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History[ edit ] In approximately 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. Hydrodynamica front cover In Daniel Bernoulli published Hydrodynamica , which laid the basis for the kinetic theory of gases. In this work, Bernoulli posited the argument, still used to this day, that gases consist of great numbers of molecules moving in all directions, that their impact on a surface causes the gas pressure that we feel, and that what we experience as heat is simply the kinetic energy of their motion. Bernoulli also surmised that temperature was the effect of the kinetic energy of the molecules, and thus correlated with the ideal gas law. In this same work he introduced the concept of mean free path of a particle. Also the logarithmic connection between entropy and probability was first stated by him. In the beginning of the twentieth century, however, atoms were considered by many physicists to be purely hypothetical constructs, rather than real objects. An important turning point was Albert Einstein 's [15] and Marian Smoluchowski 's [16] papers on Brownian motion , which succeeded in making certain accurate quantitative predictions based on the kinetic theory. Assumptions[ edit ] The theory for ideal gases makes the following assumptions: The gas consists of very small particles known as molecules. This smallness of their size is such that the total volume of the individual gas molecules added up is negligible compared to the volume of the smallest open ball containing all the molecules. This is equivalent to stating that the average distance separating the gas particles is large compared to their size. These particles have the same mass.

We study the mathematical models that describe the relationship between the phenomena which are observed to cause bodies to move and the observed motion of those bodies. Two main models are of interest.

The first is the classical model due to Sir Isaac Newton, the study of which is called Newtonian or Classical mechanics. The second is the special relativistic model due to Albert Einstein , the study of which is called Relativistic mechanics. It is found that in most instances Classical mechanics leads to predictions that agree well with observations.

It is only when speeds approach the speed of light that classical mechanics is inadequate and has to be replaced. In this course we shall concentrate on classical mechanics. The study of mechanics may be divided into three branches: 1.

Statics — This branch of mechanics deals with forces which, acting on a rigid body, mutually balance each other and cause no motion. Dynamics — This deals with the forces that cause motion.

That is, they exert no forces on one another. This implies: 1.

Relativistic effects are negligible. Quantum-mechanical effects are negligible. This means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules are treated as classical objects.

Because of the above two, their dynamics can be treated classically. This means that the equations of motion of the molecules are time-reversible.

The average kinetic energy of the gas particles depends only on the absolute temperature of the system. The kinetic theory has its own definition of temperature, not identical with the thermodynamic definition. The elapsed time of a collision between a molecule and the container's wall is negligible when compared to the time between successive collisions. There are negligible gravitational force on molecules. More modern developments relax these assumptions and are based on the Boltzmann equation.

These can accurately describe the properties of dense gases, because they include the volume of the molecules. The necessary assumptions are the absence of quantum effects, molecular chaos and small gradients in bulk properties.

Expansions to higher orders in the density are known as virial expansions.

An important book on kinetic theory is that by Chapman and Cowling. This is known as the Knudsen regime and expansions can be performed in the Knudsen number.