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Kinetic Theory of Gases

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.

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Kinetic Theory of Gases

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  1. Kinetic Theory of Gases Thermal Physics Lesson 5

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. Molecular Speeds

  7. 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.

  8. 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.

  9. 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

  10. 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

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