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Physics 161 Fall 2006
AnnouncementsAnnouncements HW#2 is due next Friday, 10/20. I will give extensions HW#2 is due next Friday, 10/20. I will give extensions
only up to Sunday, 10/22!!only up to Sunday, 10/22!!
The first ‘further activity’ is due Monday, 10/16The first ‘further activity’ is due Monday, 10/16
The first quiz is scheduled for Monday, 10/23. This will The first quiz is scheduled for Monday, 10/23. This will cover chapters 1-4. cover chapters 1-4.
The Physics Department help room has been set up. The The Physics Department help room has been set up. The schedule can be found at schedule can be found at http://hendrix2.uoregon.edu/~dlivelyb/TA_assign/index.hthttp://hendrix2.uoregon.edu/~dlivelyb/TA_assign/index.htmlml
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Physics 161 Fall 2006Lecture 6
Conservation of Energy; Heat Conservation of Energy; Heat EnginesEngines
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Physics 161 Fall 2006
Energy is ConservedEnergy is Conserved
Conservation of EnergyConservation of Energy is different from is different from Energy Conservation, the latter being about Energy Conservation, the latter being about using energy wiselyusing energy wisely
Conservation of Energy means energy is Conservation of Energy means energy is neither created nor destroyedneither created nor destroyed. The amount of . The amount of (mass-)energy in the Universe is (mass-)energy in the Universe is constantconstant!!!!
Don’t we Don’t we createcreate energy at a power plant? energy at a power plant? Oh that this were trueOh that this were true—no, we simply —no, we simply
transformtransform energy at our power plants energy at our power plants Doesn’t the sun Doesn’t the sun createcreate energy? energy?
Nope—it Nope—it exchangesexchanges mass for energy mass for energy
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Physics 161 Fall 2006
Energy ExchangeEnergy Exchange Though the total energy of a system is Though the total energy of a system is
constant, the constant, the formform of the energy can change of the energy can change A simple example is that of a simple A simple example is that of a simple
pendulum, in which a continual exchange pendulum, in which a continual exchange goes on between kinetic and potential energygoes on between kinetic and potential energy
height reference
h
pivot
K.E. = 0; P. E. = mgh K.E. = 0; P. E. = mgh
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 MotionPerpetual Motion Why won’t the pendulum swing forever?Why won’t the pendulum swing forever? It’s hard to design a system free of energy pathsIt’s hard to design a system free of energy paths The pendulum slows down by several mechanismsThe pendulum slows down by several mechanisms
Friction at the contact point: requires force to Friction at the contact point: requires force to oppose; force acts through distance oppose; force acts through distance work is work is donedone
Air resistance: must push through air with a force Air resistance: must push through air with a force (through a distance) (through a distance) work is done work is done
Gets some air swirling: puts kinetic energy into Gets some air swirling: puts kinetic energy into air (not really fair to separate these last two)air (not really fair to separate these last two)
Perpetual motion means no loss of energyPerpetual motion means no loss of energy solar system orbits come very close (is the solar system orbits come very close (is the
moon’s orbit constant over a geological time moon’s orbit constant over a geological time period?)period?)
