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1、UCSDPhysics 12Heat Engines, Heat Pumps, and RefrigeratorsGetting something useful from heatGetting something useful from heatUCSDPhysics 12Heat can be usefulNormally heat is the end-product of the Normally heat is the end-product of the flow/transformation of energyflow/transformation of energyremem
2、ber examples from lecture #4 (coffee mug, automobile, bouncing ball)heat regarded as waste: as useless end resultSometimes heat is what we Sometimes heat is what we wantwant, though, thoughhot water, cooking, space heatingHeat can Heat can alsoalso be coerced into performing “useful” be coerced into
3、 performing “useful” (e.g., mechanical) work(e.g., mechanical) workthis is called a “heat engine”Spring 20072UCSDPhysics 12Heat Engine ConceptAny time a Any time a temperature differencetemperature difference exists between exists between two bodies, there is a two bodies, there is a potentialpotent
4、ial for for heat flowheat flowExamples:Examples:heat flows out of a hot pot of soupheat flows into a cold drinkheat flows from the hot sand into your feetRate of heat flow depends on nature of contact and Rate of heat flow depends on nature of contact and thermal conductivitythermal conductivity of
5、materials of materialsIf were clever, we can channel some of this flow If were clever, we can channel some of this flow of energy into mechanical workof energy into mechanical workSpring 20073UCSDPhysics 12Heat WorkWe can see examples of heat energy producing We can see examples of heat energy produ
6、cing other types of energyother types of energyAir over a hot car roof is lofted, gaining kinetic energyThat same air also gains gravitational potential energyAll of our wind is driven by temperature differencesWe already know about radiative heat energy transferOur electricity generation thrives on
7、 temperature differences: no steam would circulate if everything was at the same temperatureSpring 20074UCSDPhysics 12Power Plant ArrangementHeat flows from Th to Tc, turning turbine along the waySpring 20075UCSDPhysics 12Heat Engine Nomenclature The symbols we use to describe the heat engine are:Th
8、e symbols we use to describe the heat engine are:Th is the temperature of the hot objectTc is the temperature of the cold objectT = ThTc is the temperature differenceQh is the amount of heat that flows out of the hot bodyQc is the amount of heat flowing into the cold bodyW is the amount of “useful”
9、mechanical workSh is the change in entropy of the hot bodySc is the change in entropy of the cold bodyStot is the total change in entropy (entire system)E is the entire amount of energy involved in the flowSpring 20076UCSDPhysics 12Whats this Entropy business?Entropy is a measure of disorder (and ac
10、tually 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, steam has a lotSpring 20077UCSDPhysics 12The Laws of Thermodynamics1.Energy is conservedEnergy is conserved2.Total system entr
11、opy can never decreaseTotal system entropy can never decrease3.As the temperature goes to zero, the entropy As the temperature goes to zero, the entropy approaches a constant valueapproaches a constant valuethis value is zero this value is zero for a perfect crystal latticefor a perfect crystal latt
12、iceThe concept of the “total system” is very The concept of the “total system” is very important: entropy can decrease locally, but it important: entropy can decrease locally, but it must increase elsewhere by must increase elsewhere by at leastat least as much as muchno energy flows into or out of
13、the “total system”: if it does, theres more to the system than you thoughtSpring 20078UCSDPhysics 12Quantifying heat energyWeve already seen many examples of quantifying Weve already seen many examples of quantifying heatheat1 Calorie is the heat energy associated with raising 1 kg (1 liter) of wate
14、r 1 CIn general, Q = cpmT, where cp is the heat capacityWe 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 = T S S Adding heat increases entropy Adding heat increases en
15、tropymore energy goes into random motionsmore randomness (entropy)Spring 20079UCSDPhysics 12How much work can be extracted from heat?ThQhQcW = Qh QcTcHot source of energyCold sink of energyheat energy delivered from sourceheat energy delivered to sinkexternally delivered work:efficiency = =W work do
