Thermodynamics [ENGR 251] [Lyes KADEM 2007]

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Indeed, no restriction is imposed by the first law on the direction of the process: this is the role of the second law.

1 CHAPTER V The first law of thermodynamics is a representation of the conservation of energy. It is a necessary, but not a sufficient, condition for a process to occur. Indeed, no restriction is imposed by the first law on the direction of the process: this is the role of the second law. To illustrate this, let us assume the processes below, your opion, without any tervention from you, what is the most probable process (from left to right or the verse): g?? HOT? COLD 64

2 Consider now the followg arrangement: Liquid Paddlewheel Allowg the weight to fall will turn the paddlewheel which will do work on the fluid system. Initially this may crease the ketic energy of the fluid as it churns, but time the circulation will stop. hen this happens the temperature of the fluid will rise and the heat will be transferred to the surroundgs. From a 1 st Law perspective there is no reason why one could not simply supply this same amount of heat to the fluid so that the paddlewheel would turn and the weight would be raised. However, no one has ever built a successful enge based on this prciple. It simply wouldn t work. The 2 nd Law provides us with a basis to determe why such a process isn t feasible. I. Heat Enges hile the 2 nd Law of Thermodynamics is applicable to a wide range to topics, much of our understandg of the prciple comes from the study of heat enges. e will therefore use enges as a basis for much of our study. 23 = 2 Combustor 3 C Compressor Turbe T 1 Cooler 4 14 = out 65

3 In this cycle air will circulate through the heat enge to transport energy from one component to the next. This fluid is often referred to as the workg fluid. C = ork required to compress the workg fluid T = Usable work produced by the enge. This work may be used to drive a truck or car, turn a propeller, an electric generator or to perform some other useful task. = Thermal energy supplied to the system. This may arise from combustion, a solar collector, a nuclear reactor or any other available heat source. out = Thermal energy rejected to the environment. The cooler could be a radiator similar to that used with an automobile enge. Sce operation of the enge requires a work put to turn the compressor, a portion of the output work may be utilized for this purpose, we defe, therefore, the net work as: net = T C This is a thermodynamic cycle. By defition the cycle begs and ends at the same pot. In the case of an open cycle heat rejection occurs as the exhaust is emitted to the atmosphere. Hot exhaust gases are cooled to the temperature of the surroundgs before enterg the compressor. From the 1 st Law of Thermodynamics, we have: Δ Esystem = out For the cycle, sce the startg and endg pots are the same, there is no change ternal energy, so: T C = out I.1. Cycle Diagram It is very convenient to represent the heat enge processes on a PV diagram: P Constant Pressure Heat Addition 2 3 Adiabatic Expansion Note that without a heat rejection, the cycle does not return to its itial state Adiabatic Compression 1 4 Constant Pressure Heat Rejection V 66

4 I.2. Thermal Efficiency of a heat enge The efficiency of a heat enge can be defed as the ratio of the useful work out (the net work) to the energy that must be put (the energy that we pay for). η = Sce we have that net = out, we may substitute to the above equation and fd: η net ( ) out = 1 = It is probably not too surprisg that we want to mimize the fraction of rejected heat the last part of the equation order to atta the maximum efficiency. out I.3. Second law of Thermodynamics: Kelv-Planck statement GAS o 30 C GAS 90 o C GAS 30 o C Reservoir at 100 o C Reservoir at 20 o C In the drawg above, a piston-cylder contas a gas at 30 o C. A weight is placed on the piston. Heat is then added to the gas from a reservoir at 100 o C so that the gas expands. As the gas expands it does work to raise the weight and piston. The weight now is at a higher potential energy than at state one. e slide the weight off of the piston at the higher elevation. Assume that the frictional forces slidg the weight are negligible. Now, we wish to raise a second weight. That is, we wish the heat enge to contue to do work. The gas side the cylder is still heated and will not return to its itial position unless the gas is cooled. If you consider the gas turbe cycle and the piston-cylder arrangement, both cases we have seen that it is necessary to reject heat at the end of the work process order to return the cycle to its itial state and repeat the process. e generalize this observation as the 2 nd Law of Thermodynamics: 67

