Continuum mechanics deals with deformable bodies. In its early stages it was confined to a few special materials and to particular situations, namely to ideal liquids or to elastic solids under isothermal or adiabatic conditions. In these special cases it is possible to solve the basic problem, i.e., to determine the flow and pressure distributions or the deformation and stress fields in purely mechanical terms. This is due to the fact that the solution can be developed from a set of differential equations which does not contain the energy balance.
From the viewpoint of general continuum mechanics, however, problems of this type are singular. Anyone working in this field knows that sooner or later he gets involved in thermodynamics. The reason for this is that in general a complete set of differential equations contains the energy balance. Since part of the energy exchange takes place as heat flow, the appropriate form of the energy balance is the first fundamental law of thermodynamics, and it becomes clear therefore that it is generally impossible to separate the mechanical aspect of a problem from the thermodynamic processes accompanying the motion. To obtain a solution,
the fundamental laws of both mechanics and thermodynamics must be applied. In gas dynamics and in thermoelasticity this has long been recognized.
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