In an adiabatic expansion of ideal gas:

In an adiabatic expansion the heat is not exchanged by the system with the surrounding. The work done in an adiabatic expansion of ideal gas is zero.

So, $∆E=q+w$

$=>∆E=0+W=W$

Hence, In an adiabatic expansion of ideal gas $W=∆E$.

Therefore, option (B) is correct.