5 It is impossible for any device that operates on a cycle to receive heat from a sgle reservoir and produce a net amount of work. -- Kelv-Planck statement of 2 nd Law. I.4. Refrigeration Cycles and Clausius statement of the second law of Thermodynamics Up to this pot we have only considered heat enges. Refrigeration cycles operate a similar manner. 23 = out [to outdoor environment] 2 Condenser 3 C Compressor 1 Evaporator 4 14 = out [from door environment] The vapor refrigeration cycle volves four components, designed to produce four respective process on the workg fluid. (Process 1-2) The compressor is designed to raise the pressure of the workg fluid adiabatically. As the vapor is compressed, the temperature will rise. (Process 2-3) The fluid is passed through the condenser. Here no work is done on the fluid, but it is cooled to a saturated liquid. (This is the part of a residential AC unit which is located outdoors. Air is circulated around tubes contag the workg fluid by a fan.) (Process 3-4) An expansion valve is simply a device, which does no work, nor does it transfer heat to or from the workg fluid. It is simply a device to allow the pressure to drop to a lower value. A First Law analysis of this process will show that it is a constant enthalpy process. It is common for some of the liquid to flash to vapor as the fluid expands. At the same time, the temperature will drop significantly. (Process 4-1) The fluid is passed through the evaporator. This device consists of cold tubes often seen located side the house a residential unit. Here air from side the house is blown over the cold tubes contag the workg fluid. As the cold fluid gas heat, no work is done on the fluid. The workg fluid is largely vaporized this process as it returns to state 1 to beg the cycle aga. You can image that a refrigeration cycle, heat will not flow from a low temperature to a high temperature without work. e see the put of work the basic refrigeration cycle operatg 68

6 the compressor. This prciple is accepted as an alternate statement of the Second Law of Thermodynamics. It is impossible to construct a device that operates a cycle and produces no effect other than the transfer of heat from a lower-temperature body to a higher-temperature body. -- Clausius statement of 2 nd Law. The two statements of the 2 nd Law can be shown to be equivalent. Practical statement of the second law of Thermodynamics In the normal course of events, when thgs are not actively mataed, they deteriorate. Suns burn out, mountas crumble, cars rust, houses fall down, etc. The reverse process does not happen without tervention. You might buy an old, rusty car and restore it, but it will take work. In a like fashion, process volvg an energy transfer will only occur such a way so as to decrease the quality of energy. e can, with a fite control volume, transfer energy to the system so as to crease the quality of energy with that system. However, the work that we put required that we decrease the quality of energy from an area outside the system. hen we consider the universe as a whole, the quality of energy the universe has still deteriorated. I.4.1. Coefficient of performance hen describg heat enges, we troduced the concept of enge efficiency as the desired output divided by the energy put. Similarly, we defe the coefficient of performance (COP) of a refrigerator: COP = Desired Ouput Required Input = 14 net 14 = The defition is basically the same as that of thermal efficiency. The primary reason for the change termology is that a COP: is often greater than 1. The term is used to avoid speakg of any efficiency greater than 100%. I.5. Reversibility Consider a system of pulleys and weights as shown: + δ 69

7 In order for the weight on the right to raise the weight on the left, it is essential that + δ >. How large must δ be? ell, it must be large enough that it compensates for the effects of friction the pulley, the friction associated with the flexg of the cable, etc. If we use very good beargs, then the required extra weight on the right may approach zero. Can it reach zero? No, this would result static equilibrium and the weights will no move. It is essential that δ be greater than zero; it may approach, but never reach zero, even with perfect beargs. e see that, order for the process of raisg the left weight to occur, the loss potential energy on the right must be greater than the ga potential energy on the left. As an idealization only, we may assume that the weight δ may be so small that it can be treated as zero. In such a case, the weight on the right and left are equal and the direction that the pulley moves would be completely reversible. Such processes never occur nature, but may be approached the limit. 70

Thermodynamics Lecture Series

Thermodynamics Lecture Series Second Law uality of Energy Applied Sciences Education Research Group (ASERG) Faculty of Applied Sciences Universiti Teknologi MARA email: drjjlanita@hotmail.com http://www.uitm.edu.my/faculties/fsg/drjj.html