Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency Quiz

PDF page 695: predicts that it would be extremely unlikely for the water molecules contained in these particular floes to reform the distinctive alligatorlike shape they formed when the picture was taken in the summer of 2009. (credit: Patrick Kelley, U.S. Coast Guard, U.S. Geological Survey) The second law of thermodynamics deals with the direction taken by spontaneous processes. Many processes occur spontaneously in one direction only—that is, they are irreversible, under a given set of conditions. Although irreversibility is seen in day-to-day life—a broken glass does not resume its original state, for instance—complete irreversibility is a statistical statement that cannot be seen during the lifetime of the universe. More precisely, an irreversible process is one that depends on path. If the process can go in only one direction, then the reverse path differs fundamentally and the process cannot be reversible. For example, as noted in the previous section, heat involves the transfer of energy from higher to lower temperature. A cold object in contact with a hot one never gets colder, transferring heat to the hot object and making it hotter. Furthermore, mechanical energy, such as kinetic energy, can be completely converted to thermal energy by friction, but the reverse is impossible. A hot stationary object never spontaneously cools off and starts moving. Yet another example is the expansion of a puff of gas introduced into one corner of a vacuum chamber. The gas expands to fill the chamber, but it never regroups in the corner. The random motion of the gas molecules could take them all back to the corner, but this is never observed to happen. (See Figure 15.15.)

PDF page 695: predicts that it would be extremely unlikely for the water molecules contained in these particular floes to reform the distinctive alligatorlike shape they formed when the picture was taken in the summer of 2009. (credit: Patrick Kelley, U.S. Coast Guard, U.S. Geological Survey) The second law of thermodynamics deals with the direction taken by spontaneous processes. Many processes occur spontaneously in one direction only—that is, they are irreversible, under a given set of conditions. Although irreversibility is seen in day-to-day life—a broken glass does not resume its original state, for instance—complete irreversibility is a statistical statement that cannot be seen during the lifetime of the universe. More precisely, an irreversible process is one that depends on path. If the process can go in only one direction, then the reverse path differs fundamentally and the process cannot be reversible. For example, as noted in the previous section, heat involves the transfer of energy from higher to lower temperature. A cold object in contact with a hot one never gets colder, transferring heat to the hot object and making it hotter. Furthermore, mechanical energy, such as kinetic energy, can be completely converted to thermal energy by friction, but the reverse is impossible. A hot stationary object never spontaneously cools off and starts moving. Yet another example is the expansion of a puff of gas introduced into one corner of a vacuum chamber. The gas expands to fill the chamber, but it never regroups in the corner. The random motion of the gas molecules could take them all back to the corner, but this is never observed to happen. (See Figure 15.15.)

PDF page 696: Heat transfer occurs spontaneously from higher- to lower-temperature bodies but never spontaneously in the reverse direction.

PDF page 696: gas let into this vacuum chamber quickly expands to uniformly fill every part of the chamber. The random motions of the gas molecules will never return them to the corner. The fact that certain processes never occur suggests that there is a law forbidding them to occur. The first law of thermodynamics would allow them to occur—none of those processes violate conservation of energy. The law that forbids these processes is called the second law of thermodynamics. We shall see that the second law can be stated in many ways that may seem different, but which in fact are equivalent. Like all natural laws, the second law of thermodynamics gives insights into nature, and its several statements imply that it is broadly applicable, fundamentally affecting many apparently disparate processes. The already familiar direction of heat transfer from hot to cold is the basis of our first version of the second law of thermodynamics.

PDF page 696: Another way of stating this: It is impossible for any process to have as its sole result heat transfer from a cooler to a hotter object.

PDF page 696: Now let us consider a device that uses heat transfer to do work. As noted in the previous section, such a device is called a heat engine, and one is shown schematically in Figure 15.16(b). Gasoline and diesel engines, jet engines, and steam turbines are all heat engines that do work by using part of the heat transfer from some source. Heat transfer from the hot object (or hot reservoir) is denoted as , while heat transfer into the cold object (or cold

PDF page 696: Now let us consider a device that uses heat transfer to do work. As noted in the previous section, such a device is called a heat engine, and one is shown schematically in Figure 15.16(b). Gasoline and diesel engines, jet engines, and steam turbines are all heat engines that do work by using part of the heat transfer from some source. Heat transfer from the hot object (or hot reservoir) is denoted as , while heat transfer into the cold object (or cold

PDF page 697: It is impossible in any system for heat transfer from a reservoir to completely convert to work in a cyclical process in which the system returns to its initial state.

PDF page 697: A cyclical process brings a system, such as the gas in a cylinder, back to its original state at the end of every cycle. Most heat engines, such as reciprocating piston engines and rotating turbines, use cyclical processes. The second law, just stated in its second form, clearly states that such engines cannot have perfect conversion of heat transfer into work done. Before going into the underlying reasons for the limits on converting heat transfer into work, we

PDF page 697: noted, a cyclical process brings the system back to its original condition at the end of every cycle. Such a system’s internal energy is the same at the beginning and end of every cycle—that is, . The first law of thermodynamics states that 15.22 where is the net heat transfer during the cycle ( ) and is the net work done by the system. Since for a complete cycle, we have 15.23 so that 15.24 Thus the net work done by the system equals the net heat transfer into the system, or 15.25 just as shown schematically in Figure 15.16(b). The problem is that in all processes, there is some heat transfer to the environment—and usually a very significant amount at that. In the conversion of energy to work, we are always faced with the problem of getting less out than we put in. We define conversion efficiency to be the ratio of useful work output to the energy input (or, in other words, the

PDF page 698: ratio of what we get to what we spend). In that spirit, we define the efficiency of a heat engine to be its net work

PDF page 698: output divided by heat transfer to the engine ; that is,

PDF page 698: making it clear that an efficiency of 1, or 100%, is possible only if there is no heat transfer to the environment ( ). Note that all s are positive. The direction of heat transfer is indicated by a plus or minus sign. For example, is out of the system and so is preceded by a minus sign.

PDF page 698: making it clear that an efficiency of 1, or 100%, is possible only if there is no heat transfer to the environment ( ). Note that all s are positive. The direction of heat transfer is indicated by a plus or minus sign. For example, is out of the system and so is preceded by a minus sign.