A monoatomic ideal gas initially at temperature T₁ is enclosed in a cylinder fitted with 8 frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. L₁ and L₂ are the lengths of the gas columns before and after the expansion respectively. Then (T₂)/(T₁) is (a) ((L₂)/(L₁))2/3 (b) ((L₁)/(L₂))2/3 (c) ((L₁)/(L₂))1/2 (d) ((L₂)/(L₁))1/2

Answer: (b). Adiabatic, monatomic γ = 5/3: TV2/3 = constant, and V ∝ L. T₁L₁2/3 = T₂L₂2/3 (T₂)/(T₁) = ((L₁)/(L₂))2/3 So the answer is (b).

A monoatomic ideal gas initially at temperature T₁ is enclosed in a… | MHT CET 2021 (24 Sep, Shift 1)

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Thermodynamic Processes

A monoatomic ideal gas initially at temperature $T_1$ is enclosed in a cylinder fitted with 8 frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively. Then $\frac{T_2}{T_1}$ is

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Answer: (b)

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

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