lecture14.ppt

7/27/2019 lecture14.ppt

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14.2 The Ideal Gas Law

An ideal gasis an idealized model for real gases that have

sufficiently low densities.


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The Ideal Gas Law



The condition of low density means that the molecules of the

gas are so far apart that they do not interact (except during

collisions that are effectively elastic).


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The Ideal Gas Law



The condition of low density means that the molecules of the

gas are so far apart that they do not interact (except during

collisions that are effectively elastic).

The ideal gas law expresses the relationship between the

absolutepressure (P), the Kelvintemperature (T), the volume

(V), and the number of moles (n) of the gas.

WhereRis the universal gas constant. R = 8.31 J/(mol K).

nRTPV


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The Ideal Gas Law

The constant termR/NAis referred to as Boltzmann's

constant,in honor of the Austrian physicist Ludwig

Boltzmann (18441906), and is represented by the symbol k:

PV = NkT


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14.3 Kinetic Theory of Gases


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Kinetic Theory

of Gases

Thepressurethat a gas exerts is

caused by the impact of its molecules

on the walls of the container.


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Kinetic Theory

of GasesThepressurethat a gas exerts is

caused by the impact of its molecules

on the walls of the container.

It can be shown that the average translational kinetic

energyof a molecule of an ideal gas is given by,

where kis Boltzmann's constant and Tis the Kelvintemperature.


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Derivation of,

Consider a gas molecule colliding elastically with the right

wall of the container and rebounding from it.


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The force on the molecule is obtained using Newtons second

law as follows,

,

t

PF


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The force on one of the molecule,

According to Newton's law of actionreaction, the force on

the wall is equal in magnitude to this value, but oppositely

directed.

The force exerted on the wall by one molecule,

L

mv2


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If N is the total number of molecules, since these particles

move randomly in three dimensions, one-third of them on the

average strike the right wall. Therefore, the total force is:

Vrms = root-mean-square velocity.


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Pressureis forceper unitarea, so the pressurePacting on a wall

of areaL2is


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Pressureis forceper unitarea, so the pressurePacting on a wall

of areaL2is

Since the volume of the box is V = L3, the equation above can

be written as,


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PV = NkT


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The Internal Energy of a

Monatomic Ideal Gas

lecture14.ppt

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