thermodynamics - When is $Delta U=nC_V Delta T$ true?

I am confused about the equation from thermodynamics $\Delta U=nC_V \Delta T$. I am reading the notes of my professor.

In one instance, he derives the adiabatic expansion law, which states for an isentropic transformation (reversible and adiabatic) of an ideal gas, we have that $PV^{\gamma}$ is constant. He uses the fact that $dU=nC_VdT$, even though the volume of the gas is of course not constant during such a transformation.

In another instance, he calculates the efficiency of a diesel cycle, which uses two isentropic transformations, an isobaric, and an isochoric transformation. He calculates the heat for the isochoric transformation as $Q=\Delta U=nC_V\Delta T$ and for the isobaric transformation as $Q=\Delta U=nC_P\Delta T$.

So are we or are we not allowed to say $dU=nC_VdT$ holds in general? Or does it only hold when the volume of the gas remains constant?