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Physics 161 Fall 2006 Announcements HW#2 is due next Friday, 10/20. I will give extensions only up to Sunday, 10/22!! The first ‘further activity’ is due Monday, 10/16 The first quiz is scheduled for Monday, 10/23. This will cover chapters 1-4. The Physics Department help room has been set up. The schedule can be found at http://hendrix2.uoregon.edu/~dlivelyb/TA_assign/index.html 1 Physics 161 Lecture 6 Fall 2006 Conservation of Energy; Heat Engines 2 Physics 161 Fall 2006 Energy is Conserved 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 3 Physics 161 Fall 2006 Energy Exchange 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. 4 Physics 161 Fall 2006 Perpetual Motion 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?) 5 Physics 161 Fall 2006 Some Energy Chains: 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 6 Physics 161 Fall 2006 Gasoline Example 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 7 Physics 161 Fall 2006 Bouncing Ball 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 8 Physics 161 Fall 2006 Why don’t we get hotter and hotter 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 9 Physics 161 Fall 2006 Rough numbers How much power does the earth radiate? F = T4 for T = 288ºK = 15ºC is 390 W/m2 Summed over entire surface area (4R2, where R = 6,378,000 meters) is 2.01017 W Global production is 31012 W Solar radiation incident on earth is 1.81017 W just solar luminosity of 3.91026 W divided by geometrical fraction that points at earth Amazing coincidence of numbers! (or is it…) 10 Physics 161 Fall 2006 No Energy for Free 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 11 Physics 161 Fall 2006 Heat Engines, Heat Pumps, and Refrigerators Getting something useful from heat 12 Physics 161 Fall 2006 Heat can be useful 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” 13 Physics 161 Fall 2006 Heat Engine Concept 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 14 Physics 161 Fall 2006 Heat Work 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 15 Physics 161 Fall 2006 Power Plant Arrangement Heat flows from Th to Tc, turning turbine along the way 16 Physics 161 Fall 2006 The Laws of Thermodynamics 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 17 Physics 161 Fall 2006 What’s this Entropy business? 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 18 Physics 161 Fall 2006 Heat Energy and Entropy 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 = cpmT, where cp is the heat capacity We need to also point out that a change in heat energy accompanies a change in entropy: Q = TS Adding heat increases entropy more energy goes into random motionsmore randomness (entropy) 19 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 20 Physics 161 Fall 2006 Heat Engine Nomenclature 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 21 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 22 Physics 161 Fall 2006 Not so fast… 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 = TS The gain in entropy in the sink must at least balance the loss of entropy in the source Stot = Sh + Sc = –Qh/Th + Qc/Tc ≥ 0 Qc ≥ (Tc/Th)Qh sets a minimum on Qc 23 Physics 161 Fall 2006 What does this entropy limit mean? 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 24 Physics 161 Fall 2006 Examples of Maximum Efficiency 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 25 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). 26 Physics 161 Fall 2006 What to do with the waste heat (Qc)? One option: use it for space-heating locally 27 Physics 161 Fall 2006 Overall efficiency greatly enhanced by cogeneration 28