Chapter 22

1. Chapter 22 Heat Engines, Entropy and the Second Law of Thermodynamics

2. First Law of Thermodynamics – Review • The first law states that a change in internal energy in a system can occur as a result of energy transfer by heat, by work, or by both. • The law makes no distinction between the results of heat and the results of work.

3. First Law of Thermodynamics – Review • In according with first law of thermodynamics the energy is always conserved • What does it mean to conserve energy if the total amount of energy in the universe does not change regardless of what we do? • The first law of thermodynamic does not tell the whole story: Energy is always conserved, but some forms of energy are more useful than others.

4. First Law – Missing Pieces • There is an important distinction between heat and work that is not evident from the first law • The first law makes no distinction between processes that occur spontaneously and those that do not • An example is that it is impossible to design a device that takes in energy and converts it all to work

5. The Second Law of Thermodynamics • The possibility or impossibility of putting energy to use is the subject of the Second Law of Thermodynamics. • For example, it is easy to convert work into thermal energy, but it is impossible to remove energy as heat from a single reservoir and convert it internally into work with no other changes. • This experimental fact is one statement of the second law of thermodynamics.

6. The Second Law of Thermodynamics • Kelvin’s statement: No system can take energy as heat from a single reservoir and convert it entirely into work without additional net changes in the system or its surroundings. • Clausus statement:A process whose only net result is to transfer energy as heat from a cooler object to a hotter one is impossible.

7. The Second Law of Thermodynamics • A common example of conversion of work into heat is movement with friction. • Suppose you spend two minutes pushing a block along a tabletop in a closed path, leaving the block in its initial position. Also, suppose that the block-table system is initially in thermal equilibrium with the surroundings.

8. The Second Law of Thermodynamics • The work you do on the system is converted into internal energy of the system and the block-table system becomes warmer → the system is no longer in thermal equilibrium with its surroundings → the system will transfer energy as heat to its surroundings until it returns to the thermal equilibrium

9. The Second Law of Thermodynamics • Because the final and initial states of the system are the same, the 1-st Law of TD dictates that the energy transferred to the environment as heat equals to the work done on the system. • The reverse process never occur – a block and table that are warm will never spontaneously cool by converting their internal energy into the work that causes the block to push your hand around the table!

10. The Second Law of Thermodynamics • Such an amazing occurrence would not violate the first law of thermodynamics or any other physical law, it does, however, violate the second law of thermodynamics. • There is a lack of symmetry in the roles played by heat and work that is not evident from the first law. This lack of symmetry is related to the fact that some processes are irreversible.

11. The Second Law of Thermodynamics • Establishes which processes do and which do not occur • Some processes can occur in either direction according to the first law • They are observed to occur only in one direction according to the second law.

12. Irreversible Processes • An irreversible process is one that occurs naturally in one direction only • No irreversible process has been observed to run backwards • An important engineering implication is the limited efficiency of heat engines

13. Heat Engine • A heat engine is a device that takes in energy by heat and, operating in a cyclic process, expels a fraction of that energy by means of work • A heat engine carries some working substance through a cyclical process

14. Heat Engine. • The working substance absorbs energy by heat from a high temperature energy reservoir (Qh) • Work is done by the engine (Weng) • Energy is expelled as heat to a lower temperature reservoir (Qc)

15. Heat Engine. • Since it is a cyclical process, ΔEint = 0 • Its initial and final internal energies are the same • Therefore, Qnet = Weng • The work done by the engine equals the net energy absorbed by the engine • The work is equal to the area enclosed by the curve of the PV diagram • The working substance is a gas

16. Thermal Efficiency of a Heat Engine • Thermal efficiency is defined as the ratio of the net work done by the engine during one cycle to the energy input at the higher temperature • We can think of the efficiency as the ratio of what you gain to what you give

17. More About Efficiency • In practice, all heat engines expel only a fraction of the input energy by mechanical work • Therefore, their efficiency is always less than 100% • To have e = 100%, energy expelled as heat to a lower temperature reservoir, QC, must be 0

18. Perfect Heat Engine • No energy is expelled to the cold reservoir • It takes in some amount of energy and does an equal amount of work • e = 100% • It is an impossible engine

19. During each cycle a heat engine absorbs 200 J of heat from a hot reservoir, does work, and exhausts 160 J to a cold reservoir. What is the efficiency of the engine?

20. During each cycle a heat engine absorbs 200 J of heat from a hot reservoir, does work, and exhausts 160 J to a cold reservoir. What is the efficiency of the engine? Qh= 200J W = Qh – Qc = 200J – 160J = 40J

21. Heat Pumps and Refrigerators • Heat engines can run in reverse • This is not a natural direction of energy transfer • Must put some energy into a device to do this • Devices that do this are called heat pumps or refrigerators • Examples • A refrigerator is a common type of heat pump • An air conditioner is another example of a heat pump

22. Heat Pump Process • Energy is extracted from the cold reservoir, QC • Energy is transferred to the hot reservoir, Qh • Work must be done on the engine, W

23. Coefficient of Performance • The effectiveness of a heat pump is described by a number called the coefficient of performance (COP) • In heating mode, the COP is the ratio of the heat transferred in to the work required

24. COP, Heating Mode • COP is similar to efficiency • Qh is typically higher than W • Values of COP are generally greater than 1 • It is possible for them to be less than 1 • We would like the COP to be as high as possible

25. COP, Cooling Mode • In cooling mode, you “gain” energy from a cold temperature reservoir • A good refrigerator should have a high COP • Typical values are 5 or 6

26. A refrigerator has a coefficient of performance equal to 5.00. The refrigerator takes in 120 J of energy from a cold reservoir in each cycle. Find (a) the work required in each cycle and (b) the energy expelled to the hot reservoir.

