Mole (unit) measure the amount of substance (although in practice it is usual). There are many physical relationships between amount of substance and other physical quantities, the most notable one being the ideal gas law (where the relationship was first demonstrated in 1857). The term "mole" was first used in a textbook describing these colligative properties. Chemical engineers use the unit extensively, and decimal multiples may be more suitable for industrial use. For convenience in avoiding conversions in the imperial (or American customary units), some engineers adopted the "pound-mole" (notation "lb-mol" or "lbmol"), which is defined as the number of entities in
Internal energy density called "specific internal energy" which is internal energy per unit of mass (kilogram) of the system in question. The SI unit of specific internal energy is J/kg. If the specific internal energy is expressed relative to units of amount of substance (mol), then it is referred to as "molar internal energy" and the unit is J/mol. From the standpoint of statistical mechanics, the internal energy is equal to the ensemble average of the sum of the microscopic kinetic and potential energies of the system. The internal energy, , expresses the thermodynamics of a system in the "energy-language", or in