Heat And Thermodynamics

A monoatomic ideal gas initially at temperature \(\mathrm{T}_1\) is enclosed in a cylinder fitted with 8 frictionless piston. The gas is allowed to expand adiabatically to a temperature \(\mathrm{T}_2\) by releasing the piston suddenly. \(\mathrm{L}_1\) and \(\mathrm{L}_2\) are the lengths of the gas columns before and after the expansion respectively. Then \(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\) is