Which of the following is the correct option for free expansion of an ideal gas under adiabatic condition 

For the free expansion of an ideal gas, the opposing force is zero, hence work done = 0. 

$\mathrm{\Delta }U=q+w,w=0$ and $\mathrm{\Delta }U=q$

But the process is adiabatic, hence $q = 0$

$\therefore q=0,\mathrm{\Delta }T=0, w=0$