A monoatomic ideal gas, initially at temperature T1, is enclosed in a cylinder fitted with a friction less piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If L 1 and L 2 are the length of the gas column before and after expansion respectively, then T 1 / T 2 is given by

As the gas is monoatomic,T1T2=V2V1γ−1 = A.L2A.L153−1=L2L12/3

A monoatomic ideal gas, initially at temperature T1, is enclosed in a cylinder fitted with a friction less piston. The gas is allowed to expand adiabatically to a temperature T2 by releasing the piston suddenly. If L 1 and L 2 are the length of the gas column before and after expansion respectively, then T 1 / T 2 is given by

As the gas is monoatomic,T1T2=V2V1γ−1 = A.L2A.L153−1=L2L12/3

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A monoatomic ideal gas, initially at temperature T₁, is enclosed in a cylinder fitted with a friction less piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If $L_{1} a n d L_{2}$ are the length of the gas column before and after expansion respectively, then $T_{1} / T_{2}$ is given by

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(\frac{L_{1}}{L_{2}})

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

(\frac{L_{2}}{L_{1}})

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

answer is D.

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Detailed Solution

As the gas is monoatomic,

$\begin{array}{l} \frac{T_{1}}{T_{2}} = {(\frac{V_{2}}{V_{1}})}^{γ - 1} \\ = {(\frac{A . L_{2}}{A . L_{1}})}^{\frac{5}{3} - 1} = {(\frac{L_{2}}{L_{1}})}^{2 / 3} \end{array}$

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