My book says, that if a system is expanding adiabatically then $dq=0$ and $U= q+w$, so $U=w$.
It also states that $$\delta U=(C_v)\cdot\delta T$$
Here $C_v$, is the molar heat capacity at constant volume. How can they just $C_v$, which is defined for a specific volume, in a system that is expanding, i.e. its volume is changing?