A passivity based control method is presented for the diffusion process by the use of the concept of available storage and irreversible thermodynamics. A convex extension using the internal energy as generating function will be employed to define a Lyapunov functional for the distributed irreversible port Hamiltonian system (the diffusion process). The latter functional, will be used to suggest a Lyapunov stability condition by applying the so called La Salle’s Invariance principle for infinite dimensional systems on the heat and mass diffusion process.