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Announcements 9/9/11. Prayer Lab 1 due tomorrow Lab 2 starts tomorrow. 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?

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announcements 9 9 11
Announcements 9/9/11
  • Prayer
  • Lab 1 due tomorrow
  • Lab 2 starts tomorrow
worked problems
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)

reading quiz graded
Reading quiz (graded):
  • Who was the famous Austrian physicist whose name was on two equations in today’s reading assignment?
    • Niels Bohr
    • Ludwig Boltzmann
    • Johann Carl Friedrich Gauss
    • Hermann von Helmholtz
    • Erwin Schrödinger
thought question ungraded
Thought question (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?
    • Oxygen
    • Nitrogen
    • Same speed

Demo: heavy vs light molecules

equipartition theorem
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

thought quiz
Thought quiz
  • 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.

disclaimer
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

translational ke and v rms
Translational KE and vrms
  • Worked problem: what is average speed (vrms) of oxygen molecules at 300K?
molecular view of pressure
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

molecular view of pressure cont
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)
slide11
Demo
  • Demo: kinetic theory machine
  • Thought 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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