Chapter 6 Notes PDF

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Summary

6 Steam Engine Steam engine first engine driven heat, rather than animals, water, or wind o Initial function was to pump water out of mines in England o First practical and safe steam engine reciprocating device o Currently used in electric power plants and in aircraft carriers and submarines See sc...

Description

6.4 Steam Engine •

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Steam engine – first engine driven by heat, rather than animals, water, or wind o Initial function was to pump water out of mines in England o First practical and safe steam engine – reciprocating piston-cylinder device o Currently used in electric power plants and in nuclear-powered aircraft carriers and submarines See schematic and PV diagrams on p149 (169/508) Schematic: water is conveyed from the condenser, through the boiler, into the expansion chamber, and back to the condenser o The water in the condenser is at a pressure less than atmospheric and at a temperature less than the normal boiling point o By means of a pump, water is introduced into the boiler, which is at a much higher pressure and temperature o In the boiler, the water is first heated to its boiling point and then vaporized, both processes taking place approximately at constant high pressure. The steam is then raised to a temperature greater than the normal boiling point at the same pressure. It is then allowed to flow into a cylinder, where it expands approximately adiabatically against a piston or a set of turbine blades, until its pressure and temperature drop to that of the condenser. In the condenser, finally, the steam condenses into the water at the same temperature and pressure as at the beginning, and the cycle is complete In the actual operation of the steam engine, there are several processes that render an exact analysis difficult: turbulence caused by the pressure difference required to cause the flow of the steam from one part of the apparatus to another, friction, conduction of heat through the walls during expansion of the steam, and heat transfers due to a finite temperature difference between the furnace and the boiler A first approximation to the discussion of the steam engine may be made by introducing some simplifying assumptions which, although in no way realizable in practice, provide at least an upper limit to the efficiency of such a plant and which define an idealized cycle (Rankine cycle) in terms of which the actual behavior of a steam plant may be discussed In the Rankine cycle, all processes are assumed to be well behaved; complications that arise from turbulence, friction, and heat losses are thus eliminated See Figure 6-3(b) p149 (169/508) – at point 1 we have liquid water at the temperature and pressure of the condenser Four processes o 1 → 2 Adiabatic compression of water to the pressure of the boiler ▪ Only very small changes of temperature and volume of the liquid take place during this process o 2 → 3 Isobaric heating of water to the boiling point, vaporization of water into saturated steam, and superheating of steam to a temperature TH higher than the boiling point ▪ Heat |QH| enters the system from a hot reservoir o 3 → 4 Adiabatic expansion of superheated steam into wet steam o 4 → 1 Isobaric, isothermal condensation of steam into saturated water at the temperature TL (condensation process)

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Heat |QL| is rejected by the system to the atmosphere, a reservoir at TL Condensation process must exist in order to bring the system back to its initial state 1 Since heat is always rejected during the condensation of water, |QL| cannot be made equal to zero and therefore, the input |QH| cannot be converted completely into work. So the efficiency of the idealized steam engine is always less than 100% Actual operating thermal efficiency of a steam power plant: 30-40%

6.5 The Stirling Engine • • •

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Robert Stirling designed and patented a hot-air engine that could convert some of the energy liberated by a burning fuel into work See Figure 6-4(a) p151 (171/508) Two pistons, an expansion piston on the left and a compression piston on the right, are connected to the same shaft. As the shaft rotates, these pistons move out of phase, with the aid of suitable connecting linkages. The space between the two pistons is filled with a fixed amount of gas, usually hydrogen or helium, which is recycled from one cylinder to the other. The lefthand portion of the space is kept in contact with a high-temperature reservoir (burning fuel), while the right-hand portion is in contact with a low-temperature reservoir (atmosphere). Between the two cylinders is a device R, called a regenerator, consisting of a packing of fine wire screens to form a kind of metal sponge. The regenerator serves as an internal reservoir, which exchanges heat with the gas as it passes back and forth through the regenerator The Stirling cycle consists of four processes plotted in Figure 6-4(b) p151 (171/508) o 1 → 2 The left piston remains at the top of the cylinder. The right piston moves halfway up its cylinder, compressing low-temperature gas that is in contact with the lowtemperature reservoir and, therefore, causing heat |QL| to leave. This is an approximately isothermal compression and is depicted as a rigorously isothermal process at the temperature TL o 2 → 3 The left piston moves down and the right piston up, so that there is no change in volume occupied by the gas. However, gas is forced through the regenerator from the low-temperature side to the high-temperature side and enters the left-hand side at the higher temperature TH. To raise the temperature of the gas, the regenerator supplies heat |QR| to the gas. Note that the process is at constant volume o 3 → 4 The right piston remains stationary. The left piston continues moving down while in contact with the high-temperature reservoir, which causes the gas to expand approximately isothermally. Additional heat |QH| is absorbed from the outside at the temperature TH o 4 → 1 Both pistons move in opposite directions, thereby forcing gas through the regenerator from the high-temperature to the low-temperature side and giving up approximately the same amount of heat |QR| to the regenerator that is absorbed in the process 2 → 3, so the regenerator heats cancel each other during one cycle. The process takes place at practically constant volume The net result of the Stirling cycle is the absorption of heat |QH| at the high temperature TH, the rejection of heat |QL| at the low temperature TL, and the delivery of work |W| = |QH| - |QL| to the surroundings, with no net heat transfer resulting from the two constant-volume processes

