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We have a slight lead

over Hamilton’s classes

(52%-44%) but we are

nowhere near 70%!

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Average force of gas on the wall

= (# of molecules hitting the wall in the time t)

x (force each molecule exerts on the wall)

Fwall molecule = mvx

t= Fmolecule wall

Only the x-component matters.

All we need to figure this out is our three

basic equations, and a way to count

the number of molecules hitting the wall.

vx =x

t

A

vx t

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N = n Volume( ) = nA vx t( )

px = 2m vx

n = number density

= # / unit volume

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v = vx2

+ vy2

+ vz2

= 3 vx2

vx = v / 3

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F = Np

t=

12 (nAvx t)

2mvx

t= nmvx

2A

Interpret

F = pA n =N

Vvx

2= 1

3 v 2

pA = 13

N

Vmv 2A

pV = N( 13 mv 2) = N 2

312 mv 2( )

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pV = nmolesRT

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N = nmolesNA

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pV = N 23 ( 1

2 mv2 ) pV = nRT

Make the N parts look alike.

n = N / NA

pV = NR

NA

T

Define: kB =R

NA

so pV = NkBT

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p = Nmvx2 kBT = 2

312 mv 2( )

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pV = nmolesRT

pV = NkBT

Chemist’s form

Physicist’s form

nmoles =N

NA

R = kBNA

p = nmvx2 3

2 kBT =12 mv 2

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