Changes of Internal Energy un open system
Suppose you assign an reference state for internal energy such that the internal energy per mole u of the gas is zero at $T=T_r$.  This reference state is going to be held fixed for the material both entering or leaving the open system, as well as the material within the system at any time.  Then, in the initial state of a constant-temperature system, $U_{init}=n_{init}C_v(T-T_r)$ and, in the final state, $U_{final}=n_{final}C_v(T-T_r)$.  So, $$\Delta U=\Delta nC_v(T-T_r)$$Typically, in the overall energy balance on the system, including entering and exiting streams, $T_r$ will cancel out (just as it would for a closed system).  

Please note, however, that if chemical reactions are occurring, the equation for   the internal energy and the specification of the reference state has to be extended to take this into account (using the concept of "internal energy of formation").