Kinetic Theory of Gases Thermal Physics Lesson 5

Learning Objectives Explain the increase of pressure of a gas when it is compressed or heated. Describe the distribution of molecular speeds. Derive the kinetic theory equation.

Explaining the gas laws Assume a gas consists of point molecules moving about at random, continually colliding with the container walls. Each collision causes a force on the container and it is the force of these many impacts that causes the pressure of the gas on the walls.

Explaining the gas laws Boyle’s Law – reducing volume means less distance between collisions with the walls so more collisions per second. Pressure Law- raising the temperature increases the average speed of the molecules so more frequent and harder impacts with the walls.

Molecular Speeds The molecules in a gas have a range of speeds. The root mean square speed, crms, of the molecules is given by:- Where N is the number of molecules in the gas and c1,c2 are the speeds of molecules 1,2, and so on. Note that this is not the same as mean speed.

Molecular Speeds

The Kinetic Theory Equation For an ideal gas consisting of N identical molecules, each of mass m, in a container of volume V, the pressure p of the gas is given by:- Where crms is the root mean square speed of the gas molecules. This is the equation we are going to derive.

First, some assumptions Volume of the molecules negligible compared with volume of the gas. They do not attract each other. They move in continual random motion. The collisions are elastic collisions (no loss of k.e.) Duration of collisions much shorter than time between collisions.

Remembering Assumptions R - Random motion. A – Do not Attract each other. V - Volume of the molecules is negligible E - Elastic collisions D - Duration of collisions Spells - RAVED

Kinetic theory applets There are a number of simulations on the internet. You will need to pick those that suit your specification and needs. Some suggestions are below: - The following were operational in October 2005 Boyle’s Law http://www.chm.davidson.edu/ChemistryApplets/KineticMolecularTheory/PV.html Effect of temperature and volume: http://lectureonline.cl.msu.edu/~mmp/kap10/cd283.htm Distribution of velocity: http://comp.uark.edu/~jgeabana/mol_dyn/KinThI.html Molecular Model of an ideal gas: http://www.phy.ntnu.edu.tw/ntnujava/viewtopic.php?t=42