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Physics 161 Fall 2006
Some Energy Chains:Some Energy Chains:
A coffee mug with some gravitational A coffee mug with some gravitational potential energy is droppedpotential energy is dropped
potential energy turns into kinetic energypotential energy turns into kinetic energy kinetic energy of the mug goes into:kinetic energy of the mug goes into:
ripping the mug apart (chemical: breaking ripping the mug apart (chemical: breaking bonds)bonds)
sending the pieces flying (kinetic)sending the pieces flying (kinetic) into soundinto sound into heating the floor and pieces through into heating the floor and pieces through
friction as the pieces slide to a stopfriction as the pieces slide to a stop In the end, the room is slightly warmerIn the end, the room is slightly warmer
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Physics 161 Fall 2006
Gasoline ExampleGasoline Example Put gas in your car, containing 9 Cal/gPut gas in your car, containing 9 Cal/g Combust gas, turning 9 Cal/g into kinetic energy of Combust gas, turning 9 Cal/g into kinetic energy of
explosionexplosion Transfer kinetic energy of gas to piston to Transfer kinetic energy of gas to piston to
crankshaft to drive shaft to wheel to car as a wholecrankshaft to drive shaft to wheel to car as a whole That which doesn’t go into kinetic energy of the car That which doesn’t go into kinetic energy of the car
goes into heating the engine block (and radiator goes into heating the engine block (and radiator water and surrounding air), and friction of water and surrounding air), and friction of transmission system (heat)transmission system (heat)
Much of energy goes into stirring the air (ends up Much of energy goes into stirring the air (ends up as heat)as heat)
Apply the brakes and convert kinetic energy into Apply the brakes and convert kinetic energy into heat (unless you’re driving a hybrid)heat (unless you’re driving a hybrid)
It all ends up as waste heat, ultimatelyIt all ends up as waste heat, ultimately
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Physics 161 Fall 2006
Bouncing BallBouncing Ball
Superball has gravitational potential energySuperball has gravitational potential energy Drop the ball and this becomes kinetic energyDrop the ball and this becomes kinetic energy Ball hits ground and compresses (force times Ball hits ground and compresses (force times
distance), storing energy in the springdistance), storing energy in the spring Ball releases this mechanically stored energy Ball releases this mechanically stored energy
and it goes back into kinetic form (bounces and it goes back into kinetic form (bounces up)up)
Inefficiencies in “spring” end up heating the Inefficiencies in “spring” end up heating the ball and the floor, and stirring the air a bitball and the floor, and stirring the air a bit
In the end, all is heatIn the end, all is heat
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Physics 161 Fall 2006
Why don’t we get hotter and Why don’t we get hotter and hotterhotter
If all these processes end up as heat, why If all these processes end up as heat, why aren’t we continually getting hotter?aren’t we continually getting hotter?
If earth retained all its heat, we If earth retained all its heat, we wouldwould get get hotterhotter
All of earth’s heat is All of earth’s heat is radiatedradiated away away F = F = TT44
If we dump more power, the temperature goes If we dump more power, the temperature goes up, the radiated power increases dramaticallyup, the radiated power increases dramatically comes to equilibrium: power dumped = comes to equilibrium: power dumped =
power radiatedpower radiated stable against perturbation: stable against perturbation: TT tracks power tracks power
budgetbudget
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Physics 161 Fall 2006
Rough numbersRough numbers
How much power does the earth radiate?How much power does the earth radiate? F = F = TT44 for for TT = 288ºK = 15ºC is 390 W/m = 288ºK = 15ºC is 390 W/m22
Summed over entire surface area (4Summed over entire surface area (4RR22, , where where RR = 6,378,000 meters) is 2.0 = 6,378,000 meters) is 2.010101717 W W
Global production is 3Global production is 310101212 W W Solar radiation incident on earth is 1.8Solar radiation incident on earth is 1.810101717
WW just solar luminosity of 3.9just solar luminosity of 3.910102626 W divided W divided
by geometrical fraction that points at earthby geometrical fraction that points at earth Amazing coincidence of numbers! (or is it…)Amazing coincidence of numbers! (or is it…)
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Physics 161 Fall 2006
No Energy for FreeNo Energy for Free
No matter what, you can’t create energy out No matter what, you can’t create energy out of nothing: it has to come from somewhereof nothing: it has to come from somewhere
We can We can transformtransform energy from one form to energy from one form to another; we can another; we can storestore energy, we can energy, we can utilizeutilize energy being conveyed from natural sourcesenergy being conveyed from natural sources
The net (mass-)energy of the entire Universe The net (mass-)energy of the entire Universe is constantis constant
The best we can do is scrape up some useful The best we can do is scrape up some useful crumbscrumbs
