In the mechanical stream of thinking about a process of transfer of energy between two bodies or closed systems, heat transferred is defined as a residual amount of energy transferred after the energy transferred as work has been determined, assuming for the calculation the law of conservation of energy, without reference to the concept of temperature. There are five main elements of the underlying theory.
*The existence of states of thermodynamic equilibrium, determinable by precisely one (called the non-deformation variable) more variable of state than the number of independent work (deformation) variables.
*That a state of internal thermodynamic equilibrium of a body have a well defined internal energy, that is postulated by the first law of thermodynamics.
*The universality of the law of conservation of energy.
*The recognition of work as a form of energy transfer.
*The universal irreversibility of natural processes.
*The existence of adiabatic enclosures.
*The existence of walls permeable only to heat.
Axiomatic presentations of this stream of thinking vary slightly, but they intend to avoid the notions of heat and of temperature in their axioms. It is essential to this stream of thinking that heat is not presupposed as being measurable by calorimetry. It is essential to this stream of thinking that, for the specification of the thermodynamic state of a body or closed system, in addition to the variables of state called deformation variables, there be precisely one extra real-number-valued variable of state, called the non-deformation variable, though it should not be axiomatically recognized as an empirical temperature, even though it satisfies the criteria for one.