The definition of enthalpy change is
ΔH = ΔU + Pex(ΔV)
The enthalpy change is zero because both terms on the right are zero in free expansion of an ideal gas.
There is no external pressure in a free expansion, so P (ex) = 0. And the internal energy change, ΔU of free expansion in a closed system is zero since no inter molecular forces have to be overcome. The temperature remains constant and no heat is absorbed or released.
There is an explanation video available below.
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