Physics 161 Fall 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. I will give extensions only up to Sunday, 10/22!! The first ‘further activity’ is due Monday, 10/16 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 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 The Physics Department help room has been set up. The schedule can be found at

Physics 161 Fall Lecture 6 Conservation of Energy; Heat Engines

Physics 161 Fall Energy is Conserved Conservation of Energy is different from Energy Conservation, the latter being about using energy wisely 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!! 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? Don’t we create energy at a power plant? Oh that this were true—no, we simply transform energy at our power plants Oh that this were true—no, we simply transform energy at our power plants Doesn’t the sun create energy? Doesn’t the sun create energy? Nope—it exchanges mass for energy Nope—it exchanges mass for energy

Physics 161 Fall Energy Exchange Though the total energy of a system is constant, the form of the energy can change 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 A simple example is that of a simple pendulum, in which a continual exchange goes on between kinetic and potential energy height reference h pivot 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.

Physics 161 Fall Perpetual 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 paths It’s hard to design a system free of energy paths The pendulum slows down by several mechanisms The pendulum slows down by several mechanisms Friction at the contact point: requires force to oppose; force acts through distance  work is done 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 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) Gets some air swirling: puts kinetic energy into air (not really fair to separate these last two) Perpetual motion means no loss of energy Perpetual motion means no loss of energy solar system orbits come very close (is the moon’s orbit constant over a geological time period?) solar system orbits come very close (is the moon’s orbit constant over a geological time period?)

Physics 161 Fall Some Energy Chains: A coffee mug with some gravitational potential energy is dropped A coffee mug with some gravitational potential energy is dropped potential energy turns into kinetic energy potential 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 bonds) ripping the mug apart (chemical: breaking bonds) sending the pieces flying (kinetic) sending the pieces flying (kinetic) into sound into sound into heating the floor and pieces through friction as the pieces slide to a stop into heating the floor and pieces through friction as the pieces slide to a stop In the end, the room is slightly warmer In the end, the room is slightly warmer

Physics 161 Fall Gasoline Example Put gas in your car, containing 9 Cal/g Put gas in your car, containing 9 Cal/g Combust gas, turning 9 Cal/g into kinetic energy of explosion 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 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) 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) 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) Apply the brakes and convert kinetic energy into heat (unless you’re driving a hybrid) It all ends up as waste heat, ultimately It all ends up as waste heat, ultimately

Physics 161 Fall Bouncing Ball Superball has gravitational potential energy Superball has gravitational potential energy Drop the ball and this becomes kinetic energy Drop the ball and this becomes kinetic energy Ball hits ground and compresses (force times distance), storing energy in the spring 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) 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 Inefficiencies in “spring” end up heating the ball and the floor, and stirring the air a bit In the end, all is heat In the end, all is heat

Physics 161 Fall Why don’t we get hotter and hotter If all these processes end up as heat, why aren’t we continually getting 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 If earth retained all its heat, we would get hotter All of earth’s heat is radiated away All of earth’s heat is radiated away F =  T 4 F =  T 4 If we dump more power, the temperature goes up, the radiated power increases dramatically If we dump more power, the temperature goes up, the radiated power increases dramatically comes to equilibrium: power dumped = power radiated comes to equilibrium: power dumped = power radiated stable against perturbation: T tracks power budget stable against perturbation: T tracks power budget

Physics 161 Fall Rough numbers How much power does the earth radiate? How much power does the earth radiate? F =  T 4 for T = 288ºK = 15ºC is 390 W/m 2 F =  T 4 for T = 288ºK = 15ºC is 390 W/m 2 Summed over entire surface area (4  R 2, where R = 6,378,000 meters) is 2.0  W Summed over entire surface area (4  R 2, where R = 6,378,000 meters) is 2.0  W Global production is 3  W Global production is 3  W Solar radiation incident on earth is 1.8  W Solar radiation incident on earth is 1.8  W just solar luminosity of 3.9  W divided by geometrical fraction that points at earth just solar luminosity of 3.9  W divided by geometrical fraction that points at earth Amazing coincidence of numbers! (or is it…) Amazing coincidence of numbers! (or is it…)

Physics 161 Fall No Energy for Free No matter what, you can’t create energy out of nothing: it has to come from somewhere 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 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 net (mass-)energy of the entire Universe is constant The best we can do is scrape up some useful crumbs The best we can do is scrape up some useful crumbs

Physics 161 Fall Heat Engines, Heat Pumps, and Refrigerators Getting something useful from heat

Physics 161 Fall Heat can be useful Normally heat is the end-product of the flow/transformation of energy Normally heat is the end-product of the flow/transformation of energy coffee mug, automobile, bouncing ball coffee mug, automobile, bouncing ball heat regarded as waste: a useless end result heat regarded as waste: a useless end result Sometimes heat is what we want, though Sometimes heat is what we want, though hot water, cooking, space heating hot water, cooking, space heating Heat can also be coerced into performing “useful” (e.g., mechanical) work Heat can also be coerced into performing “useful” (e.g., mechanical) work this is called a “heat engine” this is called a “heat engine”

Physics 161 Fall Heat Engine Concept Any time a temperature difference exists between two bodies, there is a potential for heat flow Any time a temperature difference exists between two bodies, there is a potential for heat flow Examples: Examples: heat flows out of a hot pot of soup heat flows out of a hot pot of soup heat flows into a cold drink heat flows into a cold drink heat flows from the hot sand into your feet heat flows from the hot sand into your feet Rate of heat flow depends on nature of contact and thermal conductivity of materials 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 If we’re clever, we can channel some of this flow of energy into mechanical work

