A monoatomic ideal gas, initially at temperature T₁ is enclosed in a cylinder fitted with a frictionless piston. The gas is allowed to expand adiabatically to a temperature T₂ by releasing the piston suddenly. If l₁ and l₂ are the lengths of the gas column, before and after the expansion respectively, then the value of ${{{T_1}} \over {{T_2}}}$ will be :

1. A ${\left( {{{{l_1}} \over {{l_2}}}} \right)^{{2 \over 3}}}$
2. B ${\left( {{{{l_2}} \over {{l_1}}}} \right)^{{2 \over 3}}}$ Correct answer
3. C ${{{l_2}} \over {{l_1}}}$
4. D ${{{l_1}} \over {{l_2}}}$