27. A refrigerator has a coefficient of performance equal to 5.00. The refrigerator takes in 120 J of energy from a cold reservoir in each cycle. Find (a) the work required in each cycle and (b) the energy expelled to the hot reservoir. (a) (b) Heat expelled = Heat removed + Work done.

28. Carnot Engine • A theoretical engine developed by Sadi Carnot • A heat engine operating in an ideal, reversible cycle (now called a Carnot cycle) between two reservoirs is the most efficient engine possible • This sets an upper limit on the efficiencies of all other engines

29. Carnot’s Theorem • No real heat engine operating between two energy reservoirs can be more efficient than a Carnot engine operating between the same two reservoirs • All real engines are less efficient than a Carnot engine because they do not operate through a reversible cycle • The efficiency of a real engine is further reduced by friction, energy losses through conduction, etc.

30. Carnot Cycle Overview of the processes in a Carnot cycle

31. Carnot Cycle, A to B • A→B is an isothermal expansion • The gas is placed in contact with the high temperature reservoir, Th • The gas absorbs heat |Qh| • The gas does work WAB in raising the piston

32. Carnot Cycle, B to C • B→C is an adiabatic expansion • The base of the cylinder is replaced by a thermally insulated wall • No heat enters or leaves the system • The temperature falls from Th to Tc. The gas does work WBC

33. Carnot Cycle, C to D • The gas is placed in contact with the cold temperature reservoir • C→D is an isothermal compression • The gas expels energy Qc • Work WCD is done on the gas

34. Carnot Cycle, D to A • D → A is an adiabatic compression • The gas is again placed against a thermally nonconducting wall • So no heat is exchanged with the surroundings • The temperature of the gas increases from Tc to Th • The work done on the gas is WDA

35. Carnot Cycle, PV Diagram • The work done by the engine is shown by the area enclosed by the curve, Weng • The net work is equal to |Qh| – |Qc| • DEint = 0 for the entire cycle

36. Efficiency of a Carnot Engine • Carnot showed that the efficiency of the engine depends on the temperatures of the reservoirs • Temperatures must be in Kelvins • All Carnot engines operating between the same two temperatures will have the same efficiency

37. Notes About Carnot Efficiency • Efficiency is 0 if Th = Tc • Efficiency is 100% only if Tc = 0 K • Such reservoirs are not available • Efficiency is always less than 100% • The efficiency increases as Tc is lowered and as This raised • In most practical cases, Tcis near room temperature, 300 K • So generally This raised to increase efficiency

38. Carnot Heat Pump COPs • In heating mode: • In cooling mode:

39. A Carnot heat engine uses a steam boiler at 100C as the high-temperature reservoir. The low-temperature reservoir is the outside environment at 20.0C. Energy is exhausted to the low-temperature reservoir at the rate of 15.4 W. (a) Determine the useful power output of the heat engine. (b) How much steam will it cause to condense in the high-temperature reservoir in 1.00 h?

40. A Carnot heat engine uses a steam boiler at 100C as the high-temperature reservoir. The low-temperature reservoir is the outside environment at 20.0C. Energy is exhausted to the low-temperature reservoir at the rate of 15.4 W. (a) Determine the useful power output of the heat engine. (b) How much steam will it cause to condense in the high-temperature reservoir in 1.00 h? The efficiency is:

41. A Carnot heat engine uses a steam boiler at 100C as the high-temperature reservoir. The low-temperature reservoir is the outside environment at 20.0C. Energy is exhausted to the low-temperature reservoir at the rate of 15.4 W. (a) Determine the useful power output of the heat engine. (b) How much steam will it cause to condense in the high-temperature reservoir in 1.00 h? (a) The useful power output is: (b)

42. Gasoline Engine • In a gasoline engine, six processes occur during each cycle • For a given cycle, the piston moves up and down twice • This represents a four-stroke cycle • The processes in the cycle can be approximated by the Otto cycle

43. Otto Cycle • The PV diagram of an Otto cycle is shown at right • The Otto cycle approximates the processes occurring in an internal combustion engine

44. The Conventional Gasoline Engine

45. Gasoline Engine – Intake Stroke • During the intake stroke, the piston moves downward • A gaseous mixture of air and fuel is drawn into the cylinder • Energy enters the system as potential energy in the fuel • O→A in the Otto cycle

46. Gasoline Engine – Compression Stroke • The piston moves upward • The air-fuel mixture is compressed adiabatically • The temperature increases • The work done on the gas is positive and equal to the negative area under the curve • A→ B in the Otto cycle

47. Gasoline Engine – Spark • Combustion occurs when the spark plug fires • This is not one of the strokes of the engine • It occurs very quickly while the piston is at its highest position • Conversion from potential energy of the fuel to internal energy • B→C in the Otto cycle

48. Gasoline Engine – Power Stroke • In the power stroke, the gas expands adiabatically • This causes a temperature drop • Work is done by the gas • The work is equal to the area under the curve • C→D in the Otto cycle

49. Gasoline Engine – Valve Opens • This is process D→Ain the Otto cycle • An exhaust valve opens as the piston reaches its bottom position • The pressure drops suddenly • The volume is approximately constant • So no work is done • Energy begins to be expelled from the interior of the cylinder

50. Gasoline Engine – Exhaust Stroke • In the exhaust stroke, the piston moves upward while the exhaust valve remains open • Residual gases are expelled to the atmosphere • The volume decreases • A→O in the Otto cycle