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# 3.3 the ideal gas

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How does the Ideal Gas equation explain real gases?

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### 3.3 the ideal gas

1. 1. Topic 3 - Thermodynamics3.3 – The Ideal Gas
2. 2. Gas Pressure● Pressure is defined as the force per unit area.● Pressure is measured in Pascals (Pa)Gas pressure arises because of collisionsbetween particles (causing the force) and the wallof the container (the area over which they act)p=FA
3. 3. An Ideal Gas● Physicists made a set of observations of gasesfrom which 4 assumptions are made to definethe “ideal gas.”● A pure gas contains identical molecules incontinuous random motion. (no one particle is morespecial than another)● All collisions are elastic (energy is conserved)● The volume of the particles is negligible comparedto the volume of the container. (it is compressible)● There are no forces on the molecules except duringcollisions (the particles are very far apart)
4. 4. An Ideal Gas● Consider a box ofdimensions x, y & z asshown● A single ideal gasparticle mass m ismoving in the box withspeed u parallel to thex direction.xzy u
5. 5. An Ideal Gas● The molecule collideswith the blue wall asshown.● Its initial momentum ismu, and its finalmomentum in -mu● Its change inmomentum istherefore 2mu xzy u
6. 6. An Ideal Gas● The molecule travels adistance 2x betweencollisions with the bluewall.● The time betweencollisions is therefore:● 2x/uxzy u
7. 7. An Ideal Gas● The force exerted onthe blue wall is therate of change ofmomentum.●xzy uF=2mu2x/u=mu2x
8. 8. An Ideal Gas● The pressure on theblue wall is therefore:● Where V is the volumexzy uP=FA=mu2xyz=mu2V
9. 9. An Ideal Gas● In a real gas there are Nmolecules movingrandomly. On averageonly 1/3 of these move inthe x direction.● The molecules are not allmoving with speed u buthave an average (meansquare) speed <c2>xzy upV =13N m 〈c2〉
10. 10. Molecular Speed● For one mole of gas, the equation becomes:● This could be written as:● Where ½ m<c2> is the average kinetic energypV =13N A m 〈c2〉pV =23N A×12m〈c2〉
11. 11. Molecular Speed● From other macroscopic experiments it can beshown that:● These two equations for ideal gases mustequate.● Therefore:pV =nRTnRT =pV =23NA12m〈c2〉12m〈c2〉=32RN AT
12. 12. Molecular Speed● The ratio of the two constants (R over NA) isknown as the Boltzmann constant k● k=1.38 x 10-23JK-1● That is Kinetic Energy is proportional toabsolute temperature12m〈c2〉=32k T
13. 13. Summary of Ideal Gases● For a real gas, the ideal gas rules can be used to giveapproximate answers.● An increase in volume will cause a longer time betweencollisions, so the collisions will be less frequent, so thepressure will decrease.● An increase in temperature, will cause a higher KE, so thetime between collisions will increase and the force withwhich they strike the container will increase. The pressurewill therefore increase.● An increase in volume at constant pressure will cause theparticles to slow down, therefore causing a decrease intemperature.