A note on the equation of heat transfer

Abstract

Liquids with properties βpv/c_p ⪡ 1 and p²vκ/c_pT ⪡ 1 are defined as “incompressible liquids”. The compression work in motion of incompressible liquid is negligibly small. The change in the internal energy of incompressible liquids with respect to the temperature is, however, proportional to c_p. Motions of perfect gases in open systems under appropriate conditions and in closed systems with no net heat addition (or removal) are prescribed by the energy equation with c_p as the appropriate specific heat. Otherwise, either no reduction is possible or both c_p and c_v may become the appropriate specific heats in the energy equation.