l = Length

T = Temperature

Q = Heat 

m = Mass

c = Specific Heat

C = Latent Heat Constant

α = Linear Expansion Constant

Figure A 

   Starting a point A, the substance is in its solid phase, heating it brings the temperature up to its melting point but the material is still a solid at point B. As it is heated further, the energy from the heat source goes into breaking the bonds holding the atoms in place. This takes place from B to C. At point C all of the solid phase has been transformed into the liquid phase. Once again, as energy is added the energy goes into the kinetic energy of the particles raising the temperature, (C to D). At point D the temperature has reached its boiling point but it is still in the liquid phase. From points D to E thermal energy is overcoming the bonds and the particles have enough kinetic energy to escape from the liquid. The substance is entering the gas phase. Beyond E, further heating under pressure can raise the temperature still further is how a pressure cooker works. 

Latent Heat 

    When a substance changes phase, that is it goes from either a solid to a liquid or liquid to gas, the energy, it requires energy to do so. The potential energy stored in the interatomics forces between molecules needs to be overcome by the kinetic energy the motion of the particles before the substance can change phase.

    If we measure the temperature of the substance which is initially solid as we heat it we produce a graph like Figure A. 

Definition By Splung.com

Specific Heat 

Energy is required to raise the temperature of an object. How much energy is required depends on what the object is made of. If we are going to compare how much energy is required to heat an object we must consider we are comparing like-with-like. The specific heat capacity gives us the energy required to raise the temperature of unit mass by one-degree Centigrade.

To measure the energy required we use a source of heat, either electrical or chemical. The specific heat capacity is then the energy input = mass x specific heat capacity x the change in temperature.

Definition provided by Splung.com