nd 2 Law of Thermodynamics Lecturer: Professor Stephen T. Thornton Reading Quiz Which of the following is most true? A) The second law of thermodynamics is simply a statement of the conservation of energy. B) The Carnot Engine is the most efficient engine possible. C) Carnot built his engine as a gift to King Henry VIII. D) Heat engines normally operate between three thermal reservoirs. Answer: B The Carnot cycle and Carnot engine is it! Last Time Adiabatic expansion Heat transfer Conduction Convection Radiation Today Second Law of Thermodynamics Heat engines Carnot cycle and Carnot engine If the first law of thermodynamics is about energy conservation, then the 2nd law is about the way in which energy flows. Examples: A bowl of water sitting in this room does not spontaneously freeze. It is impossible to construct an engine that can extract thermal energy from a system and turn all that energy into work. Thermal systems spontaneously change in only certain ways. 2nd Law of Thermodynamics We can discuss this law in a number of ways. The law basically states the way in which heat flow occurs. Heat flow between two objects brought together in thermal contact always goes from the hotter object to the colder object. Lots of ways to say the same thing! Heat Engines An engine is a device that converts heat into mechanical work. Engines must operate in cycles in order to be useful. A piston and cylinder must return to original position. The change in internal energy is zero. An engine operates between two thermal reservoirs. Schematic Diagram of Heat Engine W Qh Qc W , Qh , Qc are positive. Efficiency e W Qh Qc e Qh Qh Qc e 1 Qh Heat Engines A steam engine is one type of heat engine. Copyright © 2009 Pearson Education, Inc. Do demos • Heat engine • Steam engine Our favorite heat engine. Q h Reversible processes. Qc X Tc Remember that the work is equal to the area under the P - V curve. Total work here is work enclosed in cycle. Q h Qc X Tc Carnot Cycle • Carnot’s cycle represents the most efficient engine possible. • It operates between two heat reservoirs. • All the processes are reversible – two isothermals and two adiabatics. • We can show Qc = Tc for the Carnot Qh Th cycle. Qc Tc e 1 1 Qh Th For the highest efficiency, we need the maximum difference of temperatures in thermal reservoirs. Tc emax 1 for Carnot cycle Th Because e W / Qh , we have W eQh Wmax Tc emax Qh 1 Qh Th Conceptual Quiz: A heat engine absorbs 150 J of heat from a hot reservoir and rejects 90 J of it to a cold reservoir. What is the efficiency of this engine? Qc Tc e 1 1 Qh Th A) 20% B) 40% C) 60% D) 67% E) 90% Answer: B Qc 90 e 1 1 0.40 Qh 150 Conceptual Quiz: For the previous heat engine, you are told the temperature of the hot reservoir is 200 oC and that of the cold reservoir is 11oC. Your response is to Qc Tc e 1 1 Qh Th A) believe that this is possible. B) laugh at the idea. C) contact a patent lawyer immediately. Answer: A Tc 11 273 284 e 1 1 1 0.4 Th 200 273 473 Another statement of 2nd Law of Thermodynamics It is not possible to construct an engine whose sole effect is to transform a given amount of heat completely into work! Thermography—the detailed measurement of radiation from the body—can be used in medical imaging. Warmer areas may be a sign of tumors or infection; cooler areas on the skin may be a sign of poor circulation. Copyright © 2009 Pearson Education, Inc. Conceptual Quiz Given your experience of what feels colder when you walk on it, which of the surfaces would have the highest thermal conductivity? A) a rug B) a steel surface C) a concrete floor D) has nothing to do with thermal conductivity Conceptual Quiz Given your experience of what feels colder when you walk on it, which of the A) a rug B) a steel surface surfaces would have the C) a concrete floor highest thermal conductivity? E) has nothing to do with thermal conductivity The heat flow rate is k A (T1 − T2)/L. All things being equal, bigger k leads to bigger heat loss. From the book: Steel = 40, Concrete = 0.84, Human tissue = 0.2, Wool = 0.04, in units of J/(s.m.C°). Heat engine and refrigerator This figure shows more details of a typical refrigerator. Copyright © 2009 Pearson Education, Inc. We analyze refrigerators differently. We want to remove as much heat Qc as possible for the least amount of work. Coefficient of Performance or COP Qc COP = W Remember that Qh Qc W This is the amount of heat exhausted into kitchen. For an air conditioner, this is the heat exhausted to the outside. Air conditioner and heat pump inside house Maximize Qh Maximize Qc Heat house A heat pump can heat a house in the winter: Copyright © 2009 Pearson Education, Inc. For an ideal, reversible heat pump (i.e. Carnot cycle), we have Qc Tc Q h T h Qc W Qh Qc Qh 1 Qh Tc W Qh 1 Th To minimize W we want temperatures to be similar. Conceptual Quiz: A heat engine exhausts heat QC to a cold reservoir. The amount of work done by the engine (give best answer) W Qh Qc A) B) C) D) must be QC . must be greater than QC . must be less than QC . could be greater than QC . Answer: D W = Qh – Qc > 0 We know that Qh > Qc, but that is about all we know. The work could be Qc, but we can’t tell. The work can be greater or less than Qc, but we can’t know. The only reasonable answer is D. Conceptual Quiz The heat engine below is: A) a reversible (Carnot) heat engine B) an irreversible heat engine C) a hoax D) none of the above Qc Tc e 1 1 Qh Th For what?? TC = 310 K Conceptual Quiz 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 − TC/TH = 1 − 270/600 = 0.55. But by definition e = 1 − QL/QH = 1 − 4000/8000 = 0.5, smaller than Carnot e, thus irreversible. TC = 310 K Hiker as Heat Engine. Assume that a 65 kg hiker needs 4.3 x 103 kcal of energy to supply a day’s worth of metabolism. Estimate the maximum height the person can climb in one day, using only this amount of energy. As a rough prediction, treat the person as an isolated heat engine, operating between the internal temperature of 37°C (98.6°F) and the ambient air temperature of 20°C. Heat Pump. A heat pump is used to keep a house warm at 22°C. How much work is required of the pump to deliver 3100 J of heat into the house if the outdoor temperature is (a) 0°C, (b) -15°C. Assume ideal (Carnot) behavior.