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Thermodynamic Processes

Two gases $A$ and $B$ are filled at the same pressure in separate cylinders with movable pistons of radius $r_A$ and $r_B$ , respectively. On supplying an equal amount of heat to both the systems reversibly under constant pressure, the pistons of gas $A$ and $B$ are displaced by 16 cm and 9 cm, respectively. If the change in their internal energy is the same, then the ratio $\frac{r_A}{r_B}$ is equal to

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Answer: (d)

Constant pressure: $Q = \Delta U + P\Delta V$ .
Equal $Q$ and equal $\Delta U$ give equal work, so equal $\Delta V$ (same $P$ ).
$\pi r_A^2 \times 16 = \pi r_B^2 \times 9 \Rightarrow \frac{r_A^2}{r_B^2} = \frac{9}{16}$
$\frac{r_A}{r_B} = \frac{3}{4}$ , so the answer is (d).

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