Everyone has an intuitive conception of heat as something related to temperature, but a rigorous and broadly accepted scientific definition of heat is lacking despite several centuries of study. \( \newcommand{\dbar}{{{}^{-}\mkern-12.5mu \diff}} \) Energy transfer or state quantity? Callen defines heat as the variation in internal energy \( E \) has not been caused by work \[ \dbar Q = \diff E - \dbar W . \] We find here the first anacronism. Heat is represented by an « inexact differential » (symbol \(\dbar \)) because heat is not a state function in the classic thermodynamic space. Kondepudi & Prigogine suggest the alternative definition \[ \diff Q = \diff E - \diff W - \diff_\mathrm{matter} E . \] Not only a new mechanism of interchange of energy associated to changes in the composition \( N \) produced by a mass flow with surrounds is introduced, but exact differentials are used because the classical thermodynamics space has been extended with time as variable. Th