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 \(T_{2}\) by releasing the piston suddenly. If \(L_{1}\) and \(L_{2}\) be the lengths of the gas column before and after expansion respectively, then \(\frac{T_{1}}{T_{2}}\) is