A monoatomic ideal gas, initially at temperature $\text{T}_1$ is enclosed in a cylinder fitted with massless, frictionless piston. By releasing the piston suddenly, the gas is allowed to expand adiabatically to a temperature $\text{T}_2$. If $\text{L}_1$ and $\text{L}_2$ are the lengths of the gas columns before and after expansion respectively, then $(\text{T}_2/\text{T}_1)$ is given by}