Transcript Lecture 24 - Purdue University

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First midterm violet, second - pink
Lecture 23
Purdue University, Physics 220
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PHYSICS 220
Lecture 23
Kinetic Theory and Thermal Expansion
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Ideal Gas
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Kinetic Theory
Helps to explain gas laws by applying
Newton’s law’s to the microscopic
molecular motions.
p=2mv
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Kinetic Theory
The relationship between energy and temperature
(for monatomic ideal gas)
px  2mvx
L
L
t  2
vx
Favg
px mvx2


t
L
P
For N molecules, multiply by N
Using PV = NkBT
2
F Nmvx
P 
A
V
Note <KEtr> = ½m<v2> = 3/2m<vx2>
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2N
KEtr
3V
KEtr 
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k BT
2
5
Kinetic Theory
1
3
2
KE  m v  k BT
2
2
Per molecule
vrms 
v
2

3k BT
m
Internal energy
3
3
U  N KE  N k BT  nRT
2
2
Monoatomic ideal gas
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Example
• What is the rms speed of a nitrogen N2 molecule
in this classroom?
3
KE  k BT
2
1
3
2
m v  k BT
2
2
v = 510 m/s
= 1150 mph!
v
2
v2
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
3k BT
m
3(1.38  1023 J/K)(273  20)K

(28 u)  (1.66  10-27 kg/u)
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iClicker
Suppose you want the rms (root-mean-square) speed of
molecules in a sample of gas to double. By what factor should
you increase the temperature of the gas?
A) 2
B) 2
C) 4
3
KE  k BT
2
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Maxwell-Boltzmann Distribution
How many molecules have speeds in a
certain range?
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Diffusion
xrms  2Dt
D- Diffusion constant, depends on v, l (mean
free path) and l depends on density (lV/N)
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Thermal Expansion
• When temperature rises
– molecules have more kinetic energy
• they are moving faster, on the average
– consequently, things tend to expand
• Amount of expansion depends on…
Temp: T
– change in temperature
– original length
Temp: T+T
– coefficient of thermal expansion
L0 + L = L0 +  L0 T
L =  L0 T (linear expansion)
V =  V0 T (volume expansion)
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L0
L
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Expansion Coefficients
L
 T
L0
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Question
As you heat a block of aluminum from 0 C to 100 C its
density
A) Increases
B) Decreases
C) Stays the same
T = 100 C
T=0C
M, V0
r0 = M / V0
M, V100
r100 = M / V100
< r0
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Differential Expansion
A bimetallic strip is made with aluminum =16x10-6 /K
on the left, and iron =12x10-6 /K on the right. At
room temperature, the lengths of metal are equal. If
you heat the strips up, what will it look like?
A
B
C
Aluminum gets longer, forces curve so its on outside
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Thermal Expansion
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Tight Fit
An aluminum plate has a circular hole cut in it. An aluminum
ball (solid sphere) has exactly the same diameter as the hole
when both are at room temperature, and hence can just
barely be pushed through it. If both the plate and the ball are
now heated up to a few hundred degrees Celsius, how will
the ball and the hole fit?
A) The ball won’t fit through the hole any more
B) The ball will fit more easily through the hole
C) Same as at room temperature
The ball gets larger, but so does the hole!
Since they have the same expansion rate,
everything will stay the same!
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Tight Fit
Why does the hole get bigger when the plate
expands?
Imagine a plate made from 9 smaller pieces.
Each piece expands.
If you remove one piece, it will leave an “expanded hole”
Object at temp T
Same object at higer T:
Plate and hole both get larger
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iClicker
A glass jar ( = 3x10-6 K-1) has a metal lid ( = 16x10-6 K-1)
which is stuck. If you heat them by placing them in hot water,
the lid will be
A) Easier to open
B) Harder to open
C) Same
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Amazing Water
Water is very unusual in that it has a maximum
density at 4 degrees C. That is why ice floats,
and we exist!
r (kg m-3)
1000.00
999.95
999.90
999.85
999.80
999.75
Density
999.70
999.65
999.60
999.55
T (C)
0
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Question
Not being a great athlete, and having lots of money to spend, Gill Bates
decides to keep the lake in his back yard at the exact temperature which will
maximize the buoyant force on him when he swims. Which of the following
would be the best choice?
1000.00
999.95
A) 0 C
999.90
999.85
B) 4 C
999.80
999.75
C) 32 C
999.70
999.65
D) 100 C
999.60
F
=
r
Vg
999.55
B
l
E) 212 C
0
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4
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Density
The answer is 4 C, because water has
its greatest density at 4 C. Since
bouyant force is equal to the weight
of the displaced fluid or
density*volume, when the density is
the largest, the bouyant force is
maximized.
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