A monoatomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If L₁ and L₂ be the lengths of the gas column before and after expansion respectively, then (T₁)/(T₂) is (a) ((L₁)/(L₂))2/3 (b) ((L₁)/(L₂)) L₂ (c) ((L₂)/(L₁)) (d) ((L₂)/(L₁))2/3

Answer: (d). Adiabatic, monatomic γ = 5/3: TV2/3 = constant. Same cross-section, so V ∝ L: T₁L₁2/3 = T₂L₂2/3. (T₁)/(T₂) = ((L₂)/(L₁))2/3 So the answer is (d).

A monoatomic ideal gas, initially at temperature T₁ is enclosed in a… | MHT CET 2026 (13 May, Shift 2)

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Thermodynamic Processes

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. If $L_1$ and $L_2$ be the lengths of the gas column before and after expansion respectively, then $\frac{T_1}{T_2}$ is

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Answer: (d)

Adiabatic, monatomic $\gamma = \frac{5}{3}$ : $TV^{2/3} =$ constant.
Same cross-section, so $V \propto L$ : $T_1L_1^{2/3} = T_2L_2^{2/3}$ .
$\frac{T_1}{T_2} = \left(\frac{L_2}{L_1}\right)^{2/3}$
So the answer is (d).

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