Complexity of finding 7th smallest element in a min-heap?
If you had a "black-box" min heap where the only operations available to you are adding elements and extracting (reading and simultaneously removing) the smallest item, then the time complexity is O (n) obviously. 

It is imaginable that you have a specific implementation where even finding the second smallest element cannot be done in constant time. You might have in your data structure O (log n) items that might be the second smallest, and the O (log n) operation to remove the smallest item will also determine the second largest. I find it hard to describe an algorithm that works that way, but I'm sure it's possible. 

The way a min-heap is usually implemented (or the way it is implemented if I had to implement it, or the way it is implemented in a random text book), finding the 7th smallest element can be done in constant time.