One mole of an ideal gas expands reversibly and adiabatically from volume $V$ to $2V$. Select the correct statement(s).

Adiabatic means $q=0$, so $\Delta U=w$; a reversible adiabatic path has $\Delta S=q_{rev}/T=0$. The gas does work at the expense of internal energy, so $T$ falls. In the isothermal case $T$ stays constant, the pressure stays higher along the path, and more work is done; hence the statement about smaller work than the isothermal case is true and the statement that the final temperature is unchanged is false.