Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius rA and rB, respectively. O…

Question

Two gases A and B are filled at the same pressure in separate cylinders with movable pistons of radius rA and rB, 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 rA/rB is equal to:

1. A. 4/3
2. B. 3/4 (Correct answer)
3. C. 2/√3
4. D. √3/2

Correct Answer

Option B — 3/4

Detailed Solution & Explanation

The correct answer is $\dfrac{3}{4}$.

Key Points

• First law: $\Delta Q=\Delta U+P\Delta V$. Since $\Delta Q$ and $\Delta U$ are the same for both, the work $P\Delta V$ is equal, and $P$ is the same, so $\Delta V_A=\Delta V_B$.
• $\Delta V=A\,d=\pi r^2 d$, hence $r_A^2 d_A=r_B^2 d_B$.
• $\dfrac{r_A}{r_B}=\sqrt{\dfrac{d_B}{d_A}}=\sqrt{\dfrac{9}{16}}=\dfrac{3}{4}$.