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  • 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.

Q.8) 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) $\frac{\sqrt{3}}{2}$

B) $\frac{4}{3}$

C) $\frac{3}{4}$

D) $\frac{2}{\sqrt{3}}$

Answers (1)

best_answer


Solution:
Since heat supplied and internal energy change are the same for both gases, the work done by each gas must also be equal. Work at constant pressure is given by $P \Delta V$, and volume change is $\Delta V=\pi r^2 h$. Using this, we get:

$$
\pi r_A^2 \times 16=\pi r_B^2 \times 9
$$


Simplifying, $\frac{r_A^2}{r_B^2}=\frac{9}{16}$
Taking square root, $\frac{r_A}{r_B}=\frac{3}{4}$
Hence, the answer is option (3) $3 / 4$.

 

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