JEE (Advanced) 2026, Paper 1, Chemistry, Section 1 — single correct option, +3 for the correct option, 0 if unanswered, −1 otherwise.
Q.1 An ideal gas (0.5 mol), initially at 2 bar pressure, is compressed at a constant temperature of 600 K in two steps: first, against a constant external pressure of P bar (2 < P < 8), and then against constant external pressure of 8 bar. At each step, the compression is stopped only when the pressure of the gas becomes equal to the external pressure. The total work done on the gas in these steps is W. Considering all possible values of P (2 < P < 8) and taking the gas constant as R (in J K−1 mol−1), the minimum value of |W| (in J) is
A gas-tight cylinder sits in a thermostat bath at the question's temperature. Weights on the piston set the external pressure. Press START — the experiment loads the piston in two steps, measures the work, repeats it for different first-step pressures, and finds the minimum.
0.5 mol of gas at 2 bar and 600 K. The question's values are already loaded — press START EXPERIMENT.
The first-step pressure P is not an input: the experiment tries every P between P1 and P2 itself.
Work on the gas = Pext × volume swept = the shaded area.
One point per run. The lowest point is the answer to the question.
Nothing measured yet.
Run the experiment — the solution opens with the answer.
The experiment has not finished yet. Press START and let it run to the end — or use Reveal anyway in the header if you are revising.
Find the smallest |W| over all P, as a multiple of R.
When a piston is pushed by a constant external pressure, the work done on the gas is that pressure times the volume swept, whatever the gas does inside:
Each step stops when the gas pressure equals Pext; the bath returns the gas to 600 K, so the end volume of each step is on the isotherm, V = nRT/P.
The second derivative 2nRT P2/P³ is positive, so it is a minimum. At P = 4 bar both steps cost the same, nRT(2 − 1) = 300R each — the experiment's best run showed two equal rectangles.
The work is done on the gas, so it is positive; |W| = 600R. Because the gas is ideal and isothermal, ΔU = 0 and the same 600R J leaves as heat to the bath.
(A) 207R is nRT ln 2 — only half the reversible work nRT ln 4 = 415.9R. No process at all, with any number of steps, can compress the gas with less than the reversible work, so 207R is impossible. (C) 630R is a real two-step run, but at P = 3.2 or 5 bar — not the minimum. (D) 900R is the limit P → 2 or P → 8, i.e. a single step straight against 8 bar.
For a student opening it for the first time. The whole experiment runs by itself after one press.
A gas is squeezed from 2 bar to 8 bar in two pushes. The first push can be any pressure P between them. Which P needs the least work, and how much work is that?
The question's values — 0.5 mol, 600 K, 2 bar, 8 bar — are already filled in. You do not need to enter anything.
Change any one value, or several. The rest stay at the question's values. An empty box means "use the question value". The badge switches to ⚙ USING CUSTOM VALUES; ↺ RESET TO QUESTION VALUES puts everything back.
Press ▶ START EXPERIMENT. There is nothing else to click — the experiment runs from beginning to end on its own (about 45 seconds; 2× makes it faster).
A weight lands on the piston, the gas is squeezed, molecules crowd together and hit the piston more often, heat flows out into the bath, and the work shows up as a shaded area on the indicator diagram. Then the experiment repeats this for many values of P and plots the total work for each — watch the lowest point appear.
When the experiment finishes it says ✓ EXPERIMENT COMPLETE and reveals the answer. The header answer box unlocks at the same time.
Scroll to Detailed solution. Each step points back to what you saw in the experiment.
Press ▶ REPLAY EXPERIMENT, or change a value — try 0.25 bar more at the start, or 16 bar at the end — and press ⚙ RUN WITH CUSTOM VALUES. Watch where the best P lands each time — there is a pattern. CLASSROOM MODE enlarges everything for a projector.
| Exam | JEE Advanced 2026, Paper 1, Chemistry, Section 1, Q.1 |
|---|---|
| Chapter | Thermodynamics |
| Topic | Work in isothermal compression of an ideal gas — irreversible, multi-step |
| Difficulty | Moderate |
| Answer | — run the experiment |