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 $\mathrm{T}_{2}$ by releasing the piston suddenly. If $l_{1}$ and $l_{2}$ are the lengths of the gas column, before and after the expansion respectively, then the value of $\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}$ will be :
Correct Option: , 2
$\mathrm{PV}^{\mathrm{r}}=$ const.
$\mathrm{TV}^{\mathrm{r}-1}=$ const.
$\mathrm{T}(\ell)^{\frac{5}{3}-1}=$ const.
$\frac{\mathrm{T}_{1}}{\mathrm{~T}_{2}}=\left(\frac{\ell_{2}}{\ell_{1}}\right)^{2 / 3}$
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