Q. 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
A) $\frac{4}{3}$
B) $\frac{3}{4}$
C) $\frac{2}{\sqrt3}$
D) $\frac{\sqrt3}{2}$
Explanation
[Solution by Claude - not from source] $Q=\Delta U+P\Delta V$. Equal $Q$ and equal $\Delta U$ imply equal work $P\Delta V$ at the same $P$, so $\pi r_A^2(16)=\pi r_B^2(9)$. $\frac{r_A}{r_B}=\frac34$. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.