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# Entropy

Clausius first introduced the concept of entropy was first introduced in 1850 by Clausius as an exact mathematical method of testing whether a specific process violates the second law of thermodynamics. The test starts with the interpretation that if an amount of heat Q flows right into a heat reservoir at constant temperature level T, its entropy S increases by ΔS = Q/T. (This equation provides a thermodynamic definition of temperature level that can reveal identical to the conventional thermometric one.) Assume that there are two heat reservoirs, R1 and R2, at temperature levels T1 and T2. If an amount of heat Q flows from R1 to R2, then the net entropy change for both reservoirs will be ΔS is positive, provided that T1 > T2. Therefore, the observation that heat never flows automatically from a colder region to a hotter area (the Clausius form of the second law of thermodynamics) is equivalent to requiring the net entropy change to be positive for a spontaneous flow of heat. If T1 = T2, the reservoirs remain in equilibrium and ΔS = 0.

The condition ΔS ≥ 0 identifies the maximum feasible efficiency of heat engines. Suppose that some system capable of doing work cyclically (a heat engine) absorbs heat Q1 from R1 and exhausts heat Q2 to R2 for every complete cycle. Since the system goes back to its original state at the end of a process, its energy does not change. Then, by conservation of power, the work done per cycle is W = Q1 − Q2 and the net entropy change for both reservoirs is To make W feasible, Q2 needs to keep as small as possible relative to Q1. However, Q2 can not be zero since this would undoubtedly make ΔS harmful and violate the second law of thermodynamics. The smallest potential value of Q2 corresponds to the condition ΔS = 0, yielding. This is the fundamental equation limiting the effectiveness of all heat engines whose function is to transform heat right into work (such as electrical power generators). The real effectiveness is specified to be the fraction of Q1 that is converted to work (W/Q1), which is equivalent to equation: The maximum effectiveness for a given T1 and T2 is thus: A process for which ΔS = 0 is stated to be reversible since an infinitesimal change would certainly be sufficient to make the heat engine run in reverse as a refrigerator.

## Entropy and Heat Death

The example of a heat engine illustrates the several methods by which can apply the second law of thermodynamics. One way to generalize the model is to consider the heat engine and its heat reservoir as components of an isolated (or closed) system, i.e., one that does not exchange heat or work with its surroundings. For example, the heat engine and reservoir might enclose in a rigid container with insulating wall surfaces. In this case, the second law of thermodynamics states that whatever procedure occurs inside the container, its entropy must increase or continue to be the same within the limit of a reversible process. Likewise, if the universe is an isolated system, its entropy also must increase with time. Indeed, the implication is that the universe must ultimately experience a “Heat Death” as its entropy considerably increases towards a maximum value and all components enter into thermal equilibrium at a constant temperature level. Afterwards, no additional charges would certainly be feasible, including converting heat into valuable work. Generally, the equilibrium state for an isolated system is precisely that state of maximum entropy.

## Entropy and The Arrow of Time

The unavoidable increase of entropy with time for isolated systems supplies an “Arrow of Time” for those systems. Everyday life offers no difficulty distinguishing the forward flow of time from its opposite. For example, if a movie showed a glass of warm water automatically changing into hot water with ice drifting on the top, it would quickly appear that the film was running in reverse because the procedure of heat flowing from warm water to hot water would undoubtedly violate the second law of thermodynamics. However, this evident asymmetry between the forward and reverse directions for the flow of time does not persist at the level of fundamental interactions. A viewer watching a movie revealing two water molecules colliding would certainly not have the ability to tell whether the film was running forward or backward.

So precisely, what is the link between entropy and the second law? Remember that heat at the molecular level is the random kinetic energy of particles’ motion and collisions between particles, which provide the microscopic mechanism for transferring heat energy from one place to another. Because individual crashes are unchanged by reversing the direction of time, heat can flow just as well in one direction as in the other. Hence, from the point of view of fundamental interactions, there is absolutely nothing to prevent an opportunity event in which various slow-moving (cool) particles take place to gather with each other in one place and form ice while the surrounding water becomes hotter. Such opportunity events might occur periodically in a vessel containing just a few water molecules. However, the same possible events are never observed in a full glass of water, not because they are impossible yet because they are highly improbable. It is because even a small glass of water consists of an enormous number of interacting particles, making it highly unlikely that, throughout their random thermal motion, a substantial portion of excellent particles will certainly gather with each other in one place. Although such a spontaneous violation of the second law of thermodynamics is possible, an extremely patient physicist would undoubtedly have to wait many times the universe’s age to see it takes place.

The preceding demonstrates an important point: the second law of thermodynamics is statistical. It has no significance at the degree of individual particles, whereas the law becomes essentially specific for the description of large numbers of interacting particles. On the other hand, the first law of thermodynamics, which reveals energy conservation, remains true even at the molecular level.

The example of ice melting in a glass of hot water also demonstrates the various other sense of the term entropy, such as an increase in randomness and a parallel loss of information. Initially, the total thermal energy is separated in such a way that all of the slow-moving (excellent) particles in the ice and also all of the fast-moving (hot) particles in the water (or water vapor). After the ice has melted and the system is involved in the thermal equilibrium, the thermal energy uniformly disperses throughout the system. The statistical method provides a good deal of valuable understanding of the significance of the second law of thermodynamics. However, from the point of view of applications, the microscopic framework of matter becomes irrelevant.