Part_3_Chem_215.pdf - Part 3 Transport Properties...

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Part 3 Transport Properties
Definitions Transport property. The ability of a substance to transport matter, energy, or some other property along a gradient. Examples. Diffusion - transport of matter along a concentration gradient. Thermal conductivity - transport of thermal energy along a temperature gradient.
Transport Properties Defined Examples (cont’d). Viscosity - transport of linear momentum along a velocity gradient. Electrical conductivity - transport of charge along a potential gradient.
Migration Down Gradients Rate of migration of a property is measured by a flux J. Flux (J) - the quantity of that property passing through a unit area/unit time. gradient of magnitude J
Transport Properties in an Ideal Gas Transport of matter. 0 z d matter dz dN D J 0 z x momentum dt dv J 0 z T energy dz dT J D - diffusion coefficient. =viscosity coefficient. T -thermal conductivity coefficient. Transport of energy. Transport of momentum.
Diffusion Consider the following system. Z=0 +Z -Z z N d N d (- ) N d (z=0) N d (+ )
Number Densities and Fluxes The number densities and the fluxes of the molecules are proportional to the positions of the molecules.   0 z d d d dz dN z 0 z N z N     v z N 4 1 z J d
The Net Flux The net (or total) flux is the sum of the J(L R) and the J(R L). v dz dN 2 1 L R J R L J J 0 z d Total
The Diffusion Coefficient To a first approximation. 0 z d matter dz dN D J v dz dN 2 1 J 0 z d Total v 2 1 D
The Complication of Long Trajectories Not all molecules will reach the imaginary wall at z=0! A o Collision 2/3 of all molecules will make it to the wall in a given time interval t.
The Final Equation Taking into account of the number of molecules that do not reach the wall. v 3 1 v 2 1 3 2 D
Thermal Conductivity Consider the following system.
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