A monatomic ideal gas at temperature $T_1$ is enclosed in a cylinder with frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing piston suddenly. If $L_1$ and $L_2$ are lengths of gas columns before and after expansion, then

Question

$\begin {array} {1 1} (A)\;\large\frac{T_1}{T_2} = \bigg( \large\frac{L_1}{L_2} \bigg)^{ \large\frac{2}{3}} & \quad (B)\;\large\frac{T_2}{T_1} = \bigg( \large\frac{L_1}{L_2} \bigg)^{ \large\frac{5}{3}} \\ (C)\;\large\frac{T_1}{T_2} = \bigg( \large\frac{L_2}{L_1} \bigg)^{ \large\frac{5}{3}} & \quad (D)\;\large\frac{T_1}{T_2} = \bigg( \large\frac{L_2}{L_1} \bigg)^{ \large\frac{2}{3}} \end {array}$