Announcements 9/9/11
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Prayer
Lab 1 due tomorrow
Lab 2 starts tomorrow
Worked problems:
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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):
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Who was the famous Austrian physicist
whose name was on two equations in
today’s reading assignment?
a.
b.
c.
d.
e.
Niels Bohr
Ludwig Boltzmann
Johann Carl Friedrich Gauss
Hermann von Helmholtz
Erwin Schrödinger
Thought question (ungraded):
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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. Oxygen
b. Nitrogen
c. Same speed
Demo: heavy vs light molecules
Equipartition Theorem
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“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
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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. Ne
b. O2
c. Same
d. 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/molK
Translational KE and vrms
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Worked problem: what is average
speed (vrms) of oxygen molecules at
300K?
Molecular View of Pressure
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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. Answer: 2.45 Pa
Actual problem: a cube filled with gas
a. Pressure on right wall from one molecule?
Answer: 2mvx/(L2 tbetween hits) = mvx2/L3
b. Pressure on right wall from all molecules
Answer: P = Nmvx2/V
Molecular View of Pressure, cont.
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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?
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What is temperature? (revisited)
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Demo
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Demo: kinetic theory machine
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Thought question: Which “molecules” have the
most kinetic energy?
a. The heavy ones
b. The light ones
c. Same
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(Repeat) Which ones have the fastest average
velocity?