For an ideal gas constant volume heat addition process, change of entropy equation is: 

∆S= cv ln⁡(T2/T1)+ R ln⁡(v2/v1)= ∫dq/T+S(gen) 

The term [R ln⁡(v2/v1) ] equals zero, since it’s a constant volume process.

For ideal gas  ∫dq/T =cv ln⁡(T2/T1) .

Then:

∆S= cv ln⁡(T2/T1)= cv ln⁡(T2/T1)+S(gen) 
Therefore, the S(gen) term equals zero and the process is reversible.

The question is: why does the S(gen) term equal zero and the process is reversible when this is a heat addition through a finite temperature difference?