Let's consider free expansion of an Ideal gas into vacuum. We have 2 (insulated) partitions, one with the gas, another vacuum, separated by a stop cock. I lift the cock, letting the gas expand into vacuum. I am aware that in free expansion of a gas into vacuum, the change in internal energy i.e ΔU is zero. Hence temp remains constant. Now if I take the system as the gas initially, then since the process is isothermal, we have temp constant. And now since the partitions are insulated, we have ΔQ=0. Hence the process is adiabatic. Now it confuses me, whether the process is isothermal, or adiabatic? it can't surely be both!