The fact that no heat is transferred between a system and its surroundings refers to an adiabatic free expansion.
In gas, the adiabatic compression creates an increase in the temperature while it causes a drop in temperature there is adiabatic expansion against pressure, or a spring.
Before being allowed to expand in vacuum, the gas is first contained in an
insulated container.
The work made by or on the system is zero since there is no external pressure for the gas to enlarge on against. The first law of thermodynamics then insinuates that zero is the net internal energy change of the system since the process does not incorporate any work or heat transfer.
