Question

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radii \(r_A\) and \(r_B\) respectively. On supplying an equal amount of heat to both the cylinders, their pressures remain constant and their pistons are displaced by 16 cm and 9 cm respectively. If the change in their internal energies is the same, then the ratio \(r_A / r_B\) is:

• A. \( \frac{4}{3} \)
• B. \( \frac{2}{\sqrt{3}} \)
• C. \( \frac{\sqrt{3}}{2} \)
• D. \( \frac{3}{4} \)

Hint:

For an isobaric process, the work done is \(P \Delta V\). If the heat supplied and change in internal energy are the same for two processes, the work done must also be the same. Equate the work done for both gases using the given displacements and radii.