Define Free Expansion.

Hint: Free expansion is one the few cases in which we see adiabatic and isothermal processes going on at the same place, and same time. There is no exchange of energy inside and outside the system walls because the whole system is insulated.

Complete step by step answer:
A process in which gas is allowed to expand in vacuum and this happens so quickly that no heat leaves or enters the system this type of process is also known as adiabatic process and because this happens so fast the gas does not cross the system boundaries ,hence no work is done by the system or on the system, then the expansion is called the free expansion.

 We can further equate free expansion into,

${{U}_{f}}-{{U}_{i}}=Q-W$ , now as no heat is exchanged and no work is done Q=0 and W=0.
${{U}_{f}}={{U}_{i}}$.

Further, as we see there is no change in the internal energy,
Hence, the temperature remains constant.

Now, if we consider that the process is going on inside a cylinder with partitions and a stopper, hence as it is properly insulated no exchange of heat is there hence it is an adiabatic process and as the temperature of the gas also remains constant, hence the it is also called isothermal process.

Note: In case of adiabatic expansion, there is no exchange of heat outside the system, and as there is no exchange of heat or energy hence we can say that the temperature of the gas inside the chamber or the cylinder is constant throughout. The stopper material used must be assuring that no leakage of temperature occurs inside the cylinder.