JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Heat & Thermodynamics

Pressure of an ideal gas, contained in a closed vessel, is increased by

0.4%

when heated by

1^{\circ} C

. Its initial temperature must be:

(A) $2 5^{\circ} C$
(B)2500 K
(C)250 K✓ Correct
(D) $25 0^{\circ} C$

Answer: (C)

Solution

At constant volume the pressure of a fixed mass of gas is proportional to its absolute temperature, so

\frac{Δ P}{P} = \frac{Δ T}{T}

. A rise of

1^{\circ} C

is a change of

1 K

, and the pressure rises by

0.4%

, giving

\frac{0.4}{100} = \frac{1}{T}

. The initial temperature is

T = \frac{100}{0.4} = 250 K

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Single correct option

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