16、neQh heat suppliedconservation of energySpring 200710UCSDPhysics 12Lets crank up the efficiencyThQhQcW = Qh QcTcefficiency = =W work doneQh heat suppliedLets extract a lot ofwork, and deliver very little heat to the sinkIn fact, lets demand 100%efficiency by sending no heatto the sink: all converted
17、to useful workSpring 200711UCSDPhysics 12Not so fastThe second law of thermodynamics imposes a The second law of thermodynamics imposes a constraint on this reckless attitude: constraint on this reckless attitude: total entropy total entropy must never decreasemust never decreaseThe entropy of the s
18、ource 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 = T S SThe gain in entropy in the sink must at least balance the loss of entr
19、opy in the sourceStot = Sh + Sc = Qh/Th + Qc/Tc 0 Qc (Tc/Th)Qh sets a minimum on QcSpring 200712UCSDPhysics 12What does this entropy limit mean?W = Qh Qc, so W can only be as big as the minimum Qc will allowWmax = Qh Qc,min = Qh Qh(Tc/Th) = Qh(1 Tc/Th)So the maximum efficiency is:maximum efficiency
20、= Wmax/Qh = (1 Tc/Th) = (Th Tc)/Ththis and similar formulas must have the temperature in KelvinSo perfect efficiency is only possible if Tc is zero (in K)In general, this is not trueAs Tc Th, the efficiency drops to zero: no work can be extractedSpring 200713UCSDPhysics 12Examples of Maximum Efficie
21、ncyA coal fire burning at 825 A coal fire burning at 825 K delivers heat energy K delivers heat energy to a reservoir at 300 Kto a reservoir at 300 Kmax efficiency is (825 300)/825 = 525/825 = 64%this power station can not possibly achieve a higher efficiency based on these temperaturesA car engine
22、running at 400 A car engine running at 400 K delivers heat K delivers heat energy to the ambient 290 K airenergy to the ambient 290 K airmax efficiency is (400 290)/400 = 110/400 = 27.5%not too far from realitySpring 200714UCSDPhysics 12Example efficiencies of power plantsPower plants these days (al
23、most all of which are heat-engines)typically get no better than 33% overall efficiencySpring 200715UCSDPhysics 12What to do with the waste heat (Qc)?One option: use it for space-heating locallyOne option: use it for space-heating locallySpring 200716UCSDPhysics 12Overall efficiency greatly enhanced
24、by cogenerationSpring 200717UCSDPhysics 12Heat PumpsHeat Pumps provide a means to very efficiently move heataround, and work both in the winter and the summerSpring 200718UCSDPhysics 12Heat Pump DiagramSpring 200719UCSDPhysics 12Heat Pumps and Refrigerators: ThermodynamicsThQhQcW = Qh QcTcHot entity
25、(indoor air)Cold entity(outside air or refrigerator)heat energy deliveredheat energy extracteddelivered work:conservation of energyJust a heat engine runbackwardsefficiency = =W work doneQh heat delivered(heat pump)efficiency = =W work doneQc heat extracted(refrigerator)Spring 200720UCSDPhysics 12He
26、at Pump/Refrigerator EfficienciesCan work through same sort of logic as before to Can work through same sort of logic as before to see that:see that:heat pump efficiency is: Th/(Th Tc) = Th/T in Krefrigerator efficiency is: Tc/(Th Tc) = Tc/T in KNote that heat pumps and refrigerators are most Note t
27、hat heat pumps and refrigerators are most efficient for small temperature differencesefficient for small temperature differenceshard on heat pumps in very cold climateshard on refrigerators in hot settingsSpring 200721UCSDPhysics 12Example EfficienciesA heat pump maintaining 20 A heat pump maintaini
28、ng 20 C when it is 5 C C when it is 5 C outside has a maximum possible efficiency of: outside has a maximum possible efficiency of: 293/25 = 11.72293/25 = 11.72note that this means you can get almost 12 times the heat energy than you are supplying in the form of work!this factor is called the C.O.P.
29、 (coefficient of performance)A freezer maintaining 5 C in a 20 C room has a A freezer maintaining 5 C in a 20 C room has a maximum possible efficiency of:maximum possible efficiency of:268/25 = 10.72268/25 = 10.72called EER (energy efficiency ratio)Spring 200722UCSDPhysics 12Example Labels (U.S. & C
30、anada)Spring 200723UCSDPhysics 12Announcements and AssignmentsRead Chapter 4 for next lectureRead Chapter 4 for next lectureHW #3 due Thursday 4/22:HW #3 due Thursday 4/22:Chapter 2 problems 4, 11, 12; multiple choice 2, 3, 5, 6, 7, 11, 13, 15, 17 (show work or justify answers!); Additional problems on website (hw3.html)Spring 200724