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Figure 6-4(b) is based on the assumptions that the gas is ideal, no leakage of gas takes place, no heat is lost or gained through cylinder walls, no heat is conducted from the regenerator to the surrounding, and there is no friction In practice, there would still be some heat |QL| rejected at the lower temperature, and, therefore, all the input |QH| could not be converted into work, rendering the efficiency less than 100% The actual operating thermal efficiency of Stirling engines is 35-45% Unique advantages of Stirling engine o Engine can use any heat source, from heating due to radioactivity to combustion of biomass waste products o Using open-air combustion, the engine does not produce toxic exhaust o It operates quietly o Can be used in automobiles, but internal-combustion engines are already quite good for this application o Application: implantable Stirling engine for artificial heart power Modification of Stirling engine – Ringbom Stirling engine o Uses only one reciprocating piston instead of two pistons o The regenerator (displacer) oscillates between the closed end of the cylinder and the piston. As a result, the Ringbom Stirling engine is strikingly simpler than all the Stirling engines that had preceded it

6.7 Refrigerator; Clausius’ Statement of the 2nd Law •

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Heat engine takes a working substance through a cycle in such a sequence of processes that some heat is absorbed by the system from a high-temperature heat reservoir, a smaller amount of heat is rejected to a low-temperature heat reservoir, and a net amount of work is done by the system on the surroundings If we imagine a cycle performed in a sequence of processes opposite to that of an engine, then some heat is absorbed by the system from a heat reservoir at a low temperature, a larger amount of heat is rejected to the heat reservoir at a higher temperature, and a net amount of work is done on the system by the surroundings. A machine that performs a cycle in this direction is called a refrigerator, and the working substance (system) is called a refrigerant Refrigerators used for climate control are the air-conditioner and the heat pump See schematic diagram on Figure 6-6 p155 (175/508) o |QH| is the amount of heat rejected by the refrigerant to the high-temperature reservoir o |QL| is the amount of heat absorbed by the refrigerant from the low-temperature reservoir o |W| is the net work done on the refrigerant by the surroundings Since the refrigerant undergoes a cycle, there is no change in internal energy, and the first law becomes |QL|-|QH|=|W| or |QH|=|QL|+|W| o The heat rejected to the high-temperature reservoir is larger than the heat extracted from the low-temperature reservoir by the amount of work done on the refrigerant Purpose of refrigerator is to extract as much heat |QL| as possible from the low-temperature reservoir with the expenditure of as little work |W| as possible

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Work is always necessary to transfer heat from a lower-temperature reservoir to a highertemperature reservoir, because it is a fact of nature that heat does not flow spontaneously from a lower-temperature reservoir to a higher-temperature reservoir This negative statement leads us to the Clausius statement of the second law o It is impossible to construct a refrigerator that, operating in a cycle, will produce no effect other than the transfer of heat from a lower-temperature reservoir to a highertemperature reservoir Kelvin-Planck and Clausius statements appear to be quite unconnected, but we shall see immediately that they are in all respects equivalent

