Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy Quiz

PDF page 711: Recall that the simple definition of energy is the ability to do work. Entropy is a measure of how much energy is not available to do work. Although all forms of energy are interconvertible, and all can be used to do work, it is not always possible, even in principle, to convert the entire available energy into work. That unavailable energy is of interest in thermodynamics, because the field of thermodynamics arose from efforts to convert heat to work.

PDF page 711: the absolute temperature at which the reversible process takes place. The SI unit for entropy is joules per kelvin (J/ K). If temperature changes during the process, then it is usually a good approximation (for small changes in temperature) to take to be the average temperature, avoiding the need to use integral calculus to find . The definition of is strictly valid only for reversible processes, such as used in a Carnot engine. However, we can find precisely even for real, irreversible processes. The reason is that the entropy of a system, like internal energy , depends only on the state of the system and not how it reached that condition. Entropy is a property of state. Thus the change in entropy of a system between state 1 and state 2 is the same no matter how the change occurs. We just need to find or imagine a reversible process that takes us from state 1 to state 2 and calculate for that process. That will be the change in entropy for any process going from state 1 to state 2. (See

PDF page 712: This result, which has general validity, means that the total change in entropy for a system in any reversible process is zero. The entropy of various parts of the system may change, but the total change is zero. Furthermore, the system does not affect the entropy of its surroundings, since heat transfer between them does not occur. Thus the reversible process changes neither the total entropy of the system nor the entropy of its surroundings. Sometimes this is stated as follows: Reversible processes do not affect the total entropy of the universe. Real processes are not reversible, though, and they do change total entropy. We can, however, use hypothetical reversible processes to determine the value of entropy in real, irreversible processes. The following example illustrates this point.

PDF page 713: It is reasonable that entropy increases for heat transfer from hot to cold. Since the change in entropy is , there is a larger change at lower temperatures. The decrease in entropy of the hot object is therefore less than the increase in entropy of the cold object, producing an overall increase, just as in the previous example. This result is very general: There is an increase in entropy for any system undergoing an irreversible process. With respect to entropy, there are only two possibilities: entropy is constant for a reversible process, and it increases for an irreversible process. There is a fourth version of the second law of thermodynamics stated in terms of entropy: The total entropy of a system either increases or remains constant in any process; it never decreases. For example, heat transfer cannot occur spontaneously from cold to hot, because entropy would decrease. Entropy is very different from energy. Entropy is not conserved but increases in all real processes. Reversible processes (such as in Carnot engines) are the processes in which the most heat transfer to work takes place and are also the ones that keep entropy constant. Thus we are led to make a connection between entropy and the availability of energy to do work.

PDF page 713: It is reasonable that entropy increases for heat transfer from hot to cold. Since the change in entropy is , there is a larger change at lower temperatures. The decrease in entropy of the hot object is therefore less than the increase in entropy of the cold object, producing an overall increase, just as in the previous example. This result is very general: There is an increase in entropy for any system undergoing an irreversible process. With respect to entropy, there are only two possibilities: entropy is constant for a reversible process, and it increases for an irreversible process. There is a fourth version of the second law of thermodynamics stated in terms of entropy: The total entropy of a system either increases or remains constant in any process; it never decreases. For example, heat transfer cannot occur spontaneously from cold to hot, because entropy would decrease. Entropy is very different from energy. Entropy is not conserved but increases in all real processes. Reversible processes (such as in Carnot engines) are the processes in which the most heat transfer to work takes place and are also the ones that keep entropy constant. Thus we are led to make a connection between entropy and the availability of energy to do work.

PDF page 713: It is reasonable that entropy increases for heat transfer from hot to cold. Since the change in entropy is , there is a larger change at lower temperatures. The decrease in entropy of the hot object is therefore less than the increase in entropy of the cold object, producing an overall increase, just as in the previous example. This result is very general: There is an increase in entropy for any system undergoing an irreversible process. With respect to entropy, there are only two possibilities: entropy is constant for a reversible process, and it increases for an irreversible process. There is a fourth version of the second law of thermodynamics stated in terms of entropy: The total entropy of a system either increases or remains constant in any process; it never decreases. For example, heat transfer cannot occur spontaneously from cold to hot, because entropy would decrease. Entropy is very different from energy. Entropy is not conserved but increases in all real processes. Reversible processes (such as in Carnot engines) are the processes in which the most heat transfer to work takes place and are also the ones that keep entropy constant. Thus we are led to make a connection between entropy and the availability of energy to do work.

