True or false on entropy (advanced)

Problem

True or false? (a) The entropy of an isolated system cannot decrease. (b) The entropy of part of a system can decrease. (c) In a reversible adiabatic transformation, entropy always increases. (d) Entropy is a state function. (e) A reversible heat engine has maximum efficiency for given temperatures.

Solution

(a) TRUE — this is the entropic statement of the second law: for an isolated system $\Delta S\ge 0$. (b) TRUE — a single part can give up entropy (e.g. a hot body cooling down), provided the total for the universe does not decrease. (c) FALSE — a reversible adiabatic process is isentropic: no heat exchange ($\dd Q=0$) and reversibility give $\Delta S=0$, entropy stays constant, it does not increase. (d) TRUE — $S$ depends only on the state, not on the path. (e) TRUE — Carnot’s theorem: no engine operating between two given temperatures beats the efficiency of a reversible one. $\ev{V,\ V,\ F,\ V,\ V}$

Links

Topics: Entropy and the second law Concepts: Entropy · Second law of thermodynamics Skills: Micro-macro interpretation