6.9 Reversibility and Irreversibility • •

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The performance of work may always be described by the operation of a machine that serves to increase or decrease the potential energy of a mechanical system Imagine a suspended object coupled, by means of suitable pulleys, to a system so that any work done by or on the system can be described in terms of the raising or lowering of the object. Imagine a series of reservoirs which may be put in contact with the system and in terms of which any flow of heat to or from the system may be described We shall refer to the suspended object and the series of reservoirs as the local surroundings of the system. The local surroundings are, therefore, those parts of the surroundings which interact directly with the system. Other machines and reservoirs which are accessible and which might interact with the system constitute the auxiliary surroundings of the system, or the rest of the universe (finite portion of the world consisting of the system and those surroundings which may interact with the system) Suppose a process occurs in which: o The system proceeds from an initial state i to a final state f o The suspended object is lowered to an extent that W units of work are performed on the system o A transfer of heat |Q| takes place from the system to the series of reservoirs If, at the conclusion of this process, the system may be restored to its initial state i, the object lifted to its former level, and the reservoirs caused to part with the same amount of heat |Q|, without producing any changes in any other mechanical device or reservoir in the universe, the original process is reversible o A reversible process is one that is performed in such a way that, at the conclusion of the process, both the system and the local surroundings may be restored to their initial states without producing any changes in the rest of the universe (all the initial states must be recoverable) o A process that does not fulfill these stringent requirements is irreversible Since dissipation is present in all real processes, all natural processes are irreversible

6.10 External Mechanical Irreversibility • •

See schematic process in Figure 6-9 p160 (180/508) Five examples that illustrate the isothermal transformation of work through a system (which remains unchanged) into internal energy of a reservoir o Friction from rubbing two solids in contact with a reservoir

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o Irregular stirring of a viscous liquid in contact with a reservoir o Inelastic deformation of a solid in contact with a reservoir o Transfer of charge through a resistor in contact with a reservoir o Magnetic hysteresis of a material in contact with a reservoir In order to restore the system and its local surroundings to their initial states without producing changes elsewhere, |Q| units of heat would have to be extracted from the reservoir and converted completely into work. Since this would involve a violation of the second law (Kelvin statement), all processes of the above type are irreversible See Figure 6-10 p160 (180/508) Five examples that illustrate the adiabatic transformation of work into internal energy of a system o Friction from rubbing two thermally insulated solids o Irregular stirring of a viscous thermally insulated liquid o Inelastic deformation of a thermally insulated solid o Transfer of charge through a thermally insulated resistor o Magnetic hysteresis of a thermally insulated material A process of this type is accompanied by a rise of temperature of the system from, say, Ti to Tf. In order to restore the system and its local surroundings to their initial states without producing changes elsewhere, the internal energy of the system would have to be decreased by extracting Uf – Ui units of heat, thus lowering the temperature from Tf to Ti, and this heat would have to be completely converted into work. Since this violates the second law, all processes of the above type are irreversible The transformation of work into internal energy either of a system or of a reservoir is seen to take place through the agency of such phenomena as friction, viscosity, inelasticity, electric resistance, and magnetic hysteresis. The effects are known as dissipative effects and the work is said to be dissipated. Processes involving the dissipation of work into internal energy exhibit external mechanical irreversibility It is a matter of everyday experience that dissipative effects, particularly friction, are always present in machines. Friction may be reduced considerably by suitable lubrication, but experience has shown that it can never be completely eliminated o If friction could be eliminated, then a machine could run indefinitely without violating either of the two laws of thermodynamics – it would run but produce no work o The operation of a machine that has no dissipation of work and thus violates the fact that all natural processes are irreversible is called a perpetual motion machine of the third kind o Friction renders a process irreversible, since heat is produced by friction in whichever direction the process is traversed The Kelvin-Planck statement and Clausius statement each independently and equivalently establish the second law The impossibility of creating three kinds of perpetual motion machines may be used to formulate the first and second laws of thermodynamics and the definition of reversibility If we were to state the very broad laws of thermodynamics in a positive sense, then, in principle, it would require a very large number of experiments to verify the laws. On the other hand, by

stating at least the second law in a negative sense, it is asserted that if a single, wellsubstantiated violation of the statement can be found, then the law is not valid 6.11 Internal Mechanical Irreversibility •

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The following very important natural processes involve the transformation of internal energy of a system into mechanical energy and then back into internal energy again: o Ideal gas rushing into a vacuum (free expansion, i.e. Joule expansion) o Gas flowing through a porous plug (throttling process, i.e. Joule-Thomson expansion) o Snapping of a stretched wire after it is cut o Collapse of a soap film after it is punctured Irreversibility of first process o During a free expansion, no interactions take place, and hence there are no local surroundings. The only effect produced is a change of state of an ideal gas from a volume Vi and temperature T to a larger volume Vf at the same temperature. To restore the gas to its initial state, it would have to be compressed isothermally to the volume Vi. If the compression were performed quasi-statically and there were no friction between the piston and cylinder, an amount of work W would have to be done by some outside mechanical device, and an equal amount of heat would have to flow out of the gas into a reservoir at the temperature T

6.12 External and Internal Thermal Irreversibility 6.13 Chemical Irreversibility 6.14 Conditions for Reversibility...