Why does the plot show vertical jumps at the melting and boiling points?

I think this happens because during melting or boiling at constant temperature, the entropy dramatically increases because energy is removed from the system during the change. Entropy increases with increase in temperature, entropy increases steadily with increasing temperature up to the melting point of the solid, where the entropy increases further due to addition of freedom of molecules which increases the randomness of the substance. At boiling point of liquid, another abrupt increase in entropy occurs, this results from increased volume available to the atoms or molecules as they enter the gaseous state. 

19 hertz bruh u trippin? ?