The correct option for free expansion of an ideal gas under adiabatic condition is:

For free expansion ($P_{ext}=0$), work done $w=-P_{ext}\Delta V=0$.Under adiabatic conditions, heat exchange $q=0$.According to the First Law of Thermodynamics: $\Delta U=q+w=0+0=0$.For an ideal gas, $\Delta U=n{C}_v\Delta T$. Since $\Delta U=0$, then $\Delta T=0$.