The thermodynamic stability principle requires convexity of the internal energy upon all of its independent variables.
When we pass through the Legendre transforms to build all the other thermodynamic potential, the thermodynamic stability principle is stated as "Thermodynamical potentials $(H, F, G)$ must be concave on their intensive variables and convex on their extensive ones".
I've got one question about this argument.
If i take the Helmholtz Free Energy $F(T,V,N)$, following the last statement one would say: F must be concave on T and convex on V [m^3] and N [mol].
It is reasonable to infer that if i take F(T,v,N) with v [m^3/kg] now F must be concave on v?