Maurice A. Biot presents a unified treatment of thermoelasticity using methods from irreversible thermodynamics. The concept of generalized free energy, introduced in previous work, serves as the "thermoelastic potential" and is used alongside a new definition of the dissipation function in terms of the time derivative of entropy displacement. The general laws of thermoelasticity are formulated in variational form, along with a minimum entropy production principle. This leads to Lagrangian-type equations and the introduction of the thermal force through a virtual work definition. Heat conduction problems can be formulated using matrix algebra and mechanics, leading to the property that entropy density obeys a diffusion equation. General solutions of the thermoelasticity equations are provided using Papkovich-Boussinesq potentials. Examples are presented, demonstrating how the generalized coordinate method can be used to calculate the thermoelastic internal damping of elastic bodies. The paper also discusses the extension of these methods to anisotropic media and dynamics, and includes a detailed solution of a classical heat conduction problem using the proposed methods.Maurice A. Biot presents a unified treatment of thermoelasticity using methods from irreversible thermodynamics. The concept of generalized free energy, introduced in previous work, serves as the "thermoelastic potential" and is used alongside a new definition of the dissipation function in terms of the time derivative of entropy displacement. The general laws of thermoelasticity are formulated in variational form, along with a minimum entropy production principle. This leads to Lagrangian-type equations and the introduction of the thermal force through a virtual work definition. Heat conduction problems can be formulated using matrix algebra and mechanics, leading to the property that entropy density obeys a diffusion equation. General solutions of the thermoelasticity equations are provided using Papkovich-Boussinesq potentials. Examples are presented, demonstrating how the generalized coordinate method can be used to calculate the thermoelastic internal damping of elastic bodies. The paper also discusses the extension of these methods to anisotropic media and dynamics, and includes a detailed solution of a classical heat conduction problem using the proposed methods.