A monoatomic ideal gas, initially at temperature ${\mathrm{T}}_1$, is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature. ${\mathrm{T}}_2$ by releasing the piston suddenly. lf ${\mathrm{L}}_1 \mathrm{and} {\mathrm{L}}_2$ are the lengths of the gas column before and after expansion respectively, then $\frac{{\mathrm{T}}_1}{{\mathrm{T}}_2}$, is given by

• A

  ${\left(\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}\right)}^{\frac{2}{3}}$

• B

  $\frac{{\mathrm{L}}_1}{{\mathrm{L}}_2}$

• C

  $\frac{{\mathrm{L}}_2}{{\mathrm{L}}_1}$

• D

  ${\left(\frac{{\mathrm{L}}_2}{{\mathrm{L}}_1}\right)}^{\frac{2}{3}}$