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Physics 161
Fall 2006
Announcements
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HW#2 is due next Friday, 10/20. I will give extensions only up to Sunday,
10/22!!
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The first ‘further activity’ is due Monday, 10/16
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The first quiz is scheduled for Monday, 10/23. This will cover chapters 1-4.
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The Physics Department help room has been set up. The schedule can be
found at http://hendrix2.uoregon.edu/~dlivelyb/TA_assign/index.html
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Physics 161
Lecture 6
Fall 2006
Conservation of Energy; Heat Engines
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Physics 161
Fall 2006
Energy is Conserved
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Conservation of Energy is different from Energy
Conservation, the latter being about using energy wisely
Conservation of Energy means energy is neither created nor
destroyed. The amount of (mass-)energy in the Universe is
constant!!
Don’t we create energy at a power plant?
 Oh that this were true—no, we simply transform energy at
our power plants
Doesn’t the sun create energy?
 Nope—it exchanges mass for energy
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Physics 161
Fall 2006
Energy Exchange
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Though the total energy of a system is constant, the form of
the energy can change
A simple example is that of a simple pendulum, in which a
continual exchange goes on between kinetic and potential
energy
pivot
K.E. = 0; P. E. = mgh
h
K.E. = 0; P. E. = mgh
height reference
P.E. = 0; K.E. = mgh
Perpetual motion? An even more checkered history than cold fusion. Just
search for perpetual motion and see what you get.
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Physics 161
Fall 2006
Perpetual Motion
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Why won’t the pendulum swing forever?
It’s hard to design a system free of energy paths
The pendulum slows down by several mechanisms
 Friction at the contact point: requires force to oppose;
force acts through distance  work is done
 Air resistance: must push through air with a force
(through a distance)  work is done
 Gets some air swirling: puts kinetic energy into air (not
really fair to separate these last two)
Perpetual motion means no loss of energy
 solar system orbits come very close (is the moon’s orbit
constant over a geological time period?)
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Physics 161
Fall 2006
Some Energy Chains:
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A coffee mug with some gravitational potential energy is
dropped
potential energy turns into kinetic energy
kinetic energy of the mug goes into:
 ripping the mug apart (chemical: breaking bonds)
 sending the pieces flying (kinetic)
 into sound
 into heating the floor and pieces through friction as the
pieces slide to a stop
In the end, the room is slightly warmer
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Physics 161
Fall 2006
Gasoline Example
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Put gas in your car, containing 9 Cal/g
Combust gas, turning 9 Cal/g into kinetic energy of
explosion
Transfer kinetic energy of gas to piston to crankshaft to
drive shaft to wheel to car as a whole
That which doesn’t go into kinetic energy of the car goes
into heating the engine block (and radiator water and
surrounding air), and friction of transmission system (heat)
Much of energy goes into stirring the air (ends up as heat)
Apply the brakes and convert kinetic energy into heat (unless
you’re driving a hybrid)
It all ends up as waste heat, ultimately
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Physics 161
Fall 2006
Bouncing Ball
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Superball has gravitational potential energy
Drop the ball and this becomes kinetic energy
Ball hits ground and compresses (force times distance),
storing energy in the spring
Ball releases this mechanically stored energy and it goes
back into kinetic form (bounces up)
Inefficiencies in “spring” end up heating the ball and
the floor, and stirring the air a bit
In the end, all is heat
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Physics 161
Fall 2006
Why don’t we get hotter and hotter
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If all these processes end up as heat, why aren’t we
continually getting hotter?
If earth retained all its heat, we would get hotter
All of earth’s heat is radiated away
F = T4
If we dump more power, the temperature goes up, the
radiated power increases dramatically
 comes to equilibrium: power dumped = power radiated
 stable against perturbation: T tracks power budget
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Physics 161
Fall 2006
Rough numbers
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How much power does the earth radiate?
