Announcements 1/14/11 Prayer Monday = MLK holiday Classwide HW average: 59.8% from the TA: Mathematica tips, extra credit papers Two students haven’t registered clickers, are not getting credit yet. Check your scores! If you are one of these students, please talk to me ASAP (there’s a registration issue). a. a.Bryan Abbott b. b.Colin Fluckiger

Worked problems: How much mass does the air in this room have? (MM  kg/mol) According to the ideal gas law, what is the density of air at 300K? At arbitrary T? A hot air balloon is 520 kg (including passengers). It’s spherical, with radius = 8 m. The temperature is 300K outside (80.3  F). How hot does the pilot have to get the air inside the balloon for it to lift off? Some answers: kg/m 3 ; 378K (221  F)

Thought quiz (ungraded): In air, the molecular mass of oxygen molecules is 32 g/mol; the molecular mass of nitrogen molecules is 28 g/mol. Which molecules are traveling faster on average? a. a.Oxygen b. b.Nitrogen c. c.Same speed Demo: heavy vs light molecules

Equipartition Theorem “The total kinetic energy of a system is shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium.” “independent”: e.g. x, y, z (for translational KE) “parts”: translational, rotational, vibrational Specifically, each “degree of freedom”, of each molecule, has “thermal energy” of … ½k B T

Thought quiz Compare a monatomic molecule such as Ne to a diatomic molecule such as O 2. If they are at the same temperature(*), which has more kinetic energy? a. a.Ne b. b.O 2 c. c.Same d. d.Not enough information to tell (*) let’s assume the temperature is “high”. Relative to what, we’ll discuss in a minute.

Disclaimer Thermal energy (measured by k B T) must be comparable to the quantum energy levels, or some degrees of freedom get “frozen out” From section 21.4: diatomic hydrogen Y-axis: heat added, divided by temperature change (per mole) Units: J/mol  K

Translational KE and v rms Worked problem: what is average speed (v rms ) of oxygen molecules at 300K?

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

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 T equal? What is temperature? (revisited)

Demo Demo: kinetic theory machine Thought question: Which “molecules” have the most kinetic energy? a. a.The heavy ones b. b.The light ones c. c.Same Which ones have the fastest average velocity?