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. \(L_1\) and \(L_2\) are the lengths of the gas columns before and after the expansion respectively. Then \(\frac{T_1}{T_2}\) is