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CU-Boulder PHYS 3070 - Lecture Notes

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1Homework #4 due WednesdayInquire/Inform #1 due Friday – in class.See details in Lecture #7 posted notes.Reading Chapter 3 of textbook.What did you think about the first exam?A) It was exactly what I expected and was pretty easyB) It was exactly what I expected and was challengingC) It was exactly what I expected and was very challengingD) It was not at all what I expected and was challengingE) It was not al all what I expected and was very challengingPlease feel free to come and see me or send me emails on ways of improving the course and improving the learning of material you are interested in.Exam #1 – solutions posted on the class web page…The maximum score is 60 points.Specific letter grades are not assigned to each exam.Approximate grade ranges:54-60 (A), 45-53 (B), 35-44 (C), <35 (D,F)Heat EngineQ (hot)Heat energy inputQ (cold)Heat energy wastedWork extractedFrom a hot reservoir ThotFrom a cold reservoir TcoldRecall that our heat engine had a maximum efficiency:⎟⎟⎠⎞⎜⎜⎝⎛−=hotcoldQQe 1hotcoldhotcoldTTQQ>ANDCarnot devised an “ideal heat engine” and showed it had a maximum efficiency for producing work:⎟⎟⎠⎞⎜⎜⎝⎛−=hotcoldTTe 1where the Temperatures must be given in units of Kelvin.Nicolas Léonard SadiCarnot (1796–1832)2An old fashioned steam engine heats water up to T=100 0C. That is the “hot bath”. The steam then drives pistons (doing work), and some heat is dumped into the atmosphere at T=23 0C. What is the “ideal” (i.e. Carnot maximum) efficiency of this steam engine?A) 0.10 (i.e. 10%)B) 0.21 (i.e. 21%)C) 0.77 (i.e. 77%)D) 1.00 (i.e. 100%)()()21.03732961273100273231 =−=++−=eClicker QuestionYou can NEVER build a steam engine that puts out more work than 21% of the original stored potential energy of the coal or wood fuel.The remaining 79% is wasted, heating the atmosphere up a little.A real steam engine will always be worse. In the 1800’s, steam locomotives were about 3% efficient. At their peak, they got up to about 8% efficiency.People can be creative and very smart, but they will surely never violate the laws of thermodynamics! Modern Power Plants have Thot~ 825 Kelvin (1000 0F). Again it is difficult to have anything but Tcold~ 40-70 0F.Thus efficiency(maximum) ~ 0.64.Real power plants get 30-35%, so about half of the ideal. There are still energy losses to friction, etc.Technology improvement over time.%)50(5.080040011 ==−=−=hotcoldTTefficiencySuppose Tcold= 400 K and Thot= 800 KIf you could do only one thing to improve the efficiency, should you:A) Raise the input hot temperature by 100 K to 900 KB) Lower the output cold temperature by 100 K to 300KC) It doesn’t matter which one you doClicker QuestionOption (A) changes the efficiency e = 1 - 400/900 = 5/9Option (B) changes the efficiency e = 1 – 300/800 = 5/8Thus option B is better.“Thermodynamics is the only physical theory of universal content which, within the framework of applicability of its basic concepts, I am convinced will never be overthrown.”Albert EinsteinWhy not go to higher temperatures?Material problems, thermal breakdown, corrosion, etc.Generally worse pollutants produced at higher Temperature.hotcoldTTefficiency −=13Note that average particle or molecule kinetic energy is proportional to the temperature (in Kelvin) in a material.At room temperature T = 30 degrees Celsius the air molecules are moving at 800 miles per hour. How fast are air molecules (of steam particles) moving if a furnace is at T = 3000 degrees Celsius?A) 80 miles per hourB) 260 miles per hourC) 800 miles per hourD) 2600 miles per hourE) 8000 miles per hour 10303327327330273300020800≈=++=KEKEClicker Question102/12/1222220800≈==chchvvmvmvKEKE~ 800 mph x sqrt(10)Want Thot–Tcoldto be as large as possible. Thus, cooling towers (ponds, rivers) can help some.What is a cooling tower?Details of real heat engines can vary a lot. Typical: Fluid (air, gas, or water) is heated by burning fuel. Fluid reaches Thot, expands, and pushed on a piston which does work (pushes rods in cars, turns turbines, etc.).Nuclear reactions use Uranium (235) for example as fuel, but they use this to heat water (or other working fluids). So, theyare also limited by the maximum Carnot efficiency.This applies to power plants, car engines, rocket engines, …, all heat engines.This does not apply to batteries, photovoltaic (solar) panels, windmills, hydroelectric plants – these are not THERMAL (heat) engines. They are not converting heat energy into work!••Heat is added to gas outside of the Heat is added to gas outside of the cylindercylinder••Hot, high pressure gas enters Hot, high pressure gas enters engine, does work against piston or engine, does work against piston or against fan bladesagainst fan blades••Cooler, lower pressure gas is Cooler, lower pressure gas is exhaustexhaust••Water/Steam is very favorable Water/Steam is very favorable systemsystem••Lots of energy at given temperatureLots of energy at given temperatureExternal Combustion EngineExternal Combustion EngineBoilerValveCam“Original recipe” Steam EngineBoilerValveExhaustDiameterof the bladesincreases aspressure dropsSteam inputLarge exhaust ducts to minimize backpressureExhaust4Stirling External Combustion Enginehttp://www.stirlingengine.comVery simple


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