thermodynamics - Entropy of an ideal gas vs. entropy of a non ideal gas

Question: Do you expect the entropy of an interacting gas of N particles in volume V at temperature T to be smaller or bigger than the entropy for an ideal gas of the same (N, V, T)?

My understanding could be flawed. If so, I am happy to corrected.

My guess is that the entropy of the nonideal gas should be greater. This is because nonideal processes are irreversible and by the second law of thermodynamics we have to factor in an increase in entropy of the universe. Whereas in the ideal gas situation, we don't have to factor this in.