Chemistry · Thermodynamics · NEET
A state function is a property whose value depends only on the current state of the system, which means its present temperature, pressure, volume and amount. It does NOT care how the system reached that state. So the change in a state function equals (final value − initial value). If you go from State A to State B by any route, the change is the same. Examples: internal energy U, enthalpy H, entropy S, Gibbs energy G, and also T, P, V.
A path function is a quantity whose value depends on the exact path taken between the start and the end. Heat (q) and work (w) are the two main path functions in NEET thermodynamics. For the same initial and final states, you can get different amounts of heat and work depending on whether the process is reversible, irreversible, fast or slow. That is why we never write Δq or Δw; heat and work are amounts exchanged during a process, not properties of a state.
Work is a PATH function. This is a very common NEET trap. Proof: for the same expansion of a gas from V1 to V2, reversible expansion gives more work than irreversible (single-step) expansion, and free expansion gives zero work. Same start, same end, different work. So work cannot be a state function. Small w, small q = path. Capital U, H, S = state.
Because the amount of heat exchanged changes with the route. Take a gas from the same initial to the same final state by two paths: an isothermal path exchanges heat, while an adiabatic-then-isochoric path exchanges a different amount. Heat is energy in transit during a process, so it belongs to the process (the path), not to any single state. This matters for NEET because you cannot use q as (q_final − q_initial); such a thing does not exist.
This is the deep idea of the First Law: ΔU = q + w. Individually q and w depend on the path, but their SUM always equals ΔU, which depends only on the two states. So the path-dependent parts cancel out. If you take a different path, q and w each change, but they change in opposite ways so that q + w stays the same. NEET loves testing that ΔU is fixed while q and w are not.
Trick 1: If the quantity is a property of the system at one instant (you could measure it right now, like T, P, V, U, H, S, G), it is a state function. Trick 2: If the quantity only exists while something is happening (heat flowing, work being done), it is a path function. Trick 3: Symbols with capital letters and a Δ (ΔU, ΔH, ΔS, ΔG) are state functions; small q and w with no Δ are path functions.
Two moles of an ideal gas undergo free expansion from 10 L to 100 L at 300 K. The values of ΔS(system) and ΔS(surroundings) are (R = universal gas constant):
Under isothermal condition, a gas at 300 K expands from 0.1 L to 0.25 L against a constant external pressure of 2 bar. The work done by the gas is (Given 1 L·bar = 100 J):
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Yes. Internal energy (U), enthalpy (H), entropy (S) and Gibbs free energy (G) are all state functions. Their changes depend only on initial and final states. Temperature (T), pressure (P) and volume (V) are also state functions.
Yes. Temperature is a state function because it describes the system at a given instant. The change in temperature between two states is fixed no matter what path you take.
Because U is a state function, so ΔU = U(final) − U(initial) has meaning. Heat q and work w are path functions; they are amounts exchanged during a process, not properties of a state, so 'q_final − q_initial' has no meaning. We just write q and w.
Yes. ΔH depends only on reactants and products, not on how the reaction happens. This is exactly why Hess's Law works: you can add reaction steps and the total ΔH is the same no matter the route.
No. The First Law says ΔU = q + w. Even though q and w each depend on the path, their sum always equals ΔU, which is fixed. The path-dependence of q and w cancels out perfectly.
