True or false about entropy (basic)

Problem

Determine whether each statement is true or false, justifying your answer: (1) Entropy is a state function. (2) In an irreversible process the entropy of the gas must always increase. (3) In an isolated system $\Delta S_\text{tot}\ge 0$. (4) If $Q=0$ then certainly $\Delta S_\text{gas}=0$.

Solution

(1) TRUE. Entropy depends only on the thermodynamic state of the system (defined by $p$, $V$, $T$) and not on the path followed to reach it. Its change between two states is therefore independent of the transformation.

(2) FALSE. In an irreversible process it is the TOTAL entropy (system plus environment) that cannot decrease, not that of the gas alone. The entropy of the gas can perfectly well decrease, for example if the gas is cooled or compressed: it releases heat and its entropy falls.

(3) TRUE. This is the statement of the second law for an isolated system: the total entropy can never decrease; it stays constant in reversible processes and grows in irreversible ones.

(4) FALSE. $Q=0$ does not imply $\Delta S_\text{gas}=0$. Counterexample: in the free expansion of an ideal gas there is no heat exchange ($Q=0$) nor work, but the volume increases and the entropy of the gas grows, $\Delta S_\text{gas} = nR\ln(V_B/V_A) > 0$. The equality $\Delta S = Q/T$ holds only for reversible transformations.

$\ev{T,\ F,\ T,\ F}$

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Topics: Entropia e secondo principio Concepts: Entropia · Secondo principio della termodinamica Skills: Bilancio entropico