(2006-09-14) The capability to transport microscopic momenta.
In 1860, James Clerk Maxwell (1831-1879) analyzed the viscosity of ideal gasesas microscopic transfers of horizontal momenta in response to a vertical gradientin the average horizontal velocity of particles. He obtained a surprising theoretical result, which he confirmed experimentallywith the help of his wife: The vicosity of a gas has little todo with its density and itincreases in direct proportion with thesquare root of the absolute temperature.
This remarkable result is in sharp contrast with the common knowledge about liquids (whose viscosity clearlydecreases with temperature). Maxwell's result was one of the great early successes of the kinetic theory of gases.
(2006-10-01) The motion of microscopic grains led Einstein to gauge molecular sizes.
The constant microscopic motion of very small particles was first noticed bythe Scottish botanist Robert Brown (1773-1858) in the summer of 1827,as he observed under the microscope colloidalsuspensions of pollen grains (from a type of evening primrosecalled Clarkia Pulchella).
By repeating the observation with other types of small particles, including mineral dust,Brown ruled out any biological origin for that microscopic agitation, now known as Brownian motion. This would remain a mystery for 78 years.
In his celebrated "Miracle Year" (1905), Albert Einstein proposed that Brownian motioncould be explained in terms of the kinetic theory of fluids andcould serve to estimate the size of the molecules involved.
The actual experimental measurements were first carried out in 1908 by theteam of the French physical chemist Jean Perrin (1870-1942;Nobel 1926).
The microscopic grains are in thermal equilibrium (at temperature T) with the molecules of the colloid in which they are suspended. Thus, the average (translational) kinetic energy of each grain is (3/2) kT. The speed of the grains can't be measured directly by the overall diffusioncan be: It behaves according to the rules ofkinetic theoryas if the grains formed a gas of very heavy molecules.
(2006-09-14) Thermal conductivity is the capability to transport random energy.
(2006-09-17) The transport of chemical concentration.
(2012-08-17) Linear stochastic partial differential equation.
Solve for a continuous random variable ...
(2006-09-14) Reversible propagation of a disturbance in the pressure of a fluid.
In a fluid, the square of the speed of sound is the isentropic derivative of pressure (p) with respect to mass density() :
Speed ofSound (u) in a Fluid
u 2 =
p
S
may be defined as the ratio M/V of the constant molar mass (M is roughly0.002 kg/mol for hydrogen) to the variable molar volume (V).
John James Waterston(1811-1883) was a Scottish physicist (hailing from Edinburgh) whosepioneering work on the kinetic theory of gases remainedobscure untilthat theory was firmly established (by Clausius and Maxwell).
Many of Waterston's early results (including a special case of the theorem of equipartition of energy) remained hidden in a book with a very misleading title: Thoughts on the Mental Functions (1843). In 1851, Waterston explained Laplace's formula for the speed of sound in terms of the kinetictheory of gases, in a paper which, unfortunately,remained buried in the archives of the Royal Societyuntil Lord Rayleigh arranged for its publication, in 1891.
