Plan for Today (AP Physics 2)

3. Plan for Today (AP Physics 2) • Lecture/Notes on Heat Engines, Carnot Engines, and Entropy

4. Energy Transfer by Conduction • Kinetic energy exchange between microscopic particles • Collisions take place between particles, energy transfer, and gradually it works through a material

5. Conduction • Rate depends on properties of the substance • Metals are good thermal conductors (free electrons to transfer energy)

6. Conduction • Only occurs if there is a difference in temperature • Temperature difference drives the flow in energy

7. Conduction • Rate of energy transfer is proportional to the cross sectional area of the slab and the temperature difference • H = Q/t • And is inversely proportional to the thickness of the slab

9. Conduction Equation • k is proportionality constant, depending on the material

10. Heat engine • A device that takes in heat energy and converts some of it to other forms of energy (like mechanical) • Work done by a heat engine through a cyclic process is • W = |Qh| - |Qc| • Qh is energy absorbed from hot reservoir, Qc is energy expelled to cold

11. Hot Res. TH Qhot Wout Engine Qcold Cold Res. TC HEAT ENGINES A heat engine is any device which through a cyclic process: • Absorbs heat Qhot • Performs work Wout • Rejects heat Qcold

12. Hot Res. TH It is impossible to construct an engine that, operating in a cycle, produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work. Qhot Wout Engine Qcold Cold Res. TC THE SECOND LAW OF THERMODYNAMICS Not only can you not win (1st law); you can’t even break even (2nd law)!

13. Hot Res. TH Hot Res. TH 400 J 400 J 100 J 400 J Engine Engine 300 J Cold Res. TC Cold Res. TC • An IMPOSSIBLE engine. • A possible engine. THE SECOND LAW OF THERMODYNAMICS

14. Hot Res. TH QH W W QH QH- QC QH Engine e = = QC Cold Res. TC QC QH e = 1 - EFFICIENCY OF AN ENGINE The efficiency of a heat engine is the ratio of the net work done W to the heat input QH.

15. Hot Res. TH 800 J W QC QH Engine e = 1 - 600 J 600 J 800 J Cold Res. TC e = 1 - e = 25% EFFICIENCY EXAMPLE An engine absorbs 800 J and wastes 600 J every cycle. What is the efficiency? Question: How many joules of work is done?

16. Carnot Engine • No real engine operating between two reservoirs can be more efficient than a Carnot engine

17. Carnot Engine • Substance whose temperature varies between Tc and Th • Ideal gas in a cylinder with a movable piston • Cycle consists of 2 adiabatic and 2 isothermal processes

19. Hot Res. TH QH W Engine TH- TC TH QC e = Cold Res. TC TC TH e = 1 - EFFICIENCY OF AN IDEAL ENGINE (Carnot Engine) For a perfect engine, the quantities Q of heat gained and lost are proportional to the absolute temperatures T.

20. TC TH e = 1 - W QH e = 300 K 500 K e = 1 - Work = 120 J Example 3:A steam engine absorbs 600 J of heat at 500 K and the exhaust temperature is 300 K. If the actual efficiency is only half of the ideal efficiency, how much work is done during each cycle? Actual e = 0.5ei = 20% W = eQH = 0.20 (600 J) e = 40%

21. Hot Res. TH Qhot Win Engine Qcold Cold Res. TC WIN = Qhot - Qcold REFRIGERATORS A refrigerator is an engine operating in reverse: Work is done on gas extracting heat from cold reservoir and depositing heat intohot reservoir. Win + Qcold = Qhot

22. Hot Res. TH Qhot Engine Qcold Cold Res. TC THE SECOND LAW FOR REFRIGERATORS It is impossible to construct a refrigerator that absorbs heat from a cold reservoir and deposits equal heat to a hot reservoir with W = 0. If this were possible, we could establish perpetual motion!

23. Second Law of Thermodynamics • Energy will not flow spontaneously by heat from a cold object to a hot object • No heat engine operating in a cycle can absorb energy from a reservoir and perform an equal amount of work

24. Entropy • Systems tend toward disorder • A disorderly arrangement is more probable than an orderly one • Entropy is a measure of the disorder • The entropy of the Universe increases in all natural processes (alternate 2nd law)

25. Entropy • The change in entropy is equal to the energy flowing into a system (while the system changes from one state to another) divided by the absolute temperature • Change in S = Qr/T

26. Hot Res. TH QH W Engine QH QH- QC QC QC W K = = Cold Res. TC TH TH- TC K = COEFFICIENT OF PERFORMANCE The COP (K) of a heat engine is the ratio of the HEATQc extracted to the net WORK done W. For an IDEAL refrigerator:

27. 500 K Hot Res. TH QH W Engine TC TH- TC 400 K 500 K - 400 K 800 J K = = Cold Res. TC 400 K C.O.P. (K) = 4.0 COP EXAMPLE A Carnot refrigerator operates between 500 K and 400 K. It extracts 800 J from a cold reservoir during each cycle. What is C.O.P., W and QH ?

28. 500 K Hot Res. TH QH W QC QH- QC Engine K = 800 J 800 J QH - 800 J 4.0 = Cold Res. TC 400 K QH = 1000 J COP EXAMPLE (Cont.) Next we will find QH by assuming same K for actual refrigerator (Carnot).

29. 500 K Hot Res. TH 1000 J W Engine 800 J Work = 200 J Cold Res. TC 400 K COP EXAMPLE (Cont.) Now, can you say how much work is done in each cycle? Work = 1000 J - 800 J

30. TheFirst Law of Thermodynamics:The net heat taken in by a system is equal to the sum of the change in internal energy and the work done by the system. Q = U + W final - initial) Summary • Isochoric Process: V = 0, W = 0 • Isobaric Process: P = 0 • Isothermal Process: T = 0, U = 0 • Adiabatic Process: Q = 0

31. The Molar Specific Heat capacity, C: Q n T c = Q = U + W U = nCv T PV = nRT Summary (Cont.) Units are:Joules per mole per Kelvin degree The following are true for ANY process:

32. TheSecond Law of Thermo:It is impossible to construct an engine that, operating in a cycle, produces no effect other than the extraction of heat from a reservoir and the performance of an equivalent amount of work. Hot Res. TH Qhot Wout Engine Qcold Cold Res. TC Summary (Cont.) Not only can you not win (1st law); you can’t even break even (2nd law)!

33. TC TH QC QH e = 1 - e = 1 - Summary (Cont.) The efficiency of a heat engine: The coefficient of performance of a refrigerator: