The Speed of Atoms and Kinetic Theory

James Clerk Maxwell

James Clerk Maxwell (1831–1879) was born in Edinburgh, Scotland, in 1831. His family moved to a small country estate in Middlebie, Galloway (southwestern Scotland) that his father, John Clerk inherited (the addition of the name “Maxwell” was required to satisfy legalities of this inheritance). When he was eight, James’ mother died, of abdominal cancer; she was forty-eight. John Clerk Maxwell was an attentive and perhaps overly protective father. Unfortunately, he made the mistake of entrusting James early education to a tutor who employed beatings as a teaching tactic. Fortunately, a visit from his maternal aunt, Jane Cay, discontinued this abusive treatment, as she was able to convince Maxwell’s father to allow him to continue his education at Edinburgh Academy.

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Maxwell, the Rings of Saturn and Kinetic Theory

In 1855, Maxwell devised a theory that correctly predicted the composition of the rings of Saturn. While at Aberdeen, Maxwell devoted much of his time to the problem and in a letter to Thomson describes the rings as:

“… a great stratum of rubbish jostling and jumbling round Saturn without hope of rest or agreement in itself …”

Maxwell constructed a theory that showed Saturn’s rings couldn’t be solid, liquid or gas, but rather were made of many small, solid, colliding particles orbiting the planet, which were dynamically stable and provided a solid-like appearance; the solution won him the prize. Today, we do know that Saturn’s rings are comprised of tiny rocks that collide with each other as they orbit the planet. In is interesting to note that what led Maxwell to kinetic theory was, oddly enough, Saturn’s rings.

Entropy and Atoms

Our understanding of the connection between entropy and the microscopic world of atoms is mostly due to the work of James Clerk Maxwell and Ludwig Boltzmann.

The Maxwell Distribution

Not all the atoms in a gas move at the same speed, but rather each atom takes on a speed lying in a specific range. For an ideal gas at equilibrium, this range is known as the Maxwell distribution. In 1860, Maxwell needed merely a single page to derive this amazing result, which also allowed him to calculate other important properties of a gas that matched with experimental observation.