In thermodynamics, gas laws are a set of equations that describe the behavior of bodies of gas under what are known as ideal, perfect, standard, or non-extreme conditions. The various laws, as listed below, came into existence following the invention of German engineer Otto Guericke’s vacuum pump in 1645, beginning with the experimentation's of Irish chemist Robert Boyle. The central law for most gases is the ideal gas law.

Boyle’s law
See main: Boyle’s law
In 1658, Irish chemist Robert Boyle and his assistant Robert Hooke built a combination air pump/vacuum, which they called a 'pneumatical engine', based on the design of German engineer Otto Guericke’s vacuum pump in the 1657 book Mechanical Hydraulic Pneumatics by German scientist Gaspar Schott. [1] After conducting a number of experiments with their air pump, Boyle published the results in the 1660 book New Experiments: Physico-Mechanical, Touching the Spring of the Air, and Its Effects (Made for the Most Part in a Pneumatical Engine). In the 1669 second edition of Spring of the Air, a statement of what is now known as "Boyle’s law" can be found defined in modern shorthand as: [2]

$PV = K\mid_{n,T} \,$

which says that for a body of gas at constant number of particles n and temperature T the product of the measure of the pressure P and volume V of gas will be a constant K. The Spring of the Air had a great influence on other scientists, who built their own air pumps, and devised new experiments of their own.

Marriott's law
See main: Mariotte’s law
In 1676, French physicist Edme Mariotte published an essay entitled De la Nature de l'air (The Nature of Air) in which it is said he recognized Boyle’s law, in his statement that ‘the volume of a gas varies inversely as the pressure’.

Subsequently, Boyle’s law is often synonymously called Mariotte’s law (or sometimes Boyle-Mariotte’s law), stated to the effect that ‘the pressure of an ideal gas at constant temperature varies inversely with volume’.

Amonton's equation
See main: Amontons’ law
In 1702, French physicist Guillaume Amontons, as discussed in his paper “Discourse on a Few properties of Air, and the Means to know the Temperature in all Climates of the Earth”, was said to have stated that the product of the pressure times volume equals the product of temperature times an unknown constant; in modern formulation would be an equation of the form:

$P V = k T \,$

This is the first prototype of what would later become, with the inclusion of the particle number n and the gas constant R, the ideal gas law. Dutch-born Swiss physicist Daniel Bernoulli, in his 1738 Hydrodynamica, credits Amontons as having been the originator of this formulation of the gas laws.

Charles' law
See main: Charles’ law
In circa 1787, French scientist Jacques Charles conducted an experiment where he filled five balloons to the same volume with different gases. He then raised the temperature of the balloons to 80ºC and noticed that they all increased in volume by the same amount.

In 1800, an eighteen-year-ear old French chemistry student named Joseph Gay-Lussac, a recent graduate of the École Polytechnique, met and became a lab assistant and protégé of chemist Claude Berthollet. While working under Berthollet, Gay-Lussac discovered that gases expand by the same proportion for an equivalent rise in temperature. Gay-Lussac’s approach to chemistry was to express laws mathematically. [3]

Supposedly, Charles' unpublished experiment was later referenced by Gay-Lussac in 1802 when he published a paper on the precise relationship between the volume and temperature of a gas, which Gay-Lussac named "Charles' Law" in honor of Jacques Charles' original experiment. In modern terms, Charles’ law is define as:

$V = KT\mid_{n,P} \,$

which states that for a body of gas at constant particle number n and pressure P the volume V of the gas will be constant K.

Gay-Lussac’s law
See main: Gay-Lussac’s law
In 1802, French chemist Joseph Gay-Lussac published the results of his findings in what is now known as Gay-Lussac’s law, which in modern terms is:

$P = KT\mid_{n,V} \,$

which states that the pressure P of a body of gas at constant volume V and particle count n will be proportional K to its temperature T.

Law of Mariotte and Gay-Lussac
In 1834, French engineer Emile Clapyron gave a derivation in which he stated that Mariotte’s law (PV = k, at constant temperature) combined with that of Gay-Lussac's law (P = kT, at constant volume) gives the expression: [4]

$~ Pv = R(267 + t) ~$

This is sometimes referred to as the 'G-M law' (e.g. by German chemist August Horstmann, 1873) or the 'law of Mariotte and Gay-Lussac' (according to Ingo Muller, A History of Thermodynamics, 2007).

Boyle-Charles law
See main: Boyle-Charles law
Into the 1890s, the phrase “ideal perfect gas” was being used in relation to gases that obeyed the laws of Charles and Boyle (or Boyle-Charles law), as defined by the following “characteristic equation”: [5]

$\frac{PV}{T} = K\,$

which says that the ratio of the product of the pressure and the volume of the gas by the temperature is constant for in ideal perfect gas. The term 'perfect' in this case a residual carry-over from the earlier days of attempts to make a 'perfect vacuum' (perfect gas) in gunpowder engine. In most cases the phrase Boyle-Charles law was a precursor synonym for the later term 'ideal gas law', which arrived after the concept of the mole or particle count unit n was invented.

Ideal gas law
See main: Ideal gas law
The ideal gas law is a single combined expression of all of the various gas laws in one equation:

$~ PV = nRT ~$

which states that the product of the pressure and volume of an ideal gas is proportional to the product of the particle count and temperature of the gas. This modern version of the ideal gas law was being used in 1895 by Germans chemist Walther Nernst and in 1897 by physicist Max Planck.

Boyle-Charles law
Social ideal gas law

References
1. (a) Schott, Gaspar. (1657). Mechanical Hydraulic Pneumatics (Mechanicahydraulica-pneumatica). Würtzburg.
(b) Wilson, George. (1849). “On the Early History of the Air-Pump in England”, The Edinburgh New Philosophical Journal, (pgs. 330-54).
2. Morris, Richard. (2005). The Last Sorcerers: the Path from Alchemy to the Periodic Table (pg. 55). The National Academies.
3. Burns, William E. (2003). Science in the Enlightenment: an Encyclopedia (section: Gay-Lussac (1778-1850), pgs. 109-11). ABC-CLIO.
4. Clapeyron, Émile. (1834). “Memoir on the Motive Power of Heat”, Journal de l’Ecole Polytechnique. XIV, 153 (and Poggendorff's Annalender Physick, LIX, [1843] 446, 566).
5. Robinson, William. (1890). Gas and Petroleum Engines: A Practical Treatise on the Internal Combustion Engine, (pg. 422). E. & F.N. Spon.