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A monatomic 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 are the length of the gas column before and after expansion respectively, then $\frac{T_{1}}{T_{2}}$ is given by

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${(\frac{L_{2}}{L_{1}})}^{2 / 3}$

$\frac{L_{2}}{L_{1}}$

$\frac{L_{1}}{L_{2}}$

${(\frac{L_{1}}{L_{2}})}^{2 / 3}$

answer is D.

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Detailed Solution

Here ${TV}^{γ - 1} = constant$
As $γ = 5 / 3, hence {TV}^{2 / 3} = constant$
Now, $T_{1} L_{1}^{2 / 3} = T_{2} L_{2}^{2 / 3} (∵ V \propto L)$
or $\frac{T_{1}}{T_{2}} = {(\frac{L_{2}}{L_{1}})}^{2 / 3}$

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