Entropy is a thermodynamic quantity that measures how many microscopic arrangements, or microstates, are consistent with a system's observable macroscopic state. Greater disorder usually corresponds to greater entropy because a disordered state generally has more possible microstates.
The Reasoning
A macrostate is described by measurable quantities such as pressure, volume and temperature. A microstate specifies the detailed arrangement and motion of every particle within that macrostate.
Entropy is related to the number of accessible microstates by:
where is entropy, is the Boltzmann constant and is the number of possible microstates. If increases, then increases.
For example, gas particles concentrated in one corner of a container have relatively few possible arrangements. When the gas spreads throughout the container, vastly more arrangements become possible. The spread-out macrostate therefore has greater entropy and is overwhelmingly more probable.
The common misconception is that entropy is simply "messiness." Disorder is a useful qualitative description, but the precise physical idea is the number of accessible microstates and the dispersal of energy among them.
For a reversible transfer of thermal energy at constant temperature:
If a system reversibly absorbs at , its entropy change is:
The second law of thermodynamics states that the total entropy of an isolated system cannot decrease. It remains constant for an ideal reversible process and increases for an irreversible process. A subsystem's entropy may decrease, but the surroundings must undergo an equal or greater increase.
Exam Technique
This is HL-only content in B.4 Thermodynamics. For an Explain question, link more accessible microstates to greater entropy and then apply the second law to the complete isolated system, not just one component.
