State Functions And Path Functions

Question

Which of the following pairs correctly classifies both quantities as state functions?

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State functions are thermodynamic properties whose values depend only on the current state of the system (defined by variables such as temperature, pressure, and composition), not on the path taken to reach that state. Internal energy $U$, enthalpy $H = \cup + pV$, entropy $S$, and Gibbs free energy $G$ are all state functions. In contrast, heat $q$ and work $w$ are path functions — their values depend on the specific process or pathway taken. Option 'Internal energy and heat' is incorrect because heat is a path function. Option 'Work and heat' is wrong because both are path functions. Option 'Work and internal energy' is incorrect because work is a path function. Only the pair 'Enthalpy and entropy' consists of two genuine state functions. This conceptual distinction is fundamental in NCERT Chemical Thermodynamics and is frequently tested in JEE Main. Plausibility check: the differential forms $dU$, $dH$, $dS$, and $dG$ are exact differentials (path-independent), while $\delta q$ and $\delta w$ are inexact differentials — consistent with state vs. path function classification.

State Functions And Path Functions

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