A monatomic 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 length of the gas column before and after expansion respectively, then \[\frac{{{T}_{1}}}{{{T}_{2}}}\] is given by

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