Physics 161 Fall Heat  Work We can see examples of heat energy producing other types of energy We can see examples of heat energy producing other types of energy Air over a hot car roof is lofted, gaining kinetic energy Air over a hot car roof is lofted, gaining kinetic energy That same air also gains gravitational potential energy That same air also gains gravitational potential energy All of our wind is driven by temperature differences All of our wind is driven by temperature differences We already know about radiative heat energy transfer 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 Our electricity generation thrives on temperature differences: no steam would circulate if everything was at the same temperature

Physics 161 Fall Power Plant Arrangement Heat flows from T h to T c, turning turbine along the way

Physics 161 Fall The Laws of Thermodynamics Energy is conserved Energy is conserved Total system entropy can never decrease 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 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 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 no energy flows into or out of the “total system”: if it does, there’s more to the system than you thought

Physics 161 Fall What’s this Entropy business? Entropy is a measure of disorder (and actually quantifiable on an atom-by-atom basis) 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 Ice has low entropy, liquid water has more, steam has a lot

Physics 161 Fall Heat Energy and Entropy We’ve already seen many examples of quantifying heat 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 1 Calorie is the heat energy associated with raising 1 kg (1 liter) of water 1 ºC In general,  Q = c p m  T, where c p is the heat capacity In general,  Q = c p m  T, where c p is the heat capacity We need to also point out that a change in heat energy accompanies a change in entropy: We need to also point out that a change in heat energy accompanies a change in entropy:  Q = T  S  Q = T  S Adding heat increases entropy Adding heat increases entropy more energy goes into random motions  more randomness (entropy) more energy goes into random motions  more randomness (entropy)

Physics 161 Fall How much work can be extracted from heat? ThTh QhQh QcQc  W =  Q h –  Q c TcTc Hot source of energy Cold sink of energy heat energy delivered from source heat energy delivered to sink externally delivered work: efficiency = =  W work done  Q h heat supplied conservation of energy

Physics 161 Fall Heat Engine Nomenclature The symbols we use to describe the heat engine are: The symbols we use to describe the heat engine are: T h is the temperature of the hot object T h is the temperature of the hot object T c is the temperature of the cold object T c is the temperature of the cold object  T = T h –T c is the temperature difference  T = T h –T c is the temperature difference  Q h is the amount of heat that flows out of the hot body  Q h is the amount of heat that flows out of the hot body  Q c is the amount of heat flowing into the cold body  Q c is the amount of heat flowing into the cold body  W is the amount of “useful” mechanical work  W is the amount of “useful” mechanical work  S h is the change in entropy of the hot body  S h is the change in entropy of the hot body  S c is the change in entropy of the cold body  S c is the change in entropy of the cold body  S tot is the total change in entropy (entire system)  S tot is the total change in entropy (entire system)  E is the entire amount of energy involved in the flow  E is the entire amount of energy involved in the flow

Physics 161 Fall Let’s crank up the efficiency ThTh QhQh QcQc  W =  Q h –  Q c TcTc efficiency = =  W work done  Q h heat supplied Let’s extract a lot of work, and deliver very little heat to the sink In fact, let’s demand 100% efficiency by sending no heat to the sink: all converted to useful work

Physics 161 Fall Not so fast… The second law of thermodynamics imposes a constraint on this reckless attitude: total entropy must never decrease 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 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 The gain in entropy in the sink must at least balance the loss of entropy in the source  S tot =  S h +  S c = –  Q h /T h +  Q c /T c ≥ 0  S tot =  S h +  S c = –  Q h /T h +  Q c /T c ≥ 0  Q c ≥ (T c /T h )  Q h sets a minimum on  Q c  Q c ≥ (T c /T h )  Q h sets a minimum on  Q c

Physics 161 Fall What does this entropy limit mean?  W =  Q h –  Q c, so  W can only be as big as the minimum  Q c will allow  W max =  Q h –  Q c,min =  Q h –  Q h (T c /T h ) =  Q h (1 – T c /T h )  W max =  Q h –  Q c,min =  Q h –  Q h (T c /T h ) =  Q h (1 – T c /T h ) So the maximum efficiency is: maximum efficiency =  W max /  Q h = (1 – T c /T h ) = (T h – T c )/T h maximum efficiency =  W max /  Q h = (1 – T c /T h ) = (T h – T c )/T h this and similar formulas must have the temperature in Kelvin this and similar formulas must have the temperature in Kelvin So perfect efficiency is only possible if T c is zero (in ºK) In general, this is not true In general, this is not true As T c  T h, the efficiency drops to zero: no work can be extracted

Physics 161 Fall Examples of Maximum Efficiency A coal fire burning at 825 ºK delivers heat energy to a reservoir at 300 ºK 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% max efficiency is (825 – 300)/825 = 525/825 = 64% this power station can not possibly achieve a higher efficiency based on these temperatures 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 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% max efficiency is (400 – 290)/400 = 110/400 = 27.5% not too far from reality not too far from reality

Physics 161 Fall 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).

Physics 161 Fall What to do with the waste heat (  Q c )? One option: use it for space-heating locally One option: use it for space-heating locally

Physics 161 Fall Overall efficiency greatly enhanced by cogeneration