Q 11-11-004NEETNEET 2025Top questionMedium
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 $r_A/r_B$ is equal to
Answer: (B) $\dfrac{3}{4}$
First law: $W = Q - \Delta U$. Both $Q$ and $\Delta U$ are the same for the two gases, so the work done is the same.
At constant pressure, $W = P\Delta V = P\pi r^2 x$. With equal $P$:
$$r_A^2 \times 16 = r_B^2 \times 9 \;\Rightarrow\; \frac{r_A}{r_B} = \frac{3}{4}$$
Solution by Sreeraj P, M.Sc Physics