Announcements 9/10/10 Be sure to register your clicker on the

class website! (About 5 of you are not registered yet.)

a. After everyone is registered, I’ll tell the computer to go back and re-grade all of the earlier quizzes to give you credit.

Results of the TA office hour survey, effective next week:

a. Mon 3-4 pmb. Wed 5-6 pmc. Fri 5-6 pm

My own office hours are still right after class, 2-3 pm.

Video

Video: Barrel Crush

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 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 (80.3F). How hot does the pilot have to get the air inside the balloon for it to lift off?

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. Oxygenb. Nitrogenc. 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?

a. Neb. O2

c. Samed. Not enough information to tell

(*) let’s assume the temperature is “high”.Relative to what, we’ll discuss in a minute.

DisclaimerThermal 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: 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 gasa. Pressure on right wall from one moleculeb. Pressure on right wall from all molecules

Molecular View of Pressure, cont.

Result: P = N m ⅓ v2 / V What does PV equal? Compare to: PV = N kB T What does T equal? Quick writing: What does this tell

you about what temperature really is?

Demo

Demo: kinetic theory machine