A monoatomic ideal gas, initially at temperature T₁ is enclosed in a… | MHT CET 2025 (22 Apr, Shift 2)

Q91MHT CET 2025 · 22 APR · SHIFT 2Difficult

Thermodynamic Processes

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature $T_2$ . If $L_1$ and $L_2$ are the lengths of the gas columns before and after expansion respectively, then $(T_2/T_1)$ is given by

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Answer: (c)

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 (c).

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