Thermodynamics, Second Law of

Thermodynamics, Second Law of

The Second Law of Thermodynamics expresses a fundamental and limiting characteristic of all physical systems: In any closed system, the measure of disorder, or entropy, of that system must either remain the same or increase. Equivalently, in any isolated system, the amount of energy available for work—the free energy—must either remain the same or decrease. Processes in which the entropy remains the same are reversible; those in which the entropy increases are irreversible, that is, there is no realistic possibility of recovering the initial state of the system. It is principally because of the Second Law of Thermodynamics that all physical and biological systems are destined for eventual dissolution or death, even the universe itself. Without the continual input of work, energy, or material (food), every system (not necessarily closed) moves towards equilibrium, which is characterized by maximum entropy. Organization, order, and life require that the system in question be maintained far from equilibrium, and this requires input of energy from outside—from its environment.

Formulations

Long before the Second Law was expressed in terms of the change in entropy of a closed system, Sadi Carnot (1796–1832) formulated it in terms of heat and work: It is impossible to convert heat back into work at a given temperature. Although work can be converted into heat at a given temperature, the reverse cannot be effected without other changes. Heat will never travel up a temperature gradient on its own. It is only with further work that heat can be transferred from a body or a system at a given temperature to one that is either at the same temperature or at a higher temperature. Of course, heat can indeed flow from a hotter system to colder system without any work being necessary. Thus, another formulation of the Second Law is that heat cannot flow from a given system to a hotter one without work being done. A refrigerator must use energy in order to function. Other expressions of the Second Law are: A perfect heat engine is impossible to construct (Lord Kelvin's formulation), and similarly, it is impossible to construct a perfect refrigerator (Rudolf Clausius's formulation).

The clearest and most applicable formulation of the Second Law of Thermodynamics, however, is: During any process the entropy of any isolated system must either remain the same or increase. But what is entropy? It is sometimes defined as the measure of the unavailability of the energy of a system for work. An isolated system in perfect equilibrium has maximum entropy and thus has no energy available for work. It is now more usual, however, to define entropy by employing the statistical mechanical underpinnings of thermodynamics in terms of the number of microstates available to the system at a given energy. Any given macroscopic state of a system (given, for instance, by its temperature, pressure, and volume) corresponds to many different possible microscopic states of that system (arrangements and velocities of the molecules constituting it). The larger the number of possible microstates corresponding to a given macrostate, the larger the entropy of the system, and the larger the disorder of the system. The maximum entropy—and therefore the maximum disorder—is given by the situation in which the actual macrostate of the system possesses the maximum number of accessible microstates for the energy it contains. This is the state of equilibrium. Thus, what is really significant is not the absolute value of the entropy for an isolated system, but rather how far its entropy is from the maximum—how far away the system is from equilibrium. As already mentioned, this also indicates how much free energy (for work) is available in it.

The determination of the entropy and the maximum entropy, and therefore the application of the Second Law of Thermodynamics to gravitating systems, such as a cluster of stars, the galaxy, or the universe, is somewhat more complex than it is for non-gravitating systems. This is because the total entropy of such systems must include gravitational entropy as well as thermodynamic entropy, and the lowest gravitational entropy state of a system is realized when it is perfectly homogeneous—no clustering or clumping. A homogeneous self-gravitating system is obviously far from equilibrium. As the matter gradually coalesces and clumps, the gravitational entropy increases, releasing free energy through heat and radiation, which is now capable of being harnessed for work. Eventually the cores of some of these mass concentrations become hot enough for the initiation of nucleosynthesis, and even more free energy is released. Maximum gravitational entropy is achieved when the whole system becomes a single black hole. For that to happen all the free energy of the system has to be exhausted.

What was the origin of the initial extreme gravitational disequilibrium? Possibly it was an inflationary phase of the universe almost immediately after the Big Bang, during which the universe expanded incredibly fast (exponentially) in a very short time; perhaps it was certain quantum-gravity effects even earlier during the Planck era that rendered the initial state of our part of the universe very smooth. How will the universe as we know it end? In entropic death or heat death. This will occur when either the universe evolves to become something like a single black hole, or when it expands so much and so rapidly that gravity is no longer effective in drawing together whatever relic mass concentrations remain (particles or black holes). In either case, a state of equilibrium has been reached; the entropy of the universe is a maximum, and no useful energy for work or for nourishment can be found.

Sometimes people mention that life-generating or life-maintaining systems do not obey the Second Law of Thermodynamics, because in generating order they are lowering the entropy. But, in fact, they are perfect examples of the application of the Second Law. The system one must consider in this case is not just the living organism itself, nor just the community of living organisms in question, which are not isolated systems (they are in crucial and continual interaction with their environment), but rather the entire ecological system itself as isolated from what occurs outside it. Yes, the entropy of each organism and community of living organisms is kept relatively low, but only at the expense of increasing the entropy of their surroundings. The entropy of the whole isolated ecological system is increasing. If one isolates organisms in a box with a certain limited amount of food and available energy and no interactions with the world outside the box, the organisms will live and reproduce for a certain length of time. But eventually the available energy will be depleted and the food supply (both the food they started with and the food they subsequently produced) will run out, and everything in the box will reach the equilibrium that is death.

Implications for religion

The inescapable limits placed on physical and biological reality by the Second Law of Thermodynamics confront theology and religion with a serious challenge. If all is finite, transient, and destined for death and dissolution, what meaning and hope can theology and religion legitimately assert? How is the eternal destiny proclaimed by religions to be understood, and how is this seemingly insuperable limit to be transcended? These are eschatological questions. There are also questions relating to natural evil. Assuming that God works through all the laws of nature, including the Second Law, to create and maintain the world, how can one conceive God as the creator of a world in which death, disease, suffering, and the exploitation of resources is not only pervasive but essential? Finally, according to religious perspectives, the Second Law of Thermodynamics cannot have the last word. The "new heavens and the new earth," though in continuity with this world, are promised to be devoid of the transience, suffering, death, and natural evil that accompany human existence.

See also Big Bang Theory; Death; Entropy; Eschatology

Bibliography

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william r. stoeger