Answer
It is restricted to constant-volume processes.
Work Step by Step
By the definition of differentials:
$du = (\frac{\partial u}{\partial T})|_V .dT + (\frac{\partial u}{\partial V})|_T .dV$
Which, for an ideal gas, reduces to:
$du = c_vdT-pdV$
Therefore, if the process occurs at varying volume, the second term must be taken into account.
