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Announcements 9/7/12

Announcements 9/7/12. Prayer Lab 1 due tomorrow—turn it in the same place you’ve been turning in the homework Lab 2 starts tomorrow. Dilbert:. From warmup. Extra time on? Root Mean Square (several people) Going over Wednesday's cup problem would be really really good. Other comments?

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Announcements 9/7/12

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  1. Announcements 9/7/12 • Prayer • Lab 1 due tomorrow—turn it in the same place you’ve been turning in the homework • Lab 2 starts tomorrow Dilbert:

  2. From warmup Extra time on? Root Mean Square (several people) Going over Wednesday's cup problem would be really really good. Other comments? (By the way, if I don’t list your comment, please don’t take it personally.)

  3. Worked problems: • How much mass does the air in this room have? (MM  0.029 kg/mol) • According to the ideal gas law, what is the density of air at 1 atm, for 300 K? For 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), pressure is 1 atm. How hot does the pilot have to get the air inside the balloon for it to lift off? Some answers: 1.175 kg/m3; 378K (221F)

  4. Clicker question: • 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? • Oxygen • Nitrogen • Same speed Demo: heavy vs light molecules

  5. From warmup What is it that causes a gas to have a certain temperature? Temperature is a measure of the average kinetic energy of the individual molecules. Mass and velocity. Demo: heavy vs light molecules

  6. 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 … ½kBT

  7. Clicker question: • Compare a monatomic molecule such as Ne to a diatomic molecule such as O2. If they are at the same temperature(*), which has more kinetic energy? • Ne • O2 • Same • Not enough information to tell (*) let’s assume the temperature is “high”. Relative to what, we’ll discuss in a minute.

  8. Disclaimer Thermal energy (measured by kBT) 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

  9. Translational KE and vrms • Worked problem: what is average speed (vrms) of oxygen molecules at 300K?

  10. From warmup Compare vrms for various gases given in Table 21.1 to the speed of sound given in Table 17.1. Is there a connection? Why/why not? The higher vrms the faster the speed of sound. Because the molecules are moving faster so it is easier for sound waves to pass through the media.

  11. From warmup In the molecular model of ideal gases, what is it that causes a gas to exert pressure on its surroundings? Collisions against a wall. A lot of little things banging against something gives a seemingly invisible force.

  12. Molecular View of Pressure • Related problem: What is average pressure by baseballs (m = 145 g) on a wall (A = 9 m2). 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 • Pressure on right wall from one molecule? • Pressure on right wall from all molecules Answer: 2.45 Pa Answer: 2mvx/(L2 tbetween hits) = mvx2/L3 Answer: P = Nmvx2/V

  13. Molecular View of Pressure, cont. • Result for v instead of vx: P = N m ⅓ v2 / V • What does PV equal? • Compare to: PV = N kB T • What does v equal? What does T equal? • What is temperature? (revisited)

  14. Demo • Demo: kinetic theory machine • Clicker question: Which “molecules” have the most kinetic energy? • The heavy ones • The light ones • Same • (Repeat) Which ones have the fastest average velocity?

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