Thermo & Stat Mech - Spring 2006 Class 15 1 Thermodynamics and Statistical Mechanics Transport Processes

Thermo & Stat Mech - Spring 2006 Class 152 Mean Free Path The average distance that a particles travels between collisions is called the mean free path,. In order to have a collision, the centers of two particles of radius R must approach to within a distance of 2R = d. The picture on the next slide illustrates this point.

Thermo & Stat Mech - Spring 2006 Class 153 Collision Cross Section  d 2

Thermo & Stat Mech - Spring 2006 Class 154 Mean Free Path

Thermo & Stat Mech - Spring 2006 Class 155 Mean Free Paths(?)

Thermo & Stat Mech - Spring 2006 Class 156 Mean Free Path

Thermo & Stat Mech - Spring 2006 Class 157 Some Molecular Speeds

Thermo & Stat Mech - Spring 2006 Class 158 Effusion If there is a hole in a container of gas, molecules will escape through it. The rate at which they pass through the hole is equal to the flux of particles hitting the hole times the area of the hole,  A. Then the rate of change of the number of molecules in the container is:

Thermo & Stat Mech - Spring 2006 Class 159 Effusion Limit If the hole is small equilibrium conditions prevail, and  is known.

Thermo & Stat Mech - Spring 2006 Class 1510 Transport Processes 1. Molecular diffusion. The movement of the particles is of interest. This is particle transport. 2. Thermal conductivity. Particles carry energy from a high temperature region to a lower temperature region. This is energy transport. 3. Viscosity. Drag is created when particles move to a region which is moving at a different speed. This is momentum transport.

Thermo & Stat Mech - Spring 2006 Class 1511 Transport Processes

Thermo & Stat Mech - Spring 2006 Class 1512 Viscosity Consider a plate moving parallel to another plate with a layer of gas between them. The gas in contact with either plate is at rest relative to the plate, so there is a velocity gradient in the gas. A force F is applied to each plate to maintain the motion, and the area of the upper plate is A.

Thermo & Stat Mech - Spring 2006 Class 1513 Viscosity

Thermo & Stat Mech - Spring 2006 Class 1514 Viscosity Gas diffuses up and down, transferring x momentum from layer to layer. The gas that moves in the + y direction is going slower than the layer it moves into, and the gas that moves in the – y direction is going faster than the layer it moves into.

Thermo & Stat Mech - Spring 2006 Class 1515 Viscosity

Thermo & Stat Mech - Spring 2006 Class 1516 Viscosity First we need to know how far particles travel between collisions in the y direction. We must find the average value of y = cos , averaged over the flux of molecules.

Thermo & Stat Mech - Spring 2006 Class 1517 Viscosity

Thermo & Stat Mech - Spring 2006 Class 1518 Viscosity

Thermo & Stat Mech - Spring 2006 Class 1519 Viscosity

Thermo & Stat Mech - Spring 2006 Class 1520 Diffusion

Thermo & Stat Mech - Spring 2006 Class 1521 Thermal Conductivity

Thermo & Stat Mech - Spring 2006 Class 1522 Thermal Conductivity

Thermo & Stat Mech - Spring 2006 Class 1523 Transport Processes