Announcements 1/14/11

Prayer Monday = MLK holiday Classwide HW average: 59.8% Email 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. Bryan Abbottb. Colin Fluckiger

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?

Some answers: 1.175 kg/m3; 378K (221F)

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: 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 gasa. Pressure on right wall from one

molecule?

b. 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 T equal?

What is temperature? (revisited)

Demo

Demo: kinetic theory machine

Thought question: Which “molecules” have the most kinetic energy?

a. The heavy onesb. The light onesc. Same

Which ones have the fastest average velocity?