NEET 2025 — Physics solution

NEET2025Physics

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:

A
$\frac{4}{3}$
B
$\frac{3}{4}$
C
$\frac{2}{3}$
D
$\frac{3}{2}$

Solution

Constant pressure: $P_{A} = P_{B}$ . Equal heat: $Q_{A} = Q_{B}$ . Equal $Δ U$ . By first law $Q = Δ U + W$ , so $W_{A} = W_{B}$ .

Work at constant pressure: $W = P Δ V$ , so $P_{A} Δ V_{A} = P_{B} Δ V_{B} \Rightarrow Δ V_{A} = Δ V_{B}$ .

$Δ V = π r^{2} x$ (piston displacement $x$ ). So $π r_{A}^{2} (16) = π r_{B}^{2} (9)$ .

$\frac{r _{A}}{r _{B}} = \frac{9}{16} = \frac{3}{4}$ .

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