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 $L_{1} a n d L_{2}$ are the lengths of the gas column before and after expansion respectively ,then $T_{1} / T_{2}$ is given by :

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

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L_{1} / L_{2}

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L_{2} / L_{1}

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

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Solution

The correct option is B $(L_{2} / L_{1})^{2 / 3}$
For adiabatic process,

$T_{1} V_{1}^{S - 1} = T_{2} V_{2}^{γ - 1}$

$\frac{T_{1}}{T_{2}} = (\frac{A L_{2}}{A L_{1}})^{\frac{5}{3} - 1}$

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

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