Announcements 9/17/12
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Prayer
SPS Opening Social: Thursday 5-7 pm
Answer this question while you’re waiting for class to start:
Ralph is confused because he knows that when you
compress gases, they tend to heat up (think of a bicycle
pump nozzle getting hotter as you force the gas from the
pump to the tire). So, how are “isothermal” processes
even possible? How can you compress a gas without its
temperature increasing?
Calvin &
Hobbes
From warmup
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Extra time on?
a. molar specific heat (e.g. why different depending on what
you hold constant)
b. total differential
c. The book says that "This expression predicts a value of
Cv=3/2R=12.5 for all Monatomic gases", but the actual
experimental Cv values are also listed on the opposing page.
When working problems, should we use the predicted
universal value or the experimental actual value for Cv of a
Monatomic gas?
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Other comments?
a. Out of curiosity, how is our TA 's name spelled? Does it
have an accent like “Clément”? Cause his name is actually
kind-of cool.
Clicker questions:
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A gas has its pressure reduced while its volume is kept
constant. What does this look like on a PV diagram?
a. a horizontal line going to the right
b. a horizontal line going to the left
c. a vertical line going up
d. a vertical line going down
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Same situation. How did the temperature of the gas
change during that process?
a. the temperature increased
b. the temperature decreased
c. the temperature stayed the same
d. the temperature change cannot be determined from
the information given
Demo
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Constant volume change, aka “alcohol rocket”
From warmup
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For each process discuss whether Q, Won, and ΔEint
are positive, negative, or zero.
a. Process 1-volume constant
– W=0, Q=+, E=+
b. Process 2
– W=-, Q=+, E=+
Clicker question:
How will the temperature
of the gas change during
this process from A to B?
a. Increase
b. Decrease
c. First increase, then
decrease
d. First decrease, then
increase
e. Stay the same
A
2.0
1.8
1.6
Pressure (atm)
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1.4
1.2
1.0
B
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
3
Volume (m )
1.4
1.6
1.8
2.0
Worked Problem (by class)
A diatomic ideal gas
undergoes the change
from A to B. How
much heat was added
to or taken away from
the gas?
(First: was heat added
or taken away?)
A
2.0
1.8
1.6
Pressure (atm)
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1.4
1.2
1.0
B
0.8
0.6
0.4
0.2
0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
3
Volume (m )
Answer: 151500 J
1.4
1.6
1.8
2.0
Clicker question:
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What is “CV”?
a. heat capacity
b. molar heat capacity
c. molar heat capacity, but only for constant
volume changes
d. specific heat
Q = n CV DT (const. volume)
Q = n CP DT (const. pressure)
Clicker question:
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Which will be larger, the molar heat capacity for
constant volume changes or the molar heat
capacity for constant pressure changes? (Hint:
Think of the First Law--does it take more heat to
increase temperature by 1C if volume is
constant or if pressure is constant?)
a. constant volume
b. constant pressure
c. they are the same
CV and CP
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Constant volume change (monatomic):
W=0
DEint = Qadded
(3/2)nRDT = Qadded
Compare to definition of C: Qadded = nCVDT
CV = (3/2)R (monatomic)
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Constant pressure change
a. What’s different?
b. result: CP = (5/2)R (monatomic)
What would be different for gases with more
degrees of freedom?
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From warmup
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Explain why some modes (vibrational or rotational) do not
contribute to the specific heat except at higher temperatures.
a. The vibrational and rotational degrees of freedom of a
molecule are not initiated until the molecule is subjected to
higher levels of temperature so it doesn 't effective the
specific heat of a molecule until it has is at higher
temperatures.
b. Not quite: “vibrational and rotational kinetic energies can only
contribute to the specific heat when there is a significant
amount of energy stored in them.”
Isothermal vs Adiabatic
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Isothermal: PV  constant
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Adiabatic: PV  constant
What does gamma equal?
 steeper curves for adiabatic
Clicker question:
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How much would the temperature of the air
in this room would change if I compressed it
adiabatically by a factor of 2? (V2 = 1/2 V1)
a. less than 0.2 degree C
b. about 0.2 degrees C
c. about 2 degree C
d. about 20 degrees C
e. more than 20 degrees C
Demo/Video
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Demo: freeze spray
Video: adiabatic expansion
Demo: adiabatic cotton burner
From warmup
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What does it mean to “take the total differential”?
a. You take the derivative of every single variable in
an equation
b. Mostly correct: You take the derivative of both
sides, using the product rule on the first side.
Derivation of PV (for Monatomic)
DEint = Qadded + Won
(3/2) nRDT = - PdV
(3/2) nRdT = -PdV
(3/2) nR d(PV/nR) = -PdV
(3/2) (PdV + VdP) = -PdV
What’s different
if diatomic?
(3/2) VdP = -(5/2) PdV
dP/P = -(5/3) dV/V
lnP = (-5/3)lnV + constant
lnP = ln(V-5/3) + constant
P = constant  V-5/3
(it’s a different constant)
P V5/3 = constant
Clicker question (like exam):
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Which of the curves on the PV diagram below is
most likely to represent an isothermal compression,
followed by an adiabatic expansion back to the
initial volume?
a.
b.
c.
d.
e.