Heat And Thermodynamics

A monoatomic ideal gas, initially at temperature ' $\mathrm{T}_1$ '' 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. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively. Then $\frac{T_1}{T_2}$ is