1. Announcements 9/10/12 Prayer On Wednesday I will go back and regrade all of the old clicker quizzes. As long as your clicker is registered by then, all of your quizzes will count. Check to make sure you have quiz scores on your grade printout! Unregistered clickers from Friday: 971463E, 3368A2F9, C80BC30 Review: equipartition theorem & v rms Calvin & Hobbes

2. Molecular View of Pressure Related problem: What is average pressure by baseballs (m = 145 g) on a wall (A = 9 m 2 ). Speed = 85 mph (38 m/s). Elastic collisions, each lasting for 0.05 seconds. (This is the time the ball is in contact with the wall.) A baseball hits the wall every 0.5 seconds. Actual problem: a cube filled with gas a. a.Pressure on right wall from one molecule? b. b.Pressure on right wall from all molecules Answer: 2.45 Pa Answer: 2mv x /(L 2 t between hits ) = mv x 2 /L 3 Answer: P = Nmv x 2 /V where we stopped

3. Molecular View of Pressure, cont. Result for v instead of v x : P = N m ⅓ v 2 / V What does PV equal? Compare to: PV = N k B T What does v equal? What does T equal? What is temperature? (revisited)

4. Demo Demo: kinetic theory machine “Heavy” vs. “light” molecules  which ones move faster? Clicker question: Which “molecules” have the most kinetic energy? a. a.The heavy ones b. b.The light ones c. c.Same

5. From warmup Extra time on? a. a.difference between v avg and v rms (many people) – – See HW problem 5.3 b. b.supercooling demo (3 people) – – “a demonstration of supercooled water would be "supercool” (ha ha)” Other comments? a. a.Section 21.6. doesn't seem to exist in the Eighth Edition (several people)

6. From warmup The last homework assignment (due friday) took me 5 hours because I could not figure out how to do 4-5. I eventually found an equation that worked...but it was kind of pure luck.

7. Characterizing velocities Recall bouncing balls in jar. Focus on one type of molecule. Lots of questions, such as : a. a.What’s the average velocity? b. b.What’s the most popular velocity? c. c.What’s the velocity that corresponds to the average kinetic energy? d. d.How many molecules have velocities within a given range? How to answer: use statistical distributions, aka histograms

8. Height Histogram: Class of 49 students Round heights to closest integer, plot histogram What is the combined area of all bars? If I pick a student at random, what are chances he/she will be 68 inches tall? What is the area of the bar at 68 inches divided by the total area? How many students will be exactly 68.000000 inches tall? If I pick a student at random, what are chances he/she will be 61.5-64.5 inches tall? What is average height of all students? (At least, how would you figure that out?)

9. “Normalized” Histogram: Total students = 49 y-axis now divided by total # of students. What is combined area of all bars? If I pick a student at random, what are chances he/she will be 61.5-64.5 inches tall? (At least, how would you figure that out?) How many students have heights between 61.5 and 64.5 inches? What is average height of all students?

10. Probability Distribution Function Imagine total # = 10 billion. Tiny “bins”. Connect peaks of curve with line… becomes a function If I pick a person at random, what are chances he/she will be 63.6-67.2 inches tall? How many people have heights between 63.6 and 67.2 inches? What is average height of all people? (If a non-symmetric curve, this is not just the peak of the curve.)

11. Velocity Distribution: “Maxwell-Boltzmann” with some constants out in front to normalize it Where does this eqn come from? Wait a few weeks. Warmup: What is difference between v ave, v rms, and v mp ? Why is v mp the smallest of the three velocities? v-rms, the root-mean-square, based on the overall translational kinetic energy of the gas, while v-avg is the statistical average of the speed of all the particles, and v-mp is the "most probable" or the statistical mode of the speeds (the highest point on the distribution graph). v-mp is the smallest because the graph is skewed to the left

12. From warmup Answer: V_ave is just the regular average: add up the speeds and divide by number of particles. V_rms is "root mean square": add up the *squares* of the velocities, divide by the number of particles, then take the square root. It corresponds to the speed of the average kinetic energy. V_mp is the "most probable" velocity: the peak of the speed histogram. V_mp is the smallest because the distribution of speeds is skewed to the right--the peak in Fig. 21.11 (7th edition) is decidedly to the left of center.

13. Velocity Distribution: “Maxwell-Boltzmann” At 600K, how many molecules with speeds between 400 and 600 m/s? What is “v most probable ”? What is “v average ”? What is “v rms ”? How many molecules are at exactly the “most probable” velocity? with some constants out in front to normalize it Questions

14. Heat = not a fluid! Sir Benjamin Thompson, Count Rumford, 1753-1814 a. a.Boiling water with a cannon Image credit: Wikipedia

15. James Joule, 1818-1889 Image credit: Wikipedia

16. From warmup In terms that a lay person could easily understand, explain what heat capacity is. Explain the difference between "heat capacity" and "specific heat". Why do we need both? a. a.Heat capacity is the amount of energy that you need to increase a sample of whatever size by one degree Celsius while specific heat is the amount of energy needed to raise one kilogram of some substance by one degree Celsius.

17. Specific Heat Q=mc  T

18. Clicker question: If you add 500 J of heat to a mass of water, and 500 J of heat to the same mass of copper, which one increases the most in temperature? a. a.Water b. b.Copper c. c.Same

19. Clicker question: Thermal energy that is used to melt or freeze something is called: a. a.latent heat b. b.mass heat c. c.melty heat d. d.molar heat e. e.specific heat

20. From warmup: In regions B and D, energy is being added but the temperature is constant. How can energy be added to a system and the temperature not change? Where is the energy going? a. a.As I understand it, the energy is being spent in breaking apart particles that love each other too much to part their separate ways. Only after they have been broken down light enough to fly will they turn into steam.

21. Phase Changes T Heat energy added (Q) 100 o C Water boils 0 o C Ice melts Ice warming Ice melting Water warming Water boiling Steam warming

22. Latent Heats

23. Demo Boiling water with a vacuum

24. Clicker question: If you want to melt a cube of ice that’s initially at -40  C, you must first raise its temperature to 0  C, and then you must melt it. Which part takes the most energy? a. a.Raising the temperature b. b.Melting c. c.Same

25. Calorimetry Worked problem (class designed): ____ grams of hot iron at _____  C is added to ____ g of water at _____  C in a styrofoam insulated container. What is the final temperature of the mixture? (Neglect the container.) c iron = 448 J/kg  C c water = 4186 J/kg  C L water-steam = 2.26  10 6 J/kg