Partition Function of 2 State System

[HalfManHalfAmazing]

If I have a 2 state system with energy levels of the 2 states to be 0 and V. I find the partition function to be Z = 1 + e^(-V/kT). Am I correct? If so, does that not mean the average energy is V? and thus the entropy is 0? This doesn't make sense, how is the entropy of a 2 state system (when 1 state is zero energy) 0?!

Thanks!

 

[HalfManHalfAmazing]

Is the entropy of a 2 state system with 1 state with energy 0 equal to 0?