The thermodynamics of open systems exchanging mass, heat, energy, and entropy with their environment is examined as a convenient unifying framework to describe the evolution of growing solid bodies in the context of volumetric growth. Following the theory of non-equilibrium thermodynamics (NET) introduced by De Donder and followers from the Brussels School of Thermodynamics, the formulation of the NET of irreversible processes for multicomponent solid bodies is shortly reviewed. In the second part, extending the framework of NET to open thermodynamic systems, the balance laws for continuum solid bodies undergoing growth phenomena incorporating mass sources and mass fluxes are expressed, leading to a formulation of the second principle highlighting the duality between irreversible fluxes and conjugated driving forces. A connection between NET and the open system thermodynamic formulation for growing continuum solid bodies is obtained by interpreting the balance laws with source terms as contributions from an external reservoir of nutrients.