For an adiabatic free expansion of an ideal gas, the gas is kept in an insulated container and then permitted to enlarge in a vacuum. Since there is no external pressure for the gas to enlarge against, the work done by or on the system is zero. Since this process does not involve any exchange of heat transfer or work, the first law of thermodynamics states that the net internal energy change of the system is zero. 

For a free expansion, the work done will be zero.
$\mathrm{w}=0$

For an adiabatic process, the heat will be zero.
$\mathrm{q}=0$
And from the first law of thermodynamics, 

$∆\mathrm{T}=0 \text{or} ∆\mathrm{S}=0$

Hence option D is the answer.