According to thermodynamic first law, change
in internal energy of a system equal to the net
heat transfer into the system minus net work
done by the system.
So, Q = + ve adds energy to the system and
W = + ve takes energy from the system
$
\Delta U=Q-W
$
Here, $\Delta U=$ internal energy
If, $\Delta U=-W$,
then $Q=0$
i.e. no heat is exchanged.
$\therefore$ The process is adiabatic.
Hence, change in internal energy is equal to adiabatic work