Download - Announcements 9/9/11
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Announcements 9/9/11 Prayer Lab 1 due tomorrow Lab 2 starts tomorrow
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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)
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Reading quiz (graded): Who was the famous Austrian physicist
whose name was on two equations in today’s reading assignment?
a. Niels Bohrb. Ludwig Boltzmannc. Johann Carl Friedrich Gaussd. Hermann von Helmholtze. Erwin Schrödinger
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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?
a. Oxygenb. Nitrogenc. Same speed
Demo: heavy vs light molecules
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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
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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. O2c. Samed. Not enough information to tell
(*) let’s assume the temperature is “high”.Relative to what, we’ll discuss in a minute.
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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
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Translational KE and vrms
Worked problem: what is average speed (vrms) of oxygen molecules at 300K?
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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
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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)
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Demo Demo: kinetic theory machine
Thought question: Which “molecules” have the most kinetic energy?
a. The heavy onesb. The light onesc. Same
(Repeat) Which ones have the fastest average velocity?