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However, after sufficient time has passed, the system reaches a uniform color, a state much easier to describe and explain. Boltzmann formulated a simple relationship between entropy and the number of possible microstates of a system, which is denoted by the symbol Ω. The entropy S is proportional to the natural logarithm of this number:
However, today the classical equation of entropy, = can be explained, part by part, in modern terms describing how molecules are responsible for what is happening: Δ S {\displaystyle \Delta S} is the change in entropy of a system (some physical substance of interest) after some motional energy ("heat") has been transferred to it by fast-moving ...
Entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Thus, entropy measurement is a way of distinguishing the past from ...
In the view of Jaynes (1957), [20] thermodynamic entropy, as explained by statistical mechanics, should be seen as an application of Shannon's information theory: the thermodynamic entropy is interpreted as being proportional to the amount of further Shannon information needed to define the detailed microscopic state of the system, that remains ...
However, there is a broad class [18] of systems that manifest entropy-driven order, in which phases with organization or structural regularity, e.g. crystals, have higher entropy than structurally disordered (e.g. fluid) phases under the same thermodynamic conditions. In these systems phases that would be labeled as disordered by virtue of ...
In more detail, Clausius explained his choice of "entropy" as a name as follows: [11] I prefer going to the ancient languages for the names of important scientific quantities, so that they may mean the same thing in all living tongues. I propose, therefore, to call S the entropy of a body, after the Greek
Figure 1. A thermodynamic model system. Differences in pressure, density, and temperature of a thermodynamic system tend to equalize over time. For example, in a room containing a glass of melting ice, the difference in temperature between the warm room and the cold glass of ice and water is equalized by energy flowing as heat from the room to the cooler ice and water mixture.
The entropy of a closed system, determined relative to this zero point, is then the absolute entropy of that system. Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1.