<P> A frequent definition of heat is based on the work of Carathéodory (1909), referring to processes in a closed system . </P> <P> The internal energy U of a body in an arbitrary state X can be determined by amounts of work adiabatically performed by the body on its surroundings when it starts from a reference state O. Such work is assessed through quantities defined in the surroundings of the body . It is supposed that such work can be assessed accurately, without error due to friction in the surroundings; friction in the body is not excluded by this definition . The adiabatic performance of work is defined in terms of adiabatic walls, which allow transfer of energy as work, but no other transfer, of energy or matter . In particular they do not allow the passage of energy as heat . According to this definition, work performed adiabatically is in general accompanied by friction within the thermodynamic system or body . On the other hand, according to Carathéodory (1909), there also exist non-adiabatic, diathermal walls, which are postulated to be permeable only to heat . </P> <P> For the definition of quantity of energy transferred as heat, it is customarily envisaged that an arbitrary state of interest Y is reached from state O by a process with two components, one adiabatic and the other not adiabatic . For convenience one may say that the adiabatic component was the sum of work done by the body through volume change through movement of the walls while the non-adiabatic wall was temporarily rendered adiabatic, and of isochoric adiabatic work . Then the non-adiabatic component is a process of energy transfer through the wall that passes only heat, newly made accessible for the purpose of this transfer, from the surroundings to the body . The change in internal energy to reach the state Y from the state O is the difference of the two amounts of energy transferred . </P> <P> Although Carathéodory himself did not state such a definition, following his work it is customary in theoretical studies to define heat, Q, to the body from its surroundings, in the combined process of change to state Y from the state O, as the change in internal energy, ΔU, minus the amount of work, W, done by the body on its surrounds by the adiabatic process, so that Q = ΔU − W . </P>

List and define three types of heat transfer