1. To the Members of Mr. Jefferson’s University: By the driven dispositions that brought us to this school, we hold ourselves back from “sticky” situations much too often, preferring to not ask about potentially dangerous relationships, eating habits, or abuse of any kind, lest we be cast as meddlesome. While it is much easier to lower our blinds and ignore what might not be “our business,” the well- being of every individual within this community is, in fact, our business. We write today in the hopes of instilling a better understanding of the available resources, particularly CAPS and 295-TALK. We hope that students will come to see these lines as places they feel really comfortable calling just to ask any questions about student well-being, not just a number to report suspicions, and we encourage you to take advantage of them as a means to nourish the UVA community. We wish you the best of luck as you commence your examination preparations.

2. Lecture 25 The Laws of Thermodynamics

3. Announcements Do your Course Evaluations!!! You will be allowed to drop your lowest Mastering Physics score, ONLY IF you complete a course evaluation! Assignment #13 is not due for credit

4. Reading and Review

5. zero a) zero -153 J b) -153 J c) -41 J d) -26 J e) 41 J Reading Quiz Internal Energy Reading Quiz Internal Energy An ideal gas is taken through the four processes shown. The changes in internal energy for three of these processes is as follows: The change in internal energy for the process from C to D is:

6. Reading Quiz Internal Energy zero a) zero -153 J b) -153 J c) -41 J d) -26 J e) 41 J An ideal gas is taken through the four processes shown. The changes in internal energy for three of these processes is as follows: The change in internal energy for the process from C to D is: PV = nRT so in a PV cycle, ΔT = 0 ΔT = 0 means that ΔU = 0 ΔU CD = -41 J

7. at constant pressure a) at constant pressure if the pressure increases in proportion to the volume b) if the pressure increases in proportion to the volume c) if the pressure decreases in proportion to the volume d) at constant temperature e) adiabatically Internal Energy Internal Energy An ideal gas undergoes a reversible expansion to 2 times its original volume. In which of these processes does the gas have the largest loss of internal energy?

8. at constant pressure a) at constant pressure if the pressure increases in proportion to the volume b) if the pressure increases in proportion to the volume c) if the pressure decreases in proportion to the volume d) at constant temperature e) adiabatically Internal Energy Internal Energy An ideal gas undergoes a reversible expansion to 2 times its original volume. In which of these processes does the gas have the largest loss of internal energy? Since U = 3/2 nRT, and PV=nRT, the largest loss in internal energy corresponds to the largest drop in temperature, and so the largest drop in the product PV. a) PV doubles. U final = 2U initial b) (PV) final = 4 (PV) initial U final = 4U initial c) PV is constant, so U is constant d) U is constant e) Adiabatic, so ΔU = -W. This is the only process which reduces U!

9. The Zeroth Law of Thermodynamics If object A is in thermal equilibrium with object B, and object C is also in thermal equilibrium with object B, then objects A and C will be in thermal equilibrium if brought into thermal contact. That is, temperature is the only factor that determines whether two objects in thermal contact are in thermal equilibrium or not. Object B can then be a thermometer, providing a scale to compare objects: Temperature

10. The First Law of Thermodynamics The change in a system’s internal energy is related to the heat Q and the work W by conservation of energy: It is vital to keep track of the signs of Q and W. Combining these gives the first law of thermodynamics.

11. Reversible (frictionless pistons, etc.) and quasi-static processes For a process to be reversible, it must be possible to return both the system and its surroundings to the same states they were in before the process began. V P Quasi-static = slow enough that system is always effectively in equilibrium area under the curve W = W

12. Specific Heats for an Ideal Gas Both C V and C P can be calculated for a monatomic ideal gas using the first law of thermodynamics. For ideal gases: where for monotonic gases

13. The Second Law of Thermodynamics We observe that heat always flows spontaneously from a warmer object to a cooler one, although the opposite would not violate the conservation of energy. When objects of different temperatures are brought into thermal contact, the spontaneous flow of heat that results is always from the high temperature object to the low temperature object. Spontaneous heat flow never proceeds in the reverse direction. The Second Law of Thermodynamics:

14. Heat Engines A heat engine is a device that converts heat into work. A classic example is the steam engine. Fuel heats the water; the vapor expands and does work against the piston; the vapor condenses back into water again and the cycle repeats. All heat engines have: a working substance a high-temperature reservoir a low-temperature reservoir a cyclical engine

15. Efficiency of a Heat Engine An amount of heat Q h is supplied from the hot reservoir to the engine during each cycle. Of that heat, some appears as work, and the rest, Q c, is given off as waste heat to the cold reservoir. The efficiency is the fraction of the heat supplied to the engine that appears as work. Assumption: ΔU = 0 for each cycle, else the engine would get hotter (or colder) with every cycle

16. Efficiency of a Heat Engine The efficiency can also be written: In order for the engine to run, there must be a temperature difference; otherwise heat will not be transferred.

18. This is an idealization; no real engine can be perfectly reversible. The maximum-efficiency heat engine is described in Carnot’s theorem: If an engine operating between two constant-temperature reservoirs is to have maximum efficiency, it must be an engine in which all processes are reversible. In addition, all reversible engines operating between the same two temperatures, T c and T h, have the same efficiency.

