Announcements 9/14/12
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
Prayer
“Real” thermodynamics (more unified, fewer disjointed
topics):
a. Today
– PV diagrams
– work
– isothermal contours
– internal energy
– First Law of Thermodynamics
b. Continues for the next 4 lectures after today. Then
one more lecture. Then exam!
Pearls
Before
Swine
From warmup
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Extra time on?
a. 9 different answers
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Other comments?
a. this chapter has a lot of information and quite
confusing. I still don't understand the majority of what
this chapter is about...could you simplify this chapter
into simple points?
b. Does our reading include all the example problems as
well as the text?
Work done by an expanding gas
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
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1 m3 of an ideal gas at 300 K
supports a weight in a piston such
that the pressure in the gas is
200,000 Pa (about 2 atm). The gas
is heated up. It expands to 3 m3.
Plot the change on a graph of
pressure vs. volume (a P-V diagram)
How much work did the gas do as it
expanded?
a. How do you know it did work?
W  F  distance
  P  Area   distance
 PV
= 400,000 J
More on Work…
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PV diagrams
What if pressure doesn’t
stay constant?

Won gas   PdV
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Work done on gas vs work
done by gas
Clicker question:
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Which of the following is NOT true of the work
done on a gas as it goes from one point on a
PV diagram to another?
a. It cannot be calculated without knowing n
and T.
b. It depends on the path taken.
c. It equals minus the integral under the curve.
d. It has units of Joules.
e. It is one of the terms in the First Law of
Thermodynamics.
Quick Writing
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
First: in which path
would the gas (pushing
against some sort of
container) do the most
work?
Describe with words how
you could actually make
a gas (in some sort of
container) change as in
path 2.
From warmup
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What is a "state variable"? In your own words, and
without referring to the text if possible, why do things
like temperature, internal energy, volume, and
pressure call into this category?
a. A state variable is something that helps specify the
state of the entire system. They describe
macroscopic quantities. State variables are often
part of an "equation of state" that describes the
dependence of the system's state on these
variables. The given quantities fall into this
category because individual molecules contribute to
temperature, pressure, etc., but T and P measure
the contributions from ALL molecules.
State postulate: state is fixed by two
independent state variables
Internal Energy, Eint (aka U)
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
Eint = Sum of all of the microscopic kinetic energies.
(Also frequently called “U”.)
Return to Equipartition Theorem:
a. “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.”
b. Each “degree of freedom” of a molecule has kinetic
energy of kBT/2
c. Monatomic molecules  3 d.o.f.
d. At room temperatures, diatomic  5 d.o.f.
(3 translational, 2 rotational)
Internal Energy

Monatomic: Eint = N  3 kBT/2
= (3/2)nRT
Eint  32 nRT
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Diatomic: (around room temperature)
Eint = N  5 kBT/2
= (5/2)nRT
Eint  52 nRT
Clicker question:

The process in which
Eint is the greatest
(magnitude) is:
a. path 1
b. path 2
c. neither; it’s the same
Isothermal Contours
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A gas changes its volume and pressure
simultaneously to keep the temperature
constant the whole time as it expands to twice
the initial volume. What does this look like on a
PV diagram?
PV  nRT  xy  constant

What if the temperature is higher? Lower?
“First Law”
Eint = Qadded + Won system
 What does that mean? You can add internal
energy, by…
a. …adding heat
b. …compressing the gas
 Possibly more intuitive version:
Qadded = Eint + Wby system

When you add heat, it can either
…increase internal energy (temperature)
…be used to do work (expand the gas)
Three Specific Cases
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Constant pressure, “isobaric”
a. Work on = ? –PV
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Constant volume, “isovolumetric”
a. Work on = ? 0
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Constant temperature, “isothermal”
a. Work on = ?  PdV   nRT dV  nRT


V
 nRT ln V2 V1

dV
V
From warmup
Are Q, W, and ΔEint +, -, or 0 for the following
situations?
(A) Rapidly pumping up a bicycle tire (the system in
question is the air in the pump)
(B) Lukewarm water in a pan on a hot stove (the
system in question is the water in the pan)
(C) Air quickly leaking out of a balloon (the system in
question is the air that was originally in the balloon)
answers:
Q W deltaE
(A) 0 + +
(only 3 students correct…for now…
(B) + 0 +
by exam ALL students should be
(C) 0 - correct!)
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Worked Problems
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For each problem, draw the process on a P-V diagram,
state what happens to the temperature (by visualizing
contours), and calculate how much heat is added/removed
from gas via the First Law.
a. A monatomic gas (1.3 moles, 300K) expands from 0.1
m3 to 0.2 m3 in a constant pressure process.
T increases, Q = Eint + PV = 8102 J added
b. A diatomic gas (0.5 moles, 300K) has its pressure
increased from 100,000 Pa to 200,000 Pa in a constant
volume process.
T increases, Q = Eint = 3116 J added
c. A diatomic gas (0.7 moles, 300K) gets compressed from
0.4 m3 to 0.2 m3 in a constant temperature process.
T stays constant, Q = –Won gas = –1210 J (i.e., 1210 J of heat removed from gas)
Quick Answers From Students
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Eint will be positive if ______________
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Qadded will be positive if ______________
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Won system will be positive if ______________
From warmup
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
Match the letters A-D to the
appropriate path.
a. isovolumetric (constant volume)
b. adiabatic
c. isothermic (constant
temperature)
isobaric (constant pressure)
Which processes are most common in typical situations (motors,
heaters, calorimeters, refrigerators, leaf blowers, etc.)?
Student
answers:
My
answer:
In many applications (motors) adiabatic and
adiabatic (2x) processes are common (see Otto process in Chap.
isovolumetric
isovol.
& isothermal
22).
In many
science experiments, isothermal processes are
isotherm. &Isobaric
isobaricprocesses are important when the system is
common.
isovolto& the
isobar
open
atmosphere, such as boiling water on the stove. I guess
isovolare all important! :-)
they