JEE Main202628 January 2026Morning ShiftPhysicsThermodynamicsActual
In the following p-V diagram the equation of state along the curved path is given by (V-2)²=4 a p where a is a constant. The total work done in the closed path is
Options
- A+ 1 3 a
- B- 1 3 a
- C1 2 a
- D- 1 a
Correct answer
B. - 1 3 a
Step-by-step solution
From the equation of state (V-2)^2 = 4ap , we get p = (V-2)^2 4a . At V = 1: p = 1 4a and at V = 3: p = 1 4a . The curved path A→B→C follows the given equation, while C→A is a straight line at constant pressure. Work along the curved path: W_ ABC = ₁^3 (V-2)^2 4a dV = 1 4a [ (V-2)^3 3 ]₁^3 = 1 4a 2 3 = 1 6a . Work along C→A at constant pressure: W_ CA = 1 4a (1-3) = - 1 2a . Total work: W_ total = 1 6a - 1 2a = - 1 3a .