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Internal thermal energy in solids contributes to vibrations (phonons) energy; spin waves (magnons) energy if solid has magnetism and fermions energy across very complicated mechanisms. Debye functions, mathematically, was estimated because they are considered a main term which controls in all equations of those contributions.Semi-empirical equation has been obtained to nd (n=3,4,5) transition metals specific heat to calculate some important physical constants.Numerical analyses gives an agreement with experimental results on nd transition metals. Comparison between theoretical and experimental was investigated.