Molar Description of Thermodynamic Functions

Both descriptions in continuum mechanics and in classical chemistry are listed as follows (note that since the inelastic volume change is small enough, the volume V is used instead of F for the conventional notations)  

Here 5 is the exchangeable entropy in the molar description. Note that the internal energy per unit mass u [J/M] (M is the unit of mass) is related to the internal energy per unit substance U [J/mol] by mu = U where m is the molecular weight. Most of the textbooks using the molar description employ the pressure p (compression positive) instead of stress a (cf. Sect. 3.2.4). We here use the pressure P and volume V (expansion positive) in the molar descriptions. 

Ichikawa and A.P.S. Selvadurai, Transport Phenomena in Porous Media, DOI 10.1007/978-3-642-25333-1, Springer-Verlag Berlin Heidelberg 2012 

Thermodynamic functions (Continuum mechanics) (Molar description) Internal energy u(e, s ) U(V,S ) 

---