Find experimentally that light gases escape more

1
Find experimentally that light gases escape more
quickly than heavy ones!
Experimental Evidence for Kinetic Theory Heat
Capacities
Two kinds Cp (add heat at constant pressure)
Cv (add heat at constant volume)
2
(1) Increases kinetic energy of molecules
KE (1/2) mc2, c2 T
(2) Perform work.
Increase T from T1 to T2
KE1(3/2)RT1 KE2(3/2)RT2
Cv (3/2) R
3
L
A
p F / A
Gas
?Movable Piston
work F ? L (Ap) ? L p x (AL)
work p x (AL) p(V2 - V1) nR(T2-T1) nR?T
?
w p?V nR?T
4
Cp heat added to increase KE heat added to do
work
For n 1 mole and T2-T1 ?T 1 degree
Cp ?(KE) w (3/2) R R
Remember that Cv (3/2) R
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Heat Capacity Summary for Ideal Gases
Cv (3/2) R, KE change only.
Note, Cv independent of T.
Cp/Cv 1.67
Find for monatomic ideal gases such as He, Xe,
Ar, Kr, Ne Cp/Cv 1.67
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For diatomics and polyatomics find Cp/Cv lt 1.67!
This would make Cp/Cv lt 1.67
A possible solution
KE (1/2)kT (or 1/2 RT on a mole basis) per
degree of freedom.
7
A degree of freedom is a coordinate needed to
describe position of a molecule in space.
A diatomic molecule is a line (2 points connected
by a chemical bond). It requires 5 coordinates
to describe its position x, y, z, ?, ?
Z
?
?
Y
X
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Bonus Bonus Bonus Bonus Bonus Bonus
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Collision Frequency and Mean Free Path
???
Focus on one molecule (say a red one) flying
through a background of other molecules (say
blue ones).
Make the simplifying assumption that only the
red one is moving. (Will fix later.)
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Gas Kinetic Collision Cylinder
L c?1s
Note A ? ?2
Miss?
Hit?
? Hit
?
?
?
A
?
?
? Hit
V/sec p ?2c A ? L / t
? Miss
The red molecule sweeps out a cylinder of volume
??2c in one second. It will collide with any
molecules whose centers lie within the cylinder.
Note that the (collision) cylinder radius is the
diameter ? of the molecule NOT its radius ?!
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Red Molecule R sweeps out a Cylinder of volume
p?2c per second (c speed).
Gas Kinetic Collision Cylinder
No Collision
Collision
2 ?
?2?
?
?2?
Collision
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z volume swept out per second ? molecules
per unit volume