# Early Theories of Gases

The kinetic theory of gases originated in the ancient idea that matter consists of tiny invisible atoms in rapid motion. In the 17th century this idea was revived and used to explain, among other phenomena, the properties of gases.

The British chemist and physicist Robert Boyle (1627-1691), building on the work of several other 17th-century scientists, showed that air is "elastic": it resists compression and expands to fill the available space. The mechanical pressure P exerted by a given amount of gas at a particular temperature is inversely proportional to the volume V of its container, a relation now known as "Boyle's Law."

Boyle mentioned two alternative atomistic explanations for air pressure: (1) air is composed of particles that repel each other, like coiled-up pieces of wool or springs; (2) air is composed of whirling particles that push each other away by impacts. The first hypothesis was taken up by Isaac Newton, who proved mathematically that if air pressure is due to the repulsion of neighboring particles, then the repulsive force must be inversely proportional to their distances. The second hypothesis, which Boyle associated with Descartes' etherial vortices, lacked a quantitative foundation in the 17th century, though it gained qualitative support from the common idea that heat is related to atomic motion and the observation that air pressure increases with temperature.

The Swiss mathematical physicist Daniel Bernoulli (1700-1782) formulated a quantitative kinetic theory in his book on hydrodynamics. He derived Boyle's law for gas pressure by computing the force exerted on a movable piston by the impacts of n particles moving with speed v, in a closed space of total volume V. If V is smaller the pressure will be greater because the particles strike the piston more frequently. If the space occupied by the particles themselves is small compared to the volume V, the pressure P should be inversely proportional to V; so, as stated by Boyle's law, the product PV is constant (see Bernoulli, 1738).

Bernoulli also showed that the pressure will be proportional to the kinetic energy of the particles (= 1/2 m v^2, where m is the mass of a single particle) since the frequency of impacts is proportional to the speed v and the force of each impact is proportional to the momentum mv. This, he remarked, explained the observed fact that increases of pressure arising from equal increases of temperature are proportional to the density, and suggested that temperature itself could be defined in terms of the pressure of air at a standard density. Although other scientists had not yet accepted the concept of an absolute temperature scale, Bernoulli's theory introduced the idea that heat or temperature could be identified with the kinetic energy of particles in an ideal gas.

Experimental work on gases around 1800 confirmed the simple relation between pressure, volume and temperature assumed by Bernoulli. The French chemist Joseph Gay-Lussac (1778-1850) and others showed that pressure increases in proportion to temperature if the volume is held constant, or volume increases in proportion to temperature if pressure is held constant; these relations can be summarized in the equation

PV = NR(t + 273) ,

where N is proportional to the total mass of gas present, t is the temperature in degrees Celsius (centigrade) and R is a universal constant. But it was not yet known whether the equation would be valid down to temperatures so low that (t + 273) is zero, or whether all gases would condense before that point of "absolute cold" is reached so the equation would no longer apply.

The kinetic theory was not widely accepted in the 18th century; most scientists preferred the Newtonian repulsion theory, which was compatible with the idea that heat is a fluid, "caloric," rather than the energy of atomic motion. Caloric was sometimes thought to be composed of particles that repel each other and are attracted to the atoms of ordinary matter. Thus gas pressure increases with temperature because the gas acquires more of the self-repelling caloric fluid. Temperature itself could be defined as the density of caloric (amount of the caloric fluid divided by volume).

With this definition of temperature, the caloric theory could explain why compression can increase the temperature of a gas even though no heat is added from outside (the same amount of caloric is concentrated in a smaller volume), or expansion can decrease the temperature even though no heat is lost (the same amount of caloric is spread over a larger volume). But there was one anomalous observation, whose significance was not appreciated until much later: Gay-Lussac found that in the free expansion of a gas (into a vacuum rather than pushing back a piston) there is practically no change in temperature.

The caloric theory could also explain phenomena such as the latent heat of phase transitions (solid to liquid or liquid to gas) and the heat absorbed or released in chemical reactions, by postulating that some caloric is "bound" to the individual atoms or compounds. The ordinary pressure-volume relations of gases are determined by the unbound or "free" caloric that fills the space between particles. The kinetic theory seemed to offer no plausible account of these phenomena, and moreover its hypothesis that the atoms move at constant speed between collisions seemed incompatible with the generally-accepted idea that all space is filled with an ethereal fluid.

Finally, the caloric theory gained credibility in the early 19th century from Laplace's use of it to calculate the speed of sound in gases, resolving a long-standing discrepancy between theory and observation; and it was indirectly supported by the acceptance of the particle theory of light, since light and heat were widely viewed as qualitatively identical phenomena.

Updated 24 August 2001