To melt is the latent heat of fusion. Silly name but hey.
To boil is latent heat of vapourisation
The specific heat capacity is usually denoted as Cp or Cv and used as this :
Cp = heat absorbed/increase in temperature per gram(J/Co x gm.)can also be expressed in moles (J/Co x gmMW)(gm MW of substance/moles of substance.) = Cp in units of moles. And this is at constant pressure; the reasoning behind the subscript p, constant volume(usually when studying gases at constant volume v.
Cp is now equal to: Cp = (J/Co x mole)
Cv is equal to the same equation but the measurement is done under condition of constant pressure.
Specific heat capacity, Cp, can be defined as the energy(usually in Joules J) that is required to raise one mole the temperature 1 degree celsius; will depend upon the amount of the substance present, and what the materials MW is if the answer is to be in moles; this is so because most data refering to heat capacity are reported in units of (J/Co gm.) per gram basis. We want molar scaling.
Cp = (Joules/Co * gm.) X (gm./mole) if you want the Specific heat in terms of moles look up the moleculer weight of the substance and convert the gram value to moles.
Lets look at waters Specific Heat capacity:
Cp = 4.18 (J/Co gm.)(18 gm./mole) = 75.24 (J/Co Mole)
Some specific heat capacities: (J/Co*gm.)
Water(l) = 4.18
Water(s) = 2.03 makes sense ice melts more easily than the heating of the same amount of Water liquid!
Al(s) = 0.89
Fe(s) = 0.45
Hg(l) = 0.14
C(s) = 0.71
Hope this helps.
By the way the p in the Cp means that this heat capacity constant is determined at constant pressure.
Co = Celsius
Also: The heat equation for q (heat)
heat q = Cpdt = specific heat capacity x the change in temperature, dt = (t2-t1).
Cp(specific heat capacity) can be calculated this way if the data exists(experimentally). The change in temperature and the amount of heat generated in Joules.
Cp = q/dt = q/ (T2 - T1) = (cal./mole)/Ko