In this paper, an irreversible port-Hamiltonian formulation for 1D compressible Newtonian fluids is presented. We separate the fluid dynamics into reversible and irreversible parts. Given the compressibility assumption, we define a state-dependent matrix that modulates the skew-symmetric operators that describe the irreversible part of the fluid dynamics. As a result, we obtain an energy-based formulation that reflects appropriately the first and second laws of Thermodynamics. Copyright (C) 2021 The Authors