Unformatted text preview: UCSD Physics 12 Heat Engines, Heat Pumps, and Refrigerators
Getting something useful from heat UCSD Physics 12 Heat can be useful Normally heat is the end-product of the flow/transformation of energy remember examples from lecture #4 (coffee mug, automobile, bouncing ball) heat regarded as waste: as 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" Spring 2010 2 UCSD Physics 12 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
Spring 2010 3 UCSD Physics 12 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 Spring 2010 4 UCSD Physics 12 Power Plant Arrangement Heat flows from Th to Tc, turning turbine along the way Spring 2010 5 UCSD Physics 12 Heat Engine Nomenclature The symbols we use to describe the heat engine are: Th is the temperature of the hot object (typ. in Kelvin) Tc is the temperature of the cold object (typ. in Kelvin) T = ThTc 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 Spring 2010 6 UCSD Physics 12 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 Spring 2010 7 UCSD Physics 12 The Laws of Thermodynamics
1. 2. 3. 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
Q Spring 2010 8 UCSD Physics 12 Quantifying heat energy 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 C In general, Q = cpm T, where cp is the heat capacity We need to also point out that a change in heat energy accompanies a change in entropy: Q = T S (T expressed in K) Adding heat increases entropy more energy goes into random motionsmore randomness (entropy) Spring 2010 9 UCSD Physics 12 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 conservation of energy heat energy delivered to sink Qc W work done efficiency = = Qh heat supplied Cold sink of energy Spring 2010 Tc Q 10 UCSD Physics 12 Let's crank up the efficiency
Let's extract a lot of work, and deliver very little heat to the sink Th Qh
In fact, let's demand 100% efficiency by sending no heat to the sink: all converted to useful work W = Qh Qc Qc
Tc W work done efficiency = = Qh heat supplied Spring 2010 11 UCSD Physics 12 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 = T S 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
Spring 2010 12 UCSD Physics 12 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 K) In general, this is not true As Tc Th, the efficiency drops to zero: no work can be extracted Spring 2010 13 UCSD Physics 12 Examples of Maximum Efficiency A coal fire burning at 825 K delivers heat energy to a reservoir at 300 K 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 K delivers heat energy to the ambient 290 K air max efficiency is (400 290)/400 = 110/400 = 27.5% not too far from reality Spring 2010 2 Q 14 UCSD Physics 12 Example efficiencies of power plants Power plants these days (almost all of which are heat-engines) typically get no better than 33% overall efficiency Spring 2010 15 UCSD Physics 12 What to do with the waste heat ( Qc)? One option: use it for space-heating locally Spring 2010 16 UCSD Physics 12 Overall efficiency greatly enhanced by cogeneration Spring 2010 17 UCSD Physics 12 Heat Pumps Heat Pumps provide a means to very efficiently move heat around, and work both in the winter and the summer Spring 2010 18 UCSD Physics 12 Heat Pump Diagram Spring 2010 19 UCSD Physics 12 Heat Pumps and Refrigerators: Thermodynamics
Hot entity (indoor air) heat energy delivered Th Just a heat engine run backwards... Qh Qc
Tc delivered work: W = Qh Qc
conservation of energy heat energy extracted Cold entity (outside air or refrigerator) Spring 2010 Qh heat delivered efficiency = W = work done (heat pump) Qc heat extracted efficiency = W = work done (refrigerator) 20 UCSD Physics 12 Heat Pump/Refrigerator Efficiencies Can work through same sort of logic as before to see that: heat pump efficiency is: Th/(Th Tc) = Th/ T refrigerator efficiency is: Tc/(Th Tc) = Tc/ T in K in K Note that heat pumps and refrigerators are most efficient for small temperature differences hard on heat pumps in very cold climates hard on refrigerators in hot settings Spring 2010 21 UCSD Physics 12 Example Efficiencies A heat pump maintaining 20 C when it is 5 C outside has a maximum possible efficiency of: 293/25 = 11.72 note 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. (coefficient of performance); in practice 26 in commercial heat pumps A freezer maintaining 5 C in a 20 C room has a maximum possible efficiency of: 268/25 = 10.72 EER = 3.4 10.7 = 36 the EER (energy efficiency ratio) is a proxy to this is Btu/hr heat removed per input in Watts 1 Btu/hr is 1055 J/3600 s = 0.293 W 1 W = 3.4 Btu/hr EER > 3.4 means better than break-even Spring 2010 22 UCSD Physics 12 Example Labels (U.S. & Canada) Spring 2010 23 UCSD Physics 12 Announcements and Assignments Chapter 3 goes with this lecture HW #3 due Friday 4/23: primarily Chapter 2-related problems: (show work or justify answers!); plus Additional problems (on website) HW drop box outside my office (SERF 336) for early turn-in Remember that Quizzes happen every week available from Thurs. afternoon until Friday midnight three attempts (numbers change) the better to learn you with Spring 2010 24 ...
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