JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Heat & Thermodynamics

An ideal gas initially at

0^{\circ} C

temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is

3/2

, the change in temperature due to the thermodynamics process is

____

Answer: 273

Solution

For a sudden (adiabatic) compression,

T V^{γ - 1} = constant

, with

γ = \frac{3}{2}

, so

γ - 1 = \frac{1}{2}

.

Initial temperature

T_{1} = 0^{\circ} C = 273 K

, initial volume

V_{0}

, final volume

\frac{V _{0}}{4}

T_{1} V_{0}^{1/2} = T_{2} (\frac{V _{0}}{4})^{1/2}

T_{2} = T_{1} 4 = 2 T_{1} = 546 K

Δ T = T_{2} - T_{1} = 546 - 273 = 273 K

JEE Main · 2025 · 23 Jan 2025 · Shift 1 · Integer answer

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