Q.Identify the state and path functions out of the following: a) Enthalpy b) Entropy c) Heat d) Temperature e) Work f) Free energy.

Every thermodynamic system in a definite state is fully described by just four variables: $P$, $V$, $T$ and $n$. This split gives rise to two very different behaviours among measurable quantities. A state function (pressure, volume, temperature, internal energy $U$, enthalpy $H$, free energy $G$) has one fixed value determined entirely by the current state -- it genuinely does not matter HOW that state was reached; only the initial and final states matter for computing its change. A path function (heat $q$, work $w$) is different: it depends on the actual ROUTE taken between two states. Take the identical gas through the identical net change of state once reversibly and once irreversibly, and the $q$ and $w$ values will come out numerically different each time -- even though $\Delta U$ (a state function) is guaranteed to …