Kinetic theory
This presentation is the property of its rightful owner.
Sponsored Links
1 / 10

Kinetic Theory PowerPoint PPT Presentation


  • 74 Views
  • Uploaded on
  • Presentation posted in: General

Kinetic Theory. Microscopic Analysis. The behavior of a gas should be described by the molecules. The gas consists of a large number of identical particles of mass m . The particles have negligible size and no internal structure.

Download Presentation

Kinetic Theory

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Kinetic theory

Kinetic Theory


Microscopic analysis

Microscopic Analysis

  • The behavior of a gas should be described by the molecules.

  • The gas consists of a large number of identical particles of mass m.

  • The particles have negligible size and no internal structure.

  • The particles are moving in random dirctions with speeds independent of direction

  • Collisions between particles and with the walls are perfectly elastic.


Collision force

Collision Force

  • Follow a collision with a wall perpendicular to x.

  • Particle has mass m and a velocity vx.

    • Strike the wall: Dt = 2L/vx.

    • Impulse: Dp = 2mvx.

  • The force from one particle:

L

Fx

v

m


Pressure force

Pressure Force

  • The pressure on the wall comes from all the particles.

  • The volume is V = AL.

  • Find the value for N particles.

L

A


Three dimensions

Three Dimensions

  • The pressure come from all three dimensions, and is equal in all three.

  • Relate the pressure to the average speed.

V

P

N


Theory match

Theory Match

  • The expression from a particle level relates the average kinetic energy.

  • This almost matches the ideal gas law.

V

P

N


Temperature as energy

Temperature as Energy

  • For the particle-level theory to match the experimental law we equate them.

  • This is kinetic theory.

  • Temperature measures the average kinetic energy.


Average energy

What is the average energy of an air molecule at room temperature (293 K)?

What is average speed for a nitrogen molecule (28 g/mol)?

Energy directly relates to temperature.

(3/2)kT = 6.07 x 10-21 J.

To get the speed requires the mass.

m = (0.028 kg/mol) / (6.022 x 1023 /mol) = 4.65x10-26 kg

Average Energy


Distribution of speeds

Distribution of Speeds

  • Kinetic theory used the average speed.

  • Actual atoms fall into a range of speeds.

  • The Maxwell-Boltzmann distribution describes the probability of a molecule having a particular speed.


Real gases

Real Gases

  • The assumptions for kinetic theory are approximately true.

    • Non-zero molecular size

    • Non-zero force between molucules

  • For the Van der Waals force in air, the effect is about 1% difference from an ideal gas.

next


  • Login