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Physics 161 Fall 2006
Heat Engines, Heat Pumps, and Heat Engines, Heat Pumps, and RefrigeratorsRefrigerators
Getting something useful from heatGetting something useful from heat
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Physics 161 Fall 2006
Heat Heat cancan be useful be useful
Normally heat is the end-product of the Normally heat is the end-product of the flow/transformation of energyflow/transformation of energy coffee mug, automobile, bouncing ballcoffee mug, automobile, bouncing ball heat regarded as waste: a useless end heat regarded as waste: a useless end
resultresult Sometimes heat is what we Sometimes heat is what we wantwant, though, though
hot water, cooking, space heatinghot water, cooking, space heating Heat can Heat can alsoalso be coerced into performing be coerced into performing
“useful” (e.g., mechanical) work“useful” (e.g., mechanical) work this is called a “heat engine”this is called a “heat engine”
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Physics 161 Fall 2006
Heat Engine ConceptHeat Engine Concept
Any time a Any time a temperature differencetemperature difference exists exists between two bodies, there is a between two bodies, there is a potentialpotential for for heat flowheat flow
Examples:Examples: heat flows out of a hot pot of soupheat flows out of a hot pot of soup heat flows into a cold drinkheat flows into a cold drink heat flows from the hot sand into your feetheat flows from the hot sand into your feet
Rate of heat flow depends on nature of Rate of heat flow depends on nature of contact and contact and thermal conductivitythermal conductivity of materials of materials
If we’re clever, we can channel some of this If we’re clever, we can channel some of this flow of energy into mechanical workflow of energy into mechanical work
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Physics 161 Fall 2006
Heat Heat Work Work
We can see examples of heat energy producing We can see examples of heat energy producing other types of energyother types of energy Air over a hot car roof is lofted, gaining Air over a hot car roof is lofted, gaining kinetic kinetic
energyenergy That same air also gains That same air also gains gravitational potential gravitational potential
energyenergy All of our All of our windwind is driven by temperature is driven by temperature
differencesdifferences We already know about We already know about radiativeradiative heat energy heat energy
transfertransfer Our electricity generation thrives on temperature Our electricity generation thrives on temperature
differencesdifferences: no steam would circulate if : no steam would circulate if everything was at the same temperatureeverything was at the same temperature
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Physics 161 Fall 2006
Power Plant ArrangementPower Plant Arrangement
Heat flows from Th to Tc, turning turbine along the way
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Physics 161 Fall 2006
The Laws of ThermodynamicsThe Laws of Thermodynamics
Energy is conservedEnergy is conserved Total system entropy can never decreaseTotal system entropy can never decrease As the temperature goes to zero, the entropy As the temperature goes to zero, the entropy
approaches a constant value—this value is approaches a constant value—this value is zero for a perfect crystal latticezero for a perfect crystal lattice
The concept of the “total system” is very The concept of the “total system” is very important: entropy can decrease locally, but important: entropy can decrease locally, but it must increase elsewhere by it must increase elsewhere by at leastat least as as muchmuch
no energy flows into or out of the “total no energy flows into or out of the “total system”: if it does, there’s more to the system”: if it does, there’s more to the system than you thoughtsystem than you thought
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Physics 161 Fall 2006
What’s this What’s this EntropyEntropy business? business?
Entropy is a measure of disorder (and actually Entropy is a measure of disorder (and actually quantifiable on an atom-by-atom basis)quantifiable on an atom-by-atom basis) Ice has low entropy, liquid water has more, Ice has low entropy, liquid water has more,
steam has a lotsteam has a lot
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Physics 161 Fall 2006
Heat Energy and EntropyHeat Energy and Entropy
We’ve already seen many examples of We’ve already seen many examples of quantifying heatquantifying heat 1 Calorie is the heat energy associated with 1 Calorie is the heat energy associated with
raising 1 kg (1 liter) of water 1 ºCraising 1 kg (1 liter) of water 1 ºC In general, In general, Q = cQ = cppmmTT, where , where ccpp is the heat is the heat
capacitycapacity We need to also point out that a change in heat We need to also point out that a change in heat
energy accompanies a change in entropy:energy accompanies a change in entropy:
Q = TQ = TSS Adding heat increases entropyAdding heat increases entropy
more energy goes into random more energy goes into random motionsmotionsmore randomness (entropy)more randomness (entropy)
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Physics 161 Fall 2006
How much work can be How much work can be extracted from heat?extracted from heat?
Th
Qh
Qc
W = Qh – Qc
Tc
Hot source of energy
Cold sink of energy
heat energy delivered from source
heat energy delivered to sink
externally delivered work:
efficiency = =W work doneQh heat supplied
conservation of energy
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Physics 161 Fall 2006
Heat Engine NomenclatureHeat Engine Nomenclature
The symbols we use to describe the heat engine are:The symbols we use to describe the heat engine are: TThh is the temperature of the hot object is the temperature of the hot object
TTcc is the temperature of the cold object is the temperature of the cold object
T = TT = Thh–T–Tcc is the temperature is the temperature differencedifference
QQhh is the amount of heat that flows out of the hot is the amount of heat that flows out of the hot bodybody
QQcc is the amount of heat flowing into the cold body is the amount of heat flowing into the cold body W W is the amount of “useful” mechanical workis the amount of “useful” mechanical work SShh is the change in is the change in entropyentropy of the hot body of the hot body
SScc is the change in entropy of the cold bodyis the change in entropy of the cold body
SStottot is the total change in entropy (entire system) is the total change in entropy (entire system) E E is the entire amount of energy involved in the flowis the entire amount of energy involved in the flow
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Physics 161 Fall 2006
Let’s crank up the efficiencyLet’s crank up the efficiency
Th
Qh
Qc
W = Qh – Qc
Tc
efficiency = =W work doneQh heat supplied
Let’s extract a lot ofwork, and deliver very little heat to the sink
In fact, let’s demand 100%efficiency by sending no heatto the sink: all convertedto useful work
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Physics 161 Fall 2006
Not so fast…Not so fast…
The second law of thermodynamics imposes a The second law of thermodynamics imposes a constraint on this reckless attitude: total entropy constraint on this reckless attitude: total entropy must never decreasemust never decrease
The entropy of the source goes down (heat The entropy of the source goes down (heat extracted), and the entropy of the sink goes up extracted), and the entropy of the sink goes up (heat added): remember that (heat added): remember that Q = TQ = TSS The gain in entropy in the sink must The gain in entropy in the sink must at leastat least
balance the loss of entropy in the sourcebalance the loss of entropy in the source SStottot = = SShh + + SScc = – = –QQhh/T/Thh + + QQcc/T/Tcc
≥ 0≥ 0 QQcc ≥ ( ≥ (TTcc/T/Thh))QQhh sets a sets a
minimum on minimum on QQcc
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Physics 161 Fall 2006
What does this entropy limit What does this entropy limit mean?mean?
W = Qh – Qc, so W can only be as big as the minimum Qc will allow
WWmaxmax = = QQhh – – QQc,minc,min = = QQhh – – QQhh((TTcc/T/Thh) = ) = QQhh(1 – (1 – TTcc/T/Thh))
So the maximum efficiency is: maximum efficiency = maximum efficiency = WWmaxmax//QQhh = = (1 – (1 – TTcc/T/Thh) = () = (TThh – –
TTcc)/)/TThh
this and similar formulas this and similar formulas mustmust have the temperature have the temperature in Kelvinin Kelvin
So perfect efficiency is only possible if Tc is zero (in ºK) In general, this is not trueIn 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 EfficiencyExamples of Maximum Efficiency
A coal fire burning at 825 ºK delivers heat A coal fire burning at 825 ºK delivers heat energy to a reservoir at 300 ºKenergy to a reservoir at 300 ºK max efficiency is (825 – 300)/825 = 525/825 max efficiency is (825 – 300)/825 = 525/825
= 64%= 64% this power station can not possibly achieve a this power station can not possibly achieve a
higher efficiency based on these higher efficiency based on these temperaturestemperatures
A car engine running at 400 ºK delivers heat A car engine running at 400 ºK delivers heat energy to the ambient 290 ºK airenergy to the ambient 290 ºK air max efficiency is (400 – 290)/400 = 110/400 max efficiency is (400 – 290)/400 = 110/400
= 27.5%= 27.5% not too far from realitynot too far from reality
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Physics 161 Fall 2006
Example efficiencies of power Example efficiencies of power plantsplants
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 What to do with the waste heat ((QQcc)?)?
One option: use it for space-heating locallyOne option: use it for space-heating locally
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Physics 161 Fall 2006
Overall efficiency greatly enhanced Overall efficiency greatly enhanced by cogenerationby cogeneration