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Thermodynamics opens with vocabulary that looks easy and then costs marks in one-line questions: "Which of these is a state function?" or "Which is intensive?" Both have simple tests. This post gives the two tests, a worked example in which one change happens by three different paths, a quick quiz with answers and a practice routine.
Where does this sit in the syllabus?
Section 5.1 of the NCERT Class 11 chapter Thermodynamics introduces state functions, and section 5.2.2(b) covers extensive and intensive properties. The JEE (Main) 2026 syllabus lists "extensive and intensive properties, state functions" in its first thermodynamics line. The JEE (Advanced) 2026 brochure opens its thermodynamics section with "Intensive and extensive properties, state functions". Check the syllabus for your exam year.
What makes something a state function?
NCERT puts it this way: variables like p, V and T are state functions "because their values depend only on the state of the system and not on how it is reached." Its example is temperature. Warm a system from 25 °C to 35 °C directly, or cool it first and then warm it, and the change is +10 °C either way.
Internal energy U is a state function too. Joule showed that a given amount of adiabatic work produced the same change of state however the work was done. Enthalpy H = U + pV is a state function because U, p and V all are. Later in the chapter, NCERT treats entropy S and Gibbs energy G the same way.
Heat q and work w are different. NCERT calls q "a path dependent function". The first law, ΔU = q + w, says that q and w can change from path to path while their sum stays fixed.
Worked example: one change, three paths
Take 1.00 mol of an ideal gas at 300 K. It expands from 2.00 atm (12.3 L) to 1.00 atm (24.6 L), and the temperature is 300 K at the end. The volumes come from V = nRT/p with R = 0.08206 L atm mol⁻¹ K⁻¹.
Path A, into a vacuum. The external pressure is zero, so w = 0. NCERT notes that Joule found q = 0 for this free expansion, so ΔU = 0.
Path B, against a constant 1.00 atm. w = −pₑₓ ΔV = −1.00 × (24.6 − 12.3) = −12.3 L atm. Using 1 L atm = 101.325 J, w = −1.25 kJ. Since ΔU = 0, q = +1.25 kJ.
Path C, reversibly. w = −nRT ln(V₂/V₁) = −1.00 × 8.314 × 300 × ln 2 = −1.73 kJ, so q = +1.73 kJ.
The start and finish are the same in all three, and so is ΔU (zero, for an ideal gas at constant temperature). The heat and work are 0, 1.25 and 1.73 kJ. That is what "path function" means in practice. NCERT Problems 5.2 to 5.4 make the same point with a 2 L to 10 L expansion.
Extensive or intensive: the partition test
NCERT defines an extensive property as one "whose value depends on the quantity or size of matter present". Examples are mass, volume, internal energy, enthalpy and heat capacity. Intensive properties do not depend on the amount: temperature, density and pressure.
NCERT's test is to put a partition through the middle of a gas sample. Each half has half the volume but the same temperature. Volume is extensive and temperature is intensive.
A useful shortcut follows. The ratio of two extensive properties is intensive. Density is mass over volume. Molar volume is volume over moles. Molar heat capacity is heat capacity over moles. NCERT names molar properties as intensive for exactly this reason.
Quick quiz (answers after each)
Heat capacity C of a beaker of water: extensive. Specific heat: intensive.
Molar enthalpy of vaporisation of water: intensive. It is per mole. The total heat to boil a kettle dry is extensive.
Boiling point: intensive.
Gibbs energy G: a state function and extensive. NCERT states both.
Work done in an expansion: a path function, and not a property of the system at all.
Molarity of a solution: intensive. Pour out half and the concentration stays the same.
Common mistakes and how to avoid them
"q is a state function because ΔH = qₚ." Heat in general depends on the path. Only at constant pressure does it equal ΔH, which is why NCERT says qₚ is "also independent of path" in that special case.
Treating "intensive" as "constant". Temperature can change in a process. Intensive only means it does not scale with the amount of material.
Calling ΔU a path function because q and w are. The sum is fixed even when the parts are not.
Marking molar quantities as extensive. Divide by n and the size dependence cancels.
Why does this matter for later chapters?
Hess's law works only because enthalpy is a state function, a point NCERT makes directly. Our guide to Hess's law and thermochemistry builds on it. The signs of q and w in the worked example follow the convention explained in thermodynamics sign conventions, and the link between ΔH and ΔU is worked through in relating ΔH and ΔU with ΔngRT.
A practice routine
List 20 quantities from the chapter and mark each with two labels: state or path, extensive or intensive.
Rework the three-path example with 2.00 mol instead of 1.00 mol. Which answers double? (Volumes, q and w all double; T and p do not.)
Solve NCERT Problems 5.2 to 5.4 and say for each line whether you are computing a state or a path quantity.
A week later, mix ten of these questions into a timed set with Hess's law problems.
If thermodynamics vocabulary keeps slipping, Fermi's Concept Library covers every concept in physics, chemistry, biology, mathematics and computing, so you can revisit one definition at a time.
Take the 20-quantity list today and label each one before you open the book to check.
