Two cylinders $A$ and $B$ of equal capacity are connected to each other via a stop cock. $A$ contains an ideal gas at standard temperature and pressure. $B$ is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is:

Since the system is thermally insulated, there is no heat exchange with the surroundings ($q=0$). Sudden expansion of gas into a vacuum (free expansion) happens so quickly and in an insulated vessel that the process is adiabatic.(Note: For an ideal gas, free expansion is also isothermal because $\Delta U=0$, but technically the process is defined as adiabatic expansion).