The force of compression is approximately inversely proportional to the volume occupied by the air. This is confirmed by a variety of experiments. This law can certainly be safely applied to air less dense than normal; thought I have not adequately examined whether it also applies to air very much more dense; [also] the temperature of the air should be carefully kept constant while it is being compressed. ”

In equation form this would be:

or

where k is a proportionality constant (indicative of experimental data to be determined). He then states:

“The pressure of the air is increased not only by reduction in volume but also by the rise in temperature. As it is well known that heat is intensified as the internal motion of the particles increases, it follows that any increase in the pressure of air that has not changed its volume indicates more intense motion of its particles, which is in agreement with our hypothesis.”

In equation form this would be:

or

In conclusion of these two aspects of the laws of gas behavior, Bernoulli then summarizes combined theorem as:

“In any air whatever density, but at a given temperature, the pressure varies as the density, and furthermore, that increases of pressure arising from equal increases of temperature are proportional to the density.”

In equation form, noting that Bernoulli assigned the symbol “n” to number of particles, which gives a particle density ρ of n divided by volume V, we would have:

or

Bernoulli notes that this theorem was discovered by experiment by French physicist Guillaume Amontons, who had given an account of his work in the Memoires of the Royal Academy of Sciences in Paris for 1702. In any event, it is not to far to see how from these precursory statements of gas laws, and the equations they embody, that the modern ideal gas law can be obtained; particularly from the last equation, with substitution of the modern ideal gas constant R for k:

The form of the abover equaiton, however, did not come in use until the early 20th century.

References
1. (a) Bernoulli, Daniel. (1738). “On the Properties and Motions of Elastic Fluids, Especially Air” (Hydrodynamica, Section 10) in: The Kinetic Theory of Gases of Gases (pgs. 57-65), 2003, by Stephen G. Brush, Nancy S. Hall. Imperial College Press.
(b) Bernoulli, Daniel. (1738). Hydrodynamica, Sive Vivibus et Motimus Fluidorum Commentarii. Sectio Decima: “De affectionibus atque botimus fluidorum elasticorum, praecipue autem aeris.” (pgs. 200-204). Argentorati, Sumptibus Johannes Reinholdi Dulseckeri.

External links
● Daniel Bernoulli –Wikipedia.