A second way of stating the second law is sometimes phrased as something along the lines of “the entropy of the universe always increases.” For the purposes of thermodynamic calculations a property can be defined called “entropy.” This property is very exact and rigorous in a quantitative way, and can be used for both practical and theoretical calculations. However, for the purposes of this discussion, it will serve to think a little more loosely of entropy as being representative of the amount of “disorder” in a system. This expression of the second law signifies that for any real process the disorder of the universe will increase. It is important to note the part about “the universe”. That is, for any particular system going through a process the entropy may increase or decrease. However, if it decreases, then we can be sure that the increase in the entropy of the surroundings (i.e. the rest of the universe) caused by the process is bigger than the decrease in entropy was for the system.
This statement of the second law leads to the thermodynamic equivalent of the “frictionless pulley”, i.e. it establishes a hypothetical standard against which real processes can be measured. This standard is the very best that could theoretically be achieved by any process. For some processes (those in which no heat is transferred) this theoretical limit is for the process to occur with zero increase in entropy of the universe. That is, actual processes will have an increase in entropy, theoretically ideal processes will have no increase in entropy and no process is even theoretically possible in which the entropy of the universe decreases.
This limit, along with similar limits for processes that do include heat transfer, is often utilized as a check by people who are tasked with evaluating proposed inventions involving energy transformations. Before investing the effort to understand and evaluate all the details of what might be a very complicated machine, the evaluator can simply check whether the overall operation of the device as described would result in a net decrease in entropy for the device and the surroundings. If it does, the device would violate the second law and cannot possibly function as described.
A second implication of this expression of the second law is that all processes have directions in which they will proceed and directions in which they will not. The allowable directions will be those that result in an increase in entropy for the universe. Perhaps the easiest example of this to visualize is the case of a hot bowl of soup cooling off in a cool room. The room will never spontaneously cool off while the hot soup gets hotter even though such a process could be imagined that would not violate the first law. The total amounts of energy flowing are governed by the first law, and the direction is governed by the second law.This behavior of heat flow is sometimes expressed by saying “heat always flows downhill” where “downhill” is established by the temperature gradient. We’ll come back to this later as another statement of the second law, however, it is immediately clear that such an observation for heat is not stranger than the corresponding observation that “water always flows down hill” where “down hill” is determined by gravity, or a potential energy gradient.
Many chemical processes have a particular direction in which they will proceed for a given set of conditions (temperature, pressure, concentration, etc.) and those directions are always in accord with the second law. Further, in some cases where it is not otherwise clear, it is possible to predict the direction of a reaction from second law considerations.
Finally, it is worth noting that this statement of the second law is a preferred starting point for many of the philosophical discussions that are connected to thermodynamics. Some of the simplest and most profound of these deal with the beginning and end of the universe. For example, if the total entropy of the universe as a whole always increases, what will happen when a state of “maximum entropy” is reached? Will the universe ultimately “wind down” to a final state of complete uniformity? How did the universe get “wound up” in the first place? These and other questions flow directly from an understanding of the second law, and constitute what may be one of the more prominent and popular contact points between engineering and philosophy.
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