1. Kinetic Theory and Thermal Expansion
PHYSICS 220
Lecture 23
Kinetic Theory and Thermal Expansion
Lecture 23
Purdue University, Physics 220

2. Purdue University, Physics 220
Ideal Gas
Lecture 23
Purdue University, Physics 220

3. Purdue University, Physics 220
Kinetic Theory
Helps to explain gas laws by applying Newton’s law’s to the microscopic molecular motions.
The relationship between energy and temperature (for monatomic ideal gas)
Lecture 23
Purdue University, Physics 220

4. Purdue University, Physics 220
Kinetic Theory
The relationship between energy and temperature (for monatomic ideal gas) L
For N molecules, multiply by N
Using PV = NkBT
Note <KEtr> = ½m<v2> = 3/2m<vx2>
Lecture 23
Purdue University, Physics 220

5. Purdue University, Physics 220
Kinetic Theory
Per molecule
Internal energy
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Purdue University, Physics 220

6. Purdue University, Physics 220
Example
What is the rms speed of a nitrogen N2 molecule in this classroom?
v = 510 m/s
= 1150 mph!
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Purdue University, Physics 220

7. Purdue University, Physics 220
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)
C) 4
Lecture 23
Purdue University, Physics 220

8. Maxwell-Boltzmann Distribution
How many molecules have speeds in a certain range?
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Purdue University, Physics 220

9. Purdue University, Physics 220
Diffusion
D … Diffusion constant
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Purdue University, Physics 220

10. Purdue University, Physics 220
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…
change in temperature
original length
coefficient of thermal expansion
L0 + L = L0 +  L0 T
L =  L0 T (linear expansion)
V =  V0 T (volume expansion)
Temp: T
Temp: T+T L0 L
Lecture 23
Purdue University, Physics 220

11. Expansion Coefficients
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Purdue University, Physics 220

12. Purdue University, Physics 220
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
M, V100
r100 = M / V100
< r0
T = 0 C
M, V0
r0 = M / V0
Lecture 23
Purdue University, Physics 220

13. Differential Expansion
A bimetallic strip is made with aluminum a=16x10-6 /K on the left, and iron a=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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Purdue University, Physics 220

14. Purdue University, Physics 220
Thermal Expansion
Lecture 23
Purdue University, Physics 220

15. Purdue University, Physics 220
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!
Lecture 23
Purdue University, Physics 220

16. 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”
Same object at higer T:
Plate and hole both get larger
Object at temp T
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Purdue University, Physics 220

17. Purdue University, Physics 220
iClicker
A glass jar (a = 3x10-6 K-1) has a metal lid (a = 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
Example?
Lecture 23
Purdue University, Physics 220

18. Purdue University, Physics 220
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!
 (kg m-3)
T (C)
Lecture 23
Purdue University, Physics 220

19. Purdue University, Physics 220
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?
A) 0 C
B) 4 C
C) 32 C
D) 100 C
E) 212 C
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.
FB = rlVg
Lecture 23
Purdue University, Physics 220