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 \[{{L}_{2}}\]are the lengths of the gas column before and after expansion respectively, then \[{{T}_{1}}/{{T}_{2}}\] is given by [IIT-JEE (Screening) 2000]

• A.            \[{{\left( \frac{{{L}_{1}}}{{{L}_{2}}} \right)}^{2/3}}\]             
• B.            \[\frac{{{L}_{1}}}{{{L}_{2}}}\]
• C.            \[\frac{{{L}_{2}}}{{{L}_{1}}}\]
• D.            \[{{\left( \frac{{{L}_{2}}}{{{L}_{1}}} \right)}^{2/3}}\]