1. Lecture 23Purdue University, Physics 2201 First midterm violet, second - pink

2. Lecture 23Purdue University, Physics 2202 Lecture 23 Kinetic Theory and Thermal Expansion PHYSICS 220

3. Lecture 23Purdue University, Physics 2203 Ideal Gas

4. Kinetic Theory Lecture 23Purdue University, Physics 2204 Helps to explain gas laws by applying Newton’s law’s to the microscopic molecular motions.  p=2mv

5. Lecture 23Purdue University, Physics 2205 Kinetic Theory The relationship between energy and temperature (for monatomic ideal gas) L For N molecules, multiply by N Note = ½m = 3/2m Using PV = Nk B T

6. Lecture 23Purdue University, Physics 2206 Kinetic Theory Per molecule Internal energy Monoatomic ideal gas

7. Lecture 23Purdue University, Physics 2207 Example What is the rms speed of a nitrogen N 2 molecule in this classroom? v = 510 m/s = 1150 mph!

8. Lecture 23Purdue University, Physics 2208 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

9. Lecture 23Purdue University, Physics 2209 Maxwell-Boltzmann Distribution How many molecules have speeds in a certain range?

10. Lecture 23Purdue University, Physics 22010 Diffusion D- Diffusion constant, depends on v, l (mean free path) and l depends on density (l  V/N)

11. Lecture 23Purdue University, Physics 22011 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 L 0 +  L = L 0 +  L 0  T  L =  L 0  T (linear expansion)  V =  V 0  T (volume expansion) Thermal Expansion Temp: T Temp: T+  T L0L0 LL

12. Lecture 23Purdue University, Physics 22012 Expansion Coefficients

13. Lecture 23Purdue University, Physics 22013 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 = 0 C M, V 0  0 = M / V 0 T = 100 C M, V 100  100 = M / V 100 <  0

14. Lecture 23Purdue University, Physics 22014 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 BC Aluminum gets longer, forces curve so its on outside

15. Lecture 23Purdue University, Physics 22015 Thermal Expansion

16. Lecture 23Purdue University, Physics 22016 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!

17. Lecture 23Purdue University, Physics 22017 Why does the hole get bigger when the plate expands? Object at temp T Same object at higer T: Plate and hole both get larger Imagine a plate made from 9 smaller pieces. Each piece expands. If you remove one piece, it will leave an “expanded hole” Tight Fit

18. Lecture 23Purdue University, Physics 22018 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

19. Lecture 23Purdue University, Physics 22019 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)

20. Lecture 23Purdue University, Physics 22020 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. F B =  l Vg