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Owing to these early developments, the typical example of entropy change ΔS is that associated with phase change. In solids, for example, which are typically ordered on the molecular scale, usually have smaller entropy than liquids, and liquids have smaller entropy than gases and colder gases have smaller entropy than hotter gases.
The maximum entropy principle: For a closed system with fixed internal energy (i.e. an isolated system), the entropy is maximized at equilibrium. The minimum energy principle: For a closed system with fixed entropy, the total energy is minimized at equilibrium.
For example, the differential entropy can be negative; also it is not invariant under continuous co-ordinate transformations. This problem may be illustrated by a change of units when x is a dimensioned variable. f(x) will then have the units of 1/x. The argument of the logarithm must be dimensionless, otherwise it is improper, so that the ...
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. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0.
The T-V diagram of the rubber band experiment. The decrease in the temperature of the rubber band in a spontaneous process at ambient temperature can be explained using the Helmholtz free energy = where dF is the change in free energy, dL is the change in length, τ is the tension, dT is the change in temperature and S is the entropy.
For example, in the Carnot cycle, while the heat flow from a hot reservoir to a cold reservoir represents the increase in the entropy in a cold reservoir, the work output, if reversibly and perfectly stored, represents the decrease in the entropy which could be used to operate the heat engine in reverse, returning to the initial state; thus the ...
The definition of entropy is central to the establishment of the second law of thermodynamics, which states that the entropy of isolated systems cannot decrease with time, as they always tend to arrive at a state of thermodynamic equilibrium, where the entropy is highest. Entropy is therefore also considered to be a measure of disorder in the ...
The Otto Cycle is an example of a reversible thermodynamic cycle. 1→2: Isentropic / adiabatic expansion: Constant entropy (s), Decrease in pressure (P), Increase in volume (v), Decrease in temperature (T) 2→3: Isochoric cooling: Constant volume(v), Decrease in pressure (P), Decrease in entropy (S), Decrease in temperature (T)