Thermodynamics of Mechanical Deformation

Since the strains in the given stress situation have the form 

In transverse direction jc there is, in general, a different transverse strain and, therefore, a different Poisson s ratio 

Straining a body involves forces and displacements. Therefore, work is done in this process. To calculate this work we consider the body as a thermodynamic system that is closed but not isolated. All matter and points not belonging to the body under consideration constitute the surroundings of this system. By designating the system to be closed we infer that the boundary between the system and its surroundings does not allow any mass transfer. For an isolated system the boundary would in addition exclude the transfer of all energy. 

In a steady state the properties of a system are independent of time. If there exists a special reference frame in which all mass elements in the body are at rest and if no heat is exchanged with the surroundings the state is called a thermodynamic equilibrium state. Classical Thermo dynamics deals exclusively with such equilibrium states and it has aptly been suggested to name it thermostatics instead. Nevertheless, the name thermodynamics has persisted and we will also continue to use it. Of course, the temperature is the same everywhere in a system in thermodynamic equilibrium. 

It is not helpful to burden the discussion with the complications of complete generality. So, the treatment is restricted to homogeneous systems, i.e. to systems with properties that are independent of position. The equilibrium state, usually simply called state, of a system is uniquely determined by a set of macroscopic measurable quantities. All quantities uniquely associated with and representative for a thermodynamic state are called state quantities. They are related to each other in various ways and, appearing in functions they are called state variables. A considerable number of quantities that fulfill this requirement can be defined. However, only a limited number of them is independent. In fact the number of independent state variables is given by the number of independent energy forms involved. A proper choice of independent state variables must either include the temperature as one of them or else the selected variables must together uniquely determine the temperature. 

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