PDF page 713: It is reasonable that entropy increases for heat transfer from hot to cold. Since the change in entropy is , there is a larger change at lower temperatures. The decrease in entropy of the hot object is therefore less than the increase in entropy of the cold object, producing an overall increase, just as in the previous example. This result is very general: There is an increase in entropy for any system undergoing an irreversible process. With respect to entropy, there are only two possibilities: entropy is constant for a reversible process, and it increases for an irreversible process. There is a fourth version of the second law of thermodynamics stated in terms of entropy: The total entropy of a system either increases or remains constant in any process; it never decreases. For example, heat transfer cannot occur spontaneously from cold to hot, because entropy would decrease. Entropy is very different from energy. Entropy is not conserved but increases in all real processes. Reversible processes (such as in Carnot engines) are the processes in which the most heat transfer to work takes place and are also the ones that keep entropy constant. Thus we are led to make a connection between entropy and the availability of energy to do work.

PDF page 715: When entropy increases, a certain amount of energy becomes permanently unavailable to do work. The energy is not lost, but its character is changed, so that some of it can never be converted to doing work—that is, to an organized force acting through a distance. For instance, in the previous example, 933 J less work was done after an increase in entropy of 9.33 J/K occurred in the 4000 J heat transfer from the 600 K reservoir to the 250 K reservoir. It can be shown that the amount of energy that becomes unavailable for work is 15.59 where is the lowest temperature utilized. In the previous example, 15.60 as found.

PDF page 716: Entropy is related not only to the unavailability of energy to do work—it is also a measure of disorder. This notion was initially postulated by Ludwig Boltzmann in the 1800s. For example, melting a block of ice means taking a highly structured and orderly system of water molecules and converting it into a disorderly liquid in which molecules have no fixed positions. (See Figure 15.35.) There is a large increase in entropy in the process, as seen in the following example.

PDF page 716: for water, so that 15.63 Now the change in entropy is positive, since heat transfer occurs into the ice to cause the phase change; thus,

PDF page 717: structure is replaced by a more random and less orderly movement of molecules without fixed locations or orientations. Its entropy increases because heat transfer occurs into it. Entropy is a measure of disorder. In another easily imagined example, suppose we mix equal masses of water originally at two different temperatures, say and . The result is water at an intermediate temperature of . Three outcomes have resulted: entropy has increased, some energy has become unavailable to do work, and the system has become less orderly. Let us think about each of these results. First, entropy has increased for the same reason that it did in the example above. Mixing the two bodies of water has the same effect as heat transfer from the hot one and the same heat transfer into the cold one. The mixing decreases the entropy of the hot water but increases the entropy of the cold water by a greater amount, producing an overall increase in entropy. Second, once the two masses of water are mixed, there is only one temperature—you cannot run a heat engine with them. The energy that could have been used to run a heat engine is now unavailable to do work. Third, the mixture is less orderly, or to use another term, less structured. Rather than having two masses at different temperatures and with different distributions of molecular speeds, we now have a single mass with a uniform temperature. These three results—entropy, unavailability of energy, and disorder—are not only related but are in fact essentially equivalent.

PDF page 717: structure is replaced by a more random and less orderly movement of molecules without fixed locations or orientations. Its entropy increases because heat transfer occurs into it. Entropy is a measure of disorder. In another easily imagined example, suppose we mix equal masses of water originally at two different temperatures, say and . The result is water at an intermediate temperature of . Three outcomes have resulted: entropy has increased, some energy has become unavailable to do work, and the system has become less orderly. Let us think about each of these results. First, entropy has increased for the same reason that it did in the example above. Mixing the two bodies of water has the same effect as heat transfer from the hot one and the same heat transfer into the cold one. The mixing decreases the entropy of the hot water but increases the entropy of the cold water by a greater amount, producing an overall increase in entropy. Second, once the two masses of water are mixed, there is only one temperature—you cannot run a heat engine with them. The energy that could have been used to run a heat engine is now unavailable to do work. Third, the mixture is less orderly, or to use another term, less structured. Rather than having two masses at different temperatures and with different distributions of molecular speeds, we now have a single mass with a uniform temperature. These three results—entropy, unavailability of energy, and disorder—are not only related but are in fact essentially equivalent.