19. Show the efficiency of the Carnot Cycle:

21. Maximum Work from a Heat Engine Cycle The maximum work a heat engine can do is then: If the two reservoirs are at the same temperature, the efficiency is zero. The smaller the ratio of the cold temperature to the hot temperature, the closer the efficiency will be to 1. Perfect efficiency for T c =?

22. Heat Engine The heat engine below is: a) a reversible (Carnot) heat engine b) an irreversible heat engine c) a hoax d) none of the above

23. Heat Engine The heat engine below is: a) a reversible (Carnot) heat engine b) an irreversible heat engine c) a hoax d) none of the above Carnot e = 1 − T C /T H = 1 − 270/600 = 0.55. But by definition e = 1 − Q L /Q H = 1 − 4000/8000 = 0.5, smaller than Carnot e, thus irreversible.

24. 4-stroke Automobile Engine

25. While heat will flow spontaneously only from a higher temperature to a lower one, it can be made to flow the other way if work is done on the system. Refrigerators, air conditioners, and heat pumps all use work to transfer heat from a cold object to a hot object. Refrigerators, Air Conditioners, and Heat Pumps

26. Refrigerators If we compare the heat engine and the refrigerator, we see that the refrigerator is basically a heat engine running backwards – it uses work to extract heat from the cold reservoir (the inside of the refrigerator) and exhausts to the kitchen. Note that - more heat is exhausted to the kitchen than is removed from the refrigerator.

28. Refrigerators An ideal refrigerator would remove the most heat from the interior while requiring the smallest amount of work. This ratio is called the coefficient of performance, COP: Typical refrigerators have COP values between 2 and 6. Bigger is better! An air conditioner is essentially identical to a refrigerator; the cold reservoir is the interior of the house, and the hot reservoir is outdoors.

29. Heat Pumps Finally, a heat pump is the same as an air conditioner, except with the reservoirs reversed. Heat is removed from the cold reservoir outside, and exhausted into the house, keeping it warm. Note that the work the pump does actually contributes to the desired result (a warmer house) in this case.

30. Heat Pump Efficiency In an ideal heat pump with two operating temperatures (cold and hot), the Carnot relationship holds; the work needed to add heat Q h to a room is: The COP for a heat pump:

31. a) get warmer b) get cooler c) stay the same Room Temperature You haven’t had time to install your new air condition in the window yet, so as a short-term measure you decide to place it on the dining-room table and turn it on to cool off a bit. As a result, does the air in the dining room:

32. a) get warmer b) get cooler c) stay the same Room Temperature You haven’t had time to install your new air condition in the window yet, so as a short-term measure you decide to place it on the dining-room table and turn it on to cool off a bit. As a result, does the air in the dining room: The AC motor must do work to pull heat from one side to the other. The heat that is exhausted is the heat drawn from the room plus the work done by the motor. The net effect is that the motor of the AC is adding heat to the room.

33. AB(O)ABCCD Gasoline engines DA Idealized Diesel cycle

34. Approaching absolute zero So a reversible engine has the following relation between the heat transferred and the reservoir temperatures: so... how cold can we make something? The efficiency of a reversible engine: (irreversible engines ) As a system approaches absolute zero, heat becomes harder to extract

35. The Third Law of Thermodynamics Absolute zero is a temperature that an object can get arbitrarily close to, but never attain. Temperatures as low as 2.0 x 10 -8 K have been achieved in the laboratory, but absolute zero will remain ever elusive – there is simply nowhere to “put” that last little bit of energy. This is the third law of thermodynamics: It is impossible to lower the temperature of an object to absolute zero in a finite number of steps.

36. The Laws of Thermodynamics I) ΔU = Q - W A continuous system (which is not consuming internal energy) cannot output more work than it takes in heat energy YOU CAN’T WIN! YOU CAN’T BREAK EVEN! III) T C = 0 is not achievable II)

37. Entropy A reversible engine has the following relation between the heat transferred and the reservoir temperatures: Rewriting, This quantity, Q/T, is the same for both reservoirs. This conserved quantity is defined as the change in entropy.

38. Entropy Like internal energy, entropy is a state function In a reversible heat engine, the entropy does not change. Unlike energy, entropy is NOT conserved

39. Entropy A real engine will operate at a lower efficiency than a reversible engine; this means that less heat is converted to work. Any irreversible process results in an increase of entropy. for irreversible processes

40. Entropy To generalize: The total entropy of the universe increases whenever an irreversible process occurs. The total entropy of the universe is unchanged whenever a reversible process occurs. Since all real processes are irreversible, the entropy of the universe continually increases. If entropy decreases in a system due to work being done on it, a greater increase in entropy occurs outside the system.

41. Order, Disorder, and Entropy Entropy can be thought of as the increase in disorder in the universe. In this diagram, the end state is less ordered than the initial state – the separation between low and high temperature areas has been lost.

42. Entropy

43. As the total entropy of the universe increases, its ability to do work decreases. The excess heat exhausted during an irreversible process cannot be recovered into a more organized form of energy, or temperature difference. Doing that would require a net decrease in entropy, which is not possible.

45. So far, we have focused on the rather gloomy prospect of the universe constantly evolving toward greater disorder. Is it possible, however, that life is an exception to this rule?