Kinetic theory of gases

It treats the collisions as perfectly elastic and as the only interaction between the particles, which are additionally assumed to be much smaller than their average distance apart.

In about 50 BCE, the Roman philosopher Lucretius proposed that apparently static macroscopic bodies were composed on a small scale of rapidly moving atoms all bouncing off each other.

[1] This Epicurean atomistic point of view was rarely considered in the subsequent centuries, when Aristotlean ideas were dominant.

[citation needed] One of the first and boldest statements on the relationship between motion of particles and heat was by the English philosopher Francis Bacon in 1620.

"[3] In 1623, in The Assayer, Galileo Galilei, in turn, argued that heat, pressure, smell and other phenomena perceived by our senses are apparent properties only, caused by the movement of particles, which is a real phenomenon.

In 1665, in Micrographia, the English polymath Robert Hooke repeated Bacon's assertion,[6][7] and in 1675, his colleague, Anglo-Irish scientist Robert Boyle noted that a hammer's "impulse" is transformed into the motion of a nail's constituent particles, and that this type of motion is what heat consists of.

[8] Boyle also believed that all macroscopic properties, including color, taste and elasticity, are caused by and ultimately consist of nothing but the arrangement and motion of indivisible particles of matter.

"[10] In a manuscript published 1720, the English philosopher John Locke made a very similar statement: "What in our sensation is heat, in the object is nothing but motion.

In his 1744 paper Meditations on the Cause of Heat and Cold, Russian polymath Mikhail Lomonosov made a relatable appeal to everyday experience to gain acceptance of the microscopic and kinetic nature of matter and heat:[13]Movement should not be denied based on the fact it is not seen.

The theory was not immediately accepted, in part because conservation of energy had not yet been established, and it was not obvious to physicists how the collisions between molecules could be perfectly elastic.

[16]: 36–37 Pioneers of the kinetic theory, whose work was also largely neglected by their contemporaries, were Mikhail Lomonosov (1747),[17] Georges-Louis Le Sage (ca.

In 1856 August Krönig created a simple gas-kinetic model, which only considered the translational motion of the particles.

[21] In 1857 Rudolf Clausius developed a similar, but more sophisticated version of the theory, which included translational and, contrary to Krönig, also rotational and vibrational molecular motions.

[24] Maxwell also gave the first mechanical argument that molecular collisions entail an equalization of temperatures and hence a tendency towards equilibrium.

[25] In his 1873 thirteen page article 'Molecules', Maxwell states: "we are told that an 'atom' is a material point, invested and surrounded by 'potential forces' and that when 'flying molecules' strike against a solid body in constant succession it causes what is called pressure of air and other gases.

An important turning point was Albert Einstein's (1905)[27] and Marian Smoluchowski's (1906)[28] papers on Brownian motion, which succeeded in making certain accurate quantitative predictions based on the kinetic theory.

The framework was gradually expanded throughout the following century, eventually becoming a route to prediction of transport properties in real, dense gases.

These can accurately describe the properties of dense gases, and gases with internal degrees of freedom, because they include the volume of the particles as well as contributions from intermolecular and intramolecular forces as well as quantized molecular rotations, quantum rotational-vibrational symmetry effects, and electronic excitation.

We combine the above with Newton's second law, which states that the force experienced by a particle is related to the time rate of change of its momentum, such that

From equations (1) and (3), we have Thus, the product of pressure and volume per mole is proportional to the average translational molecular kinetic energy.

Equations (1) and (4) are called the "classical results", which could also be derived from statistical mechanics; for more details, see:[34] The equipartition theorem requires that kinetic energy is partitioned equally between all kinetic degrees of freedom, D. A monatomic gas is axially symmetric about each spatial axis, so that D = 3 comprising translational motion along each axis.

A polyatomic gas, like water, is not radially symmetric about any axis, resulting in D = 6, comprising 3 translational and 3 rotational degrees of freedom.

[35] For an ideal gas in equilibrium, the rate of collisions with the container wall and velocity distribution of particles hitting the container wall can be calculated[36] based on naive kinetic theory, and the results can be used for analyzing effusive flow rates, which is useful in applications such as the gaseous diffusion method for isotope separation.

Derivation of the kinetic model for shear viscosity usually starts by considering a Couette flow where two parallel plates are separated by a gas layer.

The transfer of momentum between molecules is explicitly accounted for in Revised Enskog theory, which relaxes the requirement of a gas being dilute.

There are no simple general relation between the collision cross section and the hard core size of the (fairly spherical) molecule.

For such interaction potentials, significantly more accurate results are obtained by numerical evaluation of the required collision integrals.

Both plates have uniform temperatures, and are so massive compared to the gas layer that they can be treated as thermal reservoirs.

is a factor that tends to unity in the limit of infinite dilution, which accounts for excluded volume and the variation chemical potentials with density.

Specifically, the fluctuation-dissipation theorem applies to the Brownian motion (or diffusion) and the drag force, which leads to the Einstein–Smoluchowski equation:[44]