I don't really understand your question. Could be more specific. Are you trying to do thermodynamic calculations of the phase diagram? If so, that would be an equilibrium calculation, however you mention DSC measurements which are done at particular heating and cooling rates, which means these are not equilibrium phase transitions. The width of the melting peak (assuming it is exothermic) will depend on the heating rate. A solid to liquid phase transformation will always happen at a constant temperature above the solidus line, unless you are talking about a peritectic phase region above the solidus, i which case you will have a liquid and solid phase in equilibrium together over a temperature range.

I'm not sure what you mean by internal energy. Could you explain in more detail what you want to calculate?

I advice you to look at EES (Engineering Equation Solver). there you can find the properties and all parameters related to phase change of different materials 

I use always this website: http://www.nist.gov/srd/materials.cfm

or you must find some correlation, because the phase change properties can be determined only in experimental methode.

The co-exitance of solid-liquid  phases under varying thermodynamic condtions  presents a classic example of heterophase equilibria, defined by Gibbs, as requiring three fundamental conditions: Equality of temperaure ior thermal equlibrium, equality of pressure or mechanical equlibrium; equality of chemical potentials or chemial equalibrium.; The internal enegies of these conjugate phases can be found out from laws of thermodynamics; 

Ref: M.E. Glicksman, Principles of Solidification, DOI 10.1007/978-1-4419-7344-3_2,

C Springer Science+Business Media, LLC 2010

I am not sure I understand your question. You are looking to determine the internal energy of a phase change material? Why? Often people are looking for the enthalpy or effective specific heat, I do not know why you would like to have the internal energy.

Anyway, the internal energy is the enthalpy plus the product of the pressure and volume of the system. So you should first determine the enthalpy of your PCM, which of course will vary with temperature. There is a procedure indicating how to do it from DSC heating and cooling curves: http://195.20.235.12/en/ral-quality.htm

You can most likely evaluate the volume of your system quite easily but did you evaluate the pressure during the DSC testing? 

If I have misunderstood your question, please clarify.

Internal energy is point function. Enthalpy is sume of internal energy and product of pressure and volume. Tthermal propeties like enthalpy and  entropy can determined  either from thermodynamic charts, tables or from experimentation, from which internal energy  can be deduced for any material including phase change material. However, internal energy can also be calculated from applicaiton of laws of thermodynamics. 

thanks Dr. Lawrence Margulies, Mr. Mohamad Kharseh, Mr. Ahmed KOUIDRI, Dr. Maddali V S Murali Krishna, Dr. Katherine D'Avignon 

Dear Dr.Lawrence Margulies

you are right melting process of a pure substance happens at constant temperature. But our PCM include some impurity. 

Internal energy is thermodynamic properties usually noted by "u"

Dear Dr.Maddali V S Murali Krishna

Knowing the trend of temperature variation as heat is give to the material help? considering that pressure stays constant and the only cause to specific volume variation is density of temperature variation.

Dr. Katherine D'Avignon

Thanks for your response and the reference. I haven't read the reference completely. But I think it will be helpful. 

These links would guide you to the answers you seek

http://www.google.com.ng/url?sa=t&rct=j&q=&esrc=s&source=web&cd=3&cad=rja&uact=8&ved=0CCwQFjAC&url=http%3A%2F%2Fwww.ohio.edu%2Fmechanical%2Fthermo%2FIntro%2FChapt.1_6%2FChapter2a.html&ei=gA5cVJimMsHxav7OgtAC&usg=AFQjCNF2Sngw7oknGBS_YZBdNHUYoMiObw&sig2=gOxTZfRuRKVAZ-NcTfnzxQ&bvm=bv.79184187,d.d2s

http://www.google.com.ng/url?sa=t&rct=j&q=&esrc=s&source=web&cd=6&cad=rja&uact=8&ved=0CEcQFjAF&url=http%3A%2F%2Fwww.arpapress.com%2Fvolumes%2Fvol8issue2%2Fijrras_8_2_03.pdf&ei=gA5cVJimMsHxav7OgtAC&usg=AFQjCNHmPen7o2JC3y3WR1Rjrp7cCExaHw&sig2=xHtkSjx9smLWES4p0fbuSA&bvm=bv.79184187,d.d2s

http://www.google.com.ng/url?sa=t&rct=j&q=&esrc=s&source=web&cd=8&cad=rja&uact=8&ved=0CFkQFjAH&url=http%3A%2F%2Fwww.researchgate.net%2Fpublication%2F253329573_Phase_change_material_Optimizing_the_thermal_properties_and_thermal_conductivity_of_myristic_acidpalmitic_acid_eutectic_mixture_with_acid-based_surfactants%2Flinks%2F0deec51f867f6bae88000000&ei=gA5cVJimMsHxav7OgtAC&usg=AFQjCNGeJKDfH5lrdxyxdkIoxKDsQnE_xQ&sig2=gC2DJ04wSV8rSuGLPdPUZw&bvm=bv.79184187,d.d2s

http://www.google.com.ng/url?sa=t&rct=j&q=&esrc=s&source=web&cd=10&cad=rja&uact=8&ved=0CGUQFjAJ&url=http%3A%2F%2Flink.springer.com%2Fchapter%2F10.1007%252F978-1-4020-5290-3_17&ei=gA5cVJimMsHxav7OgtAC&usg=AFQjCNEsB_eNFB_YKw0JA1ZB-oCfWaNb9g&sig2=783P8DKbG_fQu5-4Y3DpJg&bvm=bv.79184187,d.d2s