F = T4 for T = 288ºK = 15ºC is 390 W/m2
Summed over entire surface area (4R2, where R = 6,378,000
meters) is 2.01017 W
Global production is 31012 W
Solar radiation incident on earth is 1.81017 W
 just solar luminosity of 3.91026 W divided by
geometrical fraction that points at earth
Amazing coincidence of numbers! (or is it…)
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Physics 161
Fall 2006
No Energy for Free
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No matter what, you can’t create energy out of nothing: it
has to come from somewhere
We can transform energy from one form to another; we can
store energy, we can utilize energy being conveyed from
natural sources
The net (mass-)energy of the entire Universe is constant
The best we can do is scrape up some useful crumbs
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Physics 161
Fall 2006
Heat Engines, Heat Pumps, and
Refrigerators
Getting something useful from heat
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Physics 161
Fall 2006
Heat can be useful
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Normally heat is the end-product of the
flow/transformation of energy
 coffee mug, automobile, bouncing ball
 heat regarded as waste: a useless end result
Sometimes heat is what we want, though
 hot water, cooking, space heating
Heat can also be coerced into performing “useful” (e.g.,
mechanical) work
 this is called a “heat engine”
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Physics 161
Fall 2006
Heat Engine Concept
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Any time a temperature difference exists between two bodies,
there is a potential for heat flow
Examples:
 heat flows out of a hot pot of soup
 heat flows into a cold drink
 heat flows from the hot sand into your feet
Rate of heat flow depends on nature of contact and thermal
conductivity of materials
If we’re clever, we can channel some of this flow of energy
into mechanical work
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Physics 161
Fall 2006
Heat  Work
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We can see examples of heat energy producing other types
of energy
 Air over a hot car roof is lofted, gaining kinetic energy
 That same air also gains gravitational potential energy
 All of our wind is driven by temperature differences
 We already know about radiative heat energy transfer
 Our electricity generation thrives on temperature
differences: no steam would circulate if everything was at
the same temperature
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Physics 161
Fall 2006
Power Plant Arrangement
Heat flows from Th to Tc, turning turbine along the way
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Physics 161
Fall 2006
The Laws of Thermodynamics
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Energy is conserved
Total system entropy can never decrease
As the temperature goes to zero, the entropy approaches a
constant value—this value is zero for a perfect crystal
lattice
The concept of the “total system” is very important:
entropy can decrease locally, but it must increase elsewhere
by at least as much
 no energy flows into or out of the “total system”: if it
does, there’s more to the system than you thought
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Physics 161
Fall 2006
What’s this Entropy business?
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Entropy is a measure of disorder (and actually quantifiable
on an atom-by-atom basis)
 Ice has low entropy, liquid water has more, steam has a
lot
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Physics 161
Fall 2006
Heat Energy and Entropy
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We’ve already seen many examples of quantifying heat
 1 Calorie is the heat energy associated with raising 1 kg (1
liter) of water 1 ºC
 In general, Q = cpmT, where cp is the heat capacity
We need to also point out that a change in heat energy
accompanies a change in entropy:
Q = TS
Adding heat increases entropy
 more energy goes into random motionsmore
randomness (entropy)
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Physics 161
Fall 2006
How much work can be extracted from
heat?
Hot source of energy
Th
Qh heat energy delivered from source
externally delivered work:
W = Qh – Qc
heat energy delivered to sink
Qc
conservation of energy
efficiency =
Cold sink of energy
Tc
W
work done
=
Qh heat supplied
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Physics 161
Fall 2006
Heat Engine Nomenclature
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The symbols we use to describe the heat engine are:
 Th is the temperature of the hot object
 Tc is the temperature of the cold object
 T = Th–Tc is the temperature difference
 Qh is the amount of heat that flows out of the hot body
 Qc is the amount of heat flowing into the cold body
 W is the amount of “useful” mechanical work
 Sh is the change in entropy of the hot body
 Sc is the change in entropy of the cold body
 Stot is the total change in entropy (entire system)
 E is the entire amount of energy involved in the flow
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Physics 161
Fall 2006
Let’s crank up the efficiency
Let’s extract a lot of
work, and deliver very
little heat to the sink
Th
Qh
W = Qh – Qc
In fact, let’s demand 100%
efficiency by sending no heat
to the sink: all converted
to useful work
Qc
efficiency =
Tc
W
work done
=
Qh heat supplied
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Physics 161
Fall 2006
Not so fast…
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The second law of thermodynamics imposes a constraint on
this reckless attitude: total entropy must never decrease
The entropy of the source goes down (heat extracted), and the
entropy of the sink goes up (heat added): remember that Q =
TS
 The gain in entropy in the sink must at least balance the loss
of entropy in the source
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Stot = Sh + Sc = –Qh/Th + Qc/Tc ≥ 0
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Qc ≥ (Tc/Th)Qh sets a minimum on Qc
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Physics 161
Fall 2006
What does this entropy limit mean?
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W = Qh – Qc, so W can only be as big as the minimum
Qc will allow
 Wmax = Qh – Qc,min = Qh – Qh(Tc/Th) = Qh(1 – Tc/Th)
So the maximum efficiency is:
 maximum efficiency = Wmax/Qh = (1 – Tc/Th) = (Th – Tc)/Th
 this and similar formulas must have the temperature in Kelvin
So perfect efficiency is only possible if Tc is zero (in ºK)
 In general, this is not true
As Tc  Th, the efficiency drops to zero: no work can be
extracted
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Physics 161
Fall 2006
Examples of Maximum Efficiency
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A coal fire burning at 825 ºK delivers heat energy to a
reservoir at 300 ºK
 max efficiency is (825 – 300)/825 = 525/825 = 64%
 this power station can not possibly achieve a higher
efficiency based on these temperatures
A car engine running at 400 ºK delivers heat energy to the
ambient 290 ºK air
 max efficiency is (400 – 290)/400 = 110/400 = 27.5%
 not too far from reality
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Physics 161
Fall 2006
Example efficiencies of power plants
Power plants these days (almost all of which are heat-engines)
typically get no better than 33% overall efficiency (not true of
hydropower, of course, which does not use a heat engine).
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Physics 161
Fall 2006
What to do with the waste heat (Qc)?
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One option: use it for space-heating locally
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Physics 161
Fall 2006
Overall efficiency greatly enhanced by
cogeneration
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