Physics · Thermodynamics

NEET (UG) 2025 — Question 38

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

Option A:
$\frac{4}{3}$
Option B:
$\frac{3}{4}$
Correct
Option C:
$\frac{2}{\sqrt{3}}$
Option D:
$\frac{\sqrt{3}}{2}$

Answer: B

Step-by-step solution

Given constant pressure, work done by each gas: $W = P \Delta V$ .
For gas A: $\Delta V_A = \pi r_A^2 \times 16$ cm.
For gas B: $\Delta V_B = \pi r_B^2 \times 9$ cm.
First law: $Q = \Delta U + W$ . With same Q and same $\Delta U$ , work done must be equal: $W_A = W_B$ .
Hence $P \cdot \pi r_A^2 \cdot 16 = P \cdot \pi r_B^2 \cdot 9$ .
Cancel common factors: $16 r_A^2 = 9 r_B^2$ .
Take square root: $\frac{r_A}{r_B} = \sqrt{\frac{9}{16}} = \frac{3}{4}$ .
Therefore the required ratio is $\frac{3}{4}$ , which corresponds to option B.

Answer key and solution verified before publishing.

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Exam: NEET (UG) 2025
Paper: 2025 paper
Subject: Physics
Chapter: Thermodynamics
Topic: First Law of Thermodynamics