Question

determine the energy needed to cool 10 grams of H2O from 110 degrees C to -10 degrees C?

Answer 1

Here is a general scheme for any temperature range.
heat WITHIN a phase is
q = mass substance x specific heat in that phase (Tfinal-Tinitial)

heat at a phase change.
q = mass x heat fusion at freezing(melting point)
q = mass x heat vaporization at boiling point.
So you go through each phase change and each phase then add all of the q values together.
For water, at 110 I'll do a part of it.
q for steam = mass H2O x specific heat steam x (Tfinal-Tinitial). T final is 100 and Tinitial is 110. That gives that part.

q2 = heat to condense steam
q2 = mass water x heat vaporization (heat of condensation but they ar ethe same number).

Then you go within a phase from 100 to zero.

phase change at zero

Then within a phase from 0 C t -10C.

Post your work if you get stuck.