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

Expansion against zero external pressure is called free expansion.
$p_{\text{ext }}=0;W=-p\mathrm{\Delta }V$
Process for which dQ = 0 is adiabatic process.
Q = 0
From first Law of thermodynamics,
$\begin{array}{r}\mathrm{\Delta }E=Q+W=0\\ \mathrm{\Delta }E=n{C}_v\mathrm{\Delta }T=0\end{array}$
Therefore, q = 0, W = 0, $∆$T = 0.