Why did a cup of water empty while sitting in the sun

The Cup in question has nothing to do with the phenomenon, The Process is known as "Evaporation" When water or and other liquid will turn into gas when subjected to UV Heat.

A recent University of Florida study has found that the plastic most commonly used in water and soda bottles can release antimony and bisphenol A (the dreaded BPA) if it's exposed to heat over a long period of time. The higher the temperature, the more BPA and antimony is released.