A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800 \mathrm{~cm}^{3}$ and temperature $27^{\circ} \mathrm{C}$. The change in temperature when the gas is adiabatically compressed to $200 \mathrm{~cm}^{3}$ is : (Take $\gamma=1.5: \gamma$ is the ratio of specific heats at constant pressure and at constant volume)

JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Heat & Thermodynamics

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of

800 cm^{3}

and temperature

2 7^{\circ} C

. The change in temperature when the gas is adiabatically compressed to

200 cm^{3}

is :
(Take

γ = 1.5 : γ

is the ratio of specific heats at constant pressure and at constant volume)

(A)327 K
(B)600 K
(C)522 K
(D)300 K✓ Correct

Answer: (D)

Solution

For an adiabatic change

T V^{γ - 1}

is constant, so

T_{2} = T_{1} (\frac{V _{1}}{V _{2}})^{γ - 1} = 300 (\frac{800}{200})^{0.5} = 300 \times 4 = 600 K .

The rise in temperature is

Δ T = T_{2} - T_{1} = 600 - 300 = 300 K .

JEE Main · 2025 · 03 Apr 2025 · Shift 1 · Single correct option

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