Thermodynamic Proof That the Thermal Energy of a Uniform Fluid Never Converts into Its Own Mechanical Energy

[Image: see text] The conversion of mechanical (i.e., kinetic and potential) energy into internal (or thermal) energy is ubiquitous in fluids, while the reverse process seems less common. Little is known a priori about in what circumstances the former conversion occurs or not. The present study investigates this problem by applying thermodynamics to nonequilibrium situations. It is thereby found that if a fluid is uniform in temperature, pressure, and composition, then its mechanical energy necessarily turns into its internal energy but not vice versa (with its kinetic energy determined relative to the vessel holding it). This result is essentially based on the second law of thermodynamics, but the conventional way of evaluating the energy conversion needs to be corrected to obtain it. It may constitute the first thermodynamically general and rigorous explanation of why heat is usually generated, e.g., when a liquid is stirred vigorously or when an electric current flows through an electrolyte solution. If a fluid is not uniform, however, it is possible that its internal energy is transformed into its mechanical energy. Such behavior is illustrated by considering a representative case in which two identical pure fluids are brought into contact with each other at the same temperature but at different pressures.