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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?
- A hot air balloon is 520 kg (including passengers). It’s spherical, with radius = 8 m. The temperature is 300K outside (80.3F), 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 (221F)

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):

- 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

- “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

- 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

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/molK

Translational KE and vrms

- Worked problem: what is average speed (vrms) 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 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.

- 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)

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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