colorado/physics/ phys3070/phys3070_sp10

1. www.colorado.edu/physics/phys3070/phys3070_sp10

2. Think about a water mill. Water at height Hhigh * work Falls to Hlow CHANGE in potential energy = m g (Hhigh-Hlow) With g =9.8 m/sec2

3. How do we get ALL of the energy out? By letting the water fall all the way, to the center of the earth.

4. But--- • There is another rule, in addition to conservation of energy. • The water can fall no further than to the surface of the earth, sea level. • So maximum efficiency is emax =m x g x height above sea level/ energy if m fell all the way to the core of the earth.

7. Heat energy can only fall to the temperature of some ‘cold reservoir’, at Tcold. And we measure temperature only in MKS units of Kelvins. Absolute zero= 0 deg K=-273 deg C. Water boils at 100 deg C=373 deg K

8. Best efficiency • Every type of heat engine has same equation for its efficiency e= W/Qhot=(Qhot-Qcold)/Qhot • But the absolute best is the Carnot engine, with eCarnot = (Thot – Tcold)/Thot --page 67 =(1-Tc/Th) • Tc usually set by the outside environment • 100% ?? Only for Tc=0 deg K=absolute zero

9. But– units of temperature? • All the way would be absolute zero, • -273 deg C. • Called 0 deg Kelvin (K) • Tcent = Tkelvin +273.

10. Example-human engine • Thot = 37 deg C, Tcold = 5 deg C • Or Thot = 273+37 = 310 deg K, Tcold = 5+273=278 deg K • ecarnot = 310-278/310 =32/310 = 0.105 =10.5% (Or temp. differences can still be in deg C) • So-how can we work at Tc=104 deg F = 40deg C=313 deg K ? E Carnot is negative.

11. Lessons from the ideal/Carnot engine • Set by the laws of physics, not friction etc.. There is only so far downhill to go in temperature. Universal rule. • Better with big temp. differences • Since Tcold is fixed, operate at the hottest Thot. • Express real efficiency as fraction of the ideal.

12. Electrical generation • Thermal power plants • Turn heat energy into rotational energy • Rotate a coil in a generator. • Units again! Sell kW-hr, buy Btu.

13. Example Burn 1 ton of coal per minute, at Th=552 C, Tc=27 C (text), at 60% of ideal efficiency. How many GW can we sell? First-- Th=273+552=825 K Tc=273=27=300K Second--ecarnot=825-300/825 = 0.6364 Third--e=60% x 0.6364=0.3818 (see Fig,. 3.5)

14. W =e x Qin =0.3818 x 2.81 x 1010 J/ton x 1 ton/min x 1/60 min/sec =0.01788 x 10 10 J/sec =0.1788 x 109 J/sec =0.1788 GWe Suggestion– do this in the language of 1 ton of coal =7800 kW-hr

15. The heat pump-- • Turn around all arrows of energy flow, use work in to ‘lift’ heat energy • Energy is conserved Qhot=Qcold +W • There is an idea equivalent to efficiency, and a best value. • COP = Qhot / W =Qh/(Qh-Qc) • Best (Carnot) COP=Th/(Th-Tc)

16. Example • Your refrigerator, Tc= -5 deg C = 268 deg K • Th = 20 deg C =293 deg K • COPCarnot=Th/(Th-Tc) =293/ (293-268)=11.71 • You put Qh=11.72 joules into the kitchen for every W=1 Joule of electrical energy, and removed Qc=10.72 J from the freezer compartment, if your refrigerator is perfect.

19. Combining efficiencies You have a Carnot efficiency of 38%, but really get only 60% of that, and face a 10% loss getting electrical energy into a house. THE efficiency = 38% x 60% x (100-10)% =0.38 x 0.60 x 0.90 = 0.205=20.5%

20. Q:What happens if you turn your window air conditioner around for the winter? A; You heat your home, cool the outdoors.

21. Next week • Monday –moving electrical energy around, special guest. HW 34 due • Wednesday—Solar energy, Chapter 4 • Friday—Finish solar energy • Exam 1, in class Monday Feb. 15.

22. 4. (2) Draft a one-sentence (!!!) question (on energy and the environment only!!) you would like to ask of your representative in Washington. Then, add a brief answer that you would hope to hear.