Internal Energy Of An Ideal Gas

Free expansion of an ideal gas into a vacuum is a classic adiabatic and zero-work process: the chamber is insulated so $Q=0$, and the gas expands against nothing, so $W=0$ because there is no opposing pressure to do work against. The First Law $$\begin{gathered} \Delta \\ cup=Q-W \end{gathered}$$ then gives $$\begin{gathered} \Delta \\ cup=0 \end{gathered}$$. For an ideal gas internal energy depends only on temperature, so constant internal energy means constant temperature. The option that temperature rises is wrong because no work is done on the gas to add energy. The option that it falls confuses this with controlled adiabatic expansion against a piston, where the gas does real work and cools. The option that it depends on final volume is incorrect because ideal-gas internal energy is volume-independent. A consistency check: even though volume and pressure both change, the product $PV=nRT$ keeps $T$ fixed because $U$ and hence $T$ are unchanged, confirming the temperature is preserved.