Which term describes the amount of heat needed to change 1 kg of a substance from solid to liquid at its melting point? a. specific heat of phase changes b. specific heat capacity c. latent heat of fusion d. latent heat of vaporization

It is called the specific latent heat of fusion. C.

This is the heat change required in changing 1kg of a solid to its liquid and it occurs at the melting point. It is not associated with temperature change.

If it is to convert 1kg of liquid to vapor at its boiling point it is called the latent heat of vaporization.

The answer is  a.first and third quarters 

It really doesn't matter for any of the questions that you've listed.