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# Transport Properties of Matter

Thermodynamics is easy.  I've learned it many times.

### Related Links (Outside this Site)

History of Kinetic Theory   |   Laws of Gas Transport
Einstein's Random Walk  by Mark Haw  (Physics World, January 2005).
Kinetic Theory and Thermodynamics  by  Prof. Stephen J. Blundell  (Oxford).
Onsager reciprocal relations  (Wikipedia).

## Transport through Matter

Transport properties of matter express the way a current of a certain quantity is created by an imposed gradient of another  conjugate  quantity.  For example, a gradient of temperature causes an entropy current which is perceived as a flow of heat.

The analysis of any transport property always follows the same pattern:  Assume a given gradient and deduce the current thus produced.  (The scale of observation makes the number of microscopic components large enough for statistical physics to be relevant.)

(2006-09-14)     Viscosity
The capability to transport microscopic momenta.

In 1860, James Clerk Maxwell (1831-1879) analyzed the viscosity of ideal gases as microscopic transfers of horizontal momenta in response to a vertical gradient in the average horizontal velocity of particles.  He obtained a surprising theoretical result, which he confirmed experimentally with the help of his wife:  The vicosity of a gas has little to do with its density and it increases in direct proportion with the square root of the absolute temperature.

This remarkable result is in sharp contrast with the common knowledge about  liquids  (whose viscosity clearly decreases with temperature).  Maxwell's result was one of the great early successes of the  kinetic theory of gases.

(2006-10-01)     Brownian Motion:  Brown (1827) & Einstein (1905)
The motion of microscopic grains led Einstein to gauge molecular sizes.

The constant microscopic motion of very small particles was first noticed by the Scottish botanist Robert Brown (1773-1858)  in the summer of 1827, as he observed under the microscope colloidal suspensions of pollen grains  (from a type of evening primrose called  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 motion could be explained in terms of the  kinetic theory  of fluids and could serve to estimate the size of the  molecules  involved.

The actual experimental measurements were first carried out in 1908 by the team 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 diffusion can be:  It behaves according to the rules of kinetic theory as if the grains formed a gas of very heavy molecules.

(2006-09-14)   Thermal Conductivity
Thermal conductivity is the capability to transport random energy.

(2006-09-17)   Diffusivity
The transport of chemical concentration.

(2012-08-17)   Boltzmann Transport Equation
Linear stochastic partial differential equation.

Solve for a continuous random variable ...

Boltmann equation   |   Pierre-Louis Lions (1956-)

(2006-09-14)   Speed of Sound
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 (r) :

Speed of Sound  (u)  in a Fluid
 u 2   = ( ¶p )S ¶r

r  may be defined as the ratio  M/V  of the constant  molar mass  (M is roughly 0.002 kg/mol for hydrogen)  to the variable  molar volume  (V).

John James Waterston (1811-1883) was a Scottish physicist (hailing from Edinburgh) whose pioneering work on the  kinetic theory of gases  remained obscure until that 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 kinetic theory of gases, in a paper which, unfortunately, remained buried in the archives of the Royal Society until  Lord Rayleigh  arranged for its publication, in 1891.

Numericana :   Sound and Acoustics