JEE Mains Chemistry · Chemical Thermodynamics

Systems, State Functions and the First Law

The language of thermodynamics — systems and their walls, state versus path functions, intensive versus extensive — and the first law ΔU = q + w, with work done on the system counted positive.

All Chemical Thermodynamics notes JEE Mains Chemistry strategy

Why this matters

Twelve PYQs, ten of them multiple choice, and two from 2026. Six ask which quantities are state functions or intensive, or which textbook relation is written correctly. Six apply ΔU = q + w with the right signs: through a cycle, a stirred liquid, boiling water or an insulated box.

Concept 1 of 2: State functions, intensive properties and the standard relations

Cut the sample in half. A property that halves with it is extensive; one that stays the same is intensive. A state function depends only on where the system is now, not on how it got there. Heat and work depend on the route, so they are path functions.

Definition

Open system: exchanges matter and energy. Closed: energy only. Isolated: neither.
Adiabatic walls let no heat through, so $q = 0$ . Diathermic walls let heat through, so a system in a bath stays at the bath temperature.
Intensive: temperature, pressure, density, concentration, $E^\circ_{\mathrm{cell}}$ , and any molar or specific quantity (molar heat capacity, molar mass).
Extensive: volume, amount, mass, $U$ , $H$ , $S$ , $G$ and their changes, the heat capacity of a sample.
State functions: $U, H, S, G, p, V, T$ . Path functions: $q$ and $w$ .
Correct forms: $\Delta U = q + w$ , $\Delta H = \Delta U + \Delta n_g RT$ , $\Delta G = \Delta H - T\Delta S$ , $\Delta S = q_{\mathrm{rev}}/T$ , $\Delta S_{\mathrm{sys}} + \Delta S_{\mathrm{surr}} \ge 0$ .

Quantity	Intensive or extensive	State or path function
Temperature, pressure, density	Intensive	State function
Molarity, molar heat capacity, standard cell potential	Intensive	State function A per-mole or per-litre quantity is intensive, even though it is a ratio of two extensive ones.
Volume, amount in moles, mass	Extensive	State function
Internal energy U, enthalpy H, entropy S, Gibbs energy G	Extensive	State function Take less of a solution and G falls, even though its concentration and density stay the same.
Heat capacity of a whole sample	Extensive	State function
Heat q, work w	Extensive (they scale with the amount)	Path function Among U, V, q and H, only q is not a state variable.

Halve the sample and ask what changes.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2022 · 28 July 2022 · Q150Moderate

Example 1 · Chemical Thermodynamics · Systems, State Functions and the First Law

Among the following the number of state variable is Internal energy (U) Volume (V) Heat (q) Enthalpy (H)

Sign-reversed textbook relations

Distractors write

\Delta U = q + p\Delta V

\Delta H = \Delta U - \Delta n_g RT

\Delta H = \Delta U - p\Delta V

. With work on the system positive, expansion work is

-p\Delta V

, so

\Delta U = q - p\Delta V

and

\Delta H = \Delta U + \Delta n_g RT

Same concentration, different Gibbs energy

Two solutions with the same concentration have the same density, molar heat capacity and concentration, because those are intensive. Their Gibbs energies differ if they hold different amounts, because

G

is extensive.

Drill 5 more on state functions, intensive properties and the standard relations

Concept 2 of 2: First law sign convention: ΔU = q + w

Internal energy changes only by heat and work crossing the boundary. Count everything that goes in as positive: heat absorbed, and work done on the system. Heat given out and work done by the system are negative. Over a full cycle the system returns to its start, so ΔU is zero whatever the path.

Definition

$\Delta U = q + w$ (IUPAC and NCERT): $q > 0$ when heat is absorbed, $w > 0$ when work is done ON the system.
Expansion: the system does work, so $w < 0$ . Compression: $w > 0$ .
Adiabatic: $q = 0$ , so $\Delta U = w$ . Stirring a liquid in an insulated vessel: $w > 0$ , so $\Delta U > 0$ and it warms.
Cycle: $\Delta U_{\mathrm{cycle}} = 0$ , so the return path has $\Delta U$ equal and opposite to the forward path.
Some books write $\Delta U = q - W$ , where $W$ is the work done BY the system. It is the same law.
An exothermic reaction in an adiabatic box heats its contents. In a diathermic box in a bath, the heat leaves and the temperature stays the same.

First law of thermodynamics

\Delta U = q + w

Worked example

A gas absorbs 250 J of heat and expands, doing 400 J of work on the surroundings. Find

\Delta U

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

JEE Mains · 2026 · 2 Apr 2026 Shift 2 · Q29Moderate

Example 2 · Chemical Thermodynamics · Systems, State Functions and the First Law

Gas 'A' undergoes change from state ' X ' to state ' Y '. In this process, the heat absorbed, and work done by the gas is 10 J and 18 J respectively. Now gas is brought back to state ' X ' by another process during which 6 J of heat is evolved. In the reverse process of ' Y ' to ' X ',

Adding the magnitudes

If a system does 200 J of work and absorbs 150 J of heat,

\Delta U = 150 - 200 = -50

J. Adding them (350 J) or flipping the sign (+50 J) are the planted options.

Boiling water does work

Water heated to boiling takes in heat (

q > 0

) and stores more energy (

\Delta U > 0

). The steam it makes pushes back the atmosphere, so the system does work:

w < 0

, not zero.

Drill 5 more on first law sign convention: δu = q + w

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

First law sign convention: ΔU = q + w
First law of thermodynamics
$\Delta U = q + w$

Reference tables (1)

State functions, intensive properties and the standard relations6 rows

Quantity	Intensive or extensive	State or path function
Temperature, pressure, density	Intensive	State function
Molarity, molar heat capacity, standard cell potential	Intensive	State function A per-mole or per-litre quantity is intensive, even though it is a ratio of two extensive ones.
Volume, amount in moles, mass	Extensive	State function
Internal energy U, enthalpy H, entropy S, Gibbs energy G	Extensive	State function Take less of a solution and G falls, even though its concentration and density stay the same.
Heat capacity of a whole sample	Extensive	State function
Heat q, work w	Extensive (they scale with the amount)	Path function Among U, V, q and H, only q is not a state variable.

Halve the sample and ask what changes.

Watch out for (4)

Sign-reversed textbook relations
→ State functions, intensive properties and the standard relations
Same concentration, different Gibbs energy
→ State functions, intensive properties and the standard relations
Adding the magnitudes
→ First law sign convention: ΔU = q + w
Boiling water does work
→ First law sign convention: ΔU = q + w

Test yourself on Chemical Thermodynamics

20 past JEE Mains questions from this chapter, timed at 48 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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