Gibbs's papers from the 1870s introduced the idea of expressing the internal energy "U" of a system in terms of the entropy "S", in addition to the usual state-variables of volume "V", pressure "p", and temperature "T". He also introduced the concept of the chemical potential formula_1 of a given chemical species, defined to be the rate of the increase in "U" associated with the increase in the number "N" of molecules of that species (at constant entropy and volume). Thus, it was Gibbs who first combined the first and second laws of thermodynamics by expressing the infinitesimal change in the internal energy, d"U", of a closed system in the form: