Physics 161 Fall 2006 1 Announcements HW#2 is due next Friday, 10/20. I will give extensions only up to Sunday, 10/22!! HW#2 is due next Friday, 10/20

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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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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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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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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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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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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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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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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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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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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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Heat Engines, Heat Pumps, and Heat Engines, Heat Pumps, and RefrigeratorsRefrigerators

Getting something useful from heatGetting something useful from heat

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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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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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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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Power Plant ArrangementPower Plant Arrangement

Heat flows from Th to Tc, turning turbine along the way

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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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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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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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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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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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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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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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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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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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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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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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Overall efficiency greatly enhanced Overall efficiency greatly enhanced by cogenerationby cogeneration

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Physics 161 Fall 2006 1 Announcements HW#2 is due next Friday, 10/20. I will give extensions only up to Sunday, 10/22!! HW#2 is due next Friday, 10/20