Announcements 9/19/11
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Prayer
HW: Your responsibility is NOT just to get the right answer,
it’s to persuade Chris you know what you’re doing
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?
Frank &
Ernest
Thought 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”
Thought 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
Reading quiz
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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
e. your “curriculum vitae”, a detailed resumé
Q = n CV DT (const. volume)
Q = n CP DT (const. pressure)
Thought 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 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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Reading quiz (graded)
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What does gamma equal in the equation for an
adiabatic process: PV   constant
a. CP + CV
b. CP - CV
c. CV - CP
d. CV / CP
e. CP / CV
Isothermal vs Adiabatic
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Isothermal: PV  constant
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Adiabatic: PV  constant
 steeper curves for adiabatic
Thought 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
Video: adiabatic cotton burner
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
Thought question
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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.