Heat And Thermodynamics

A monoatomic ideal gas initially at temperature '\(\mathrm{T}_1\)' is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly the gas is allowed to expand to adiabatically to a temperature '\(\mathrm{T}_2\)'. If '\(\mathrm{L}_1\)' and '\(\mathrm{L}_2\)' are the lengths of the gas columns before and after expansion respectively, then \(\frac{\mathrm{T}_2}{\mathrm